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A Comparative Analysis of the Effectiveness of Mathematics Curriculum Taught at GCE (O-Level) and SSC Systems of Schools in KarachiA Dissertation byMUHAMMAD AKHTARIn Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Ph.D.) in EducationUnder the Supervision ofDR. AHMAD SAEEDPresented toHamdard Institute of Education and Social SciencesHAMDARD UNIVERSITY KARACHIJanuary, 2014ABSTRACTA COMPARATIVE ANALYSIS OF THE EFFECTIVENESS OF MATHEMATICS CURRICULUM TAUGHT AT GCE (O-LEVEL) AND SSC SYSTEMS OF SCHOOLS IN KARACHIThe focus of this study was on the comparison of mathematics curricula of General Certificate of Education (GCE) Ordinary Level (O-Level) and Secondary School Certificate (SSC). The purpose of this comparison was to trace out the factors responsible for the shortcomings in instructional objectives, contents, approaches, methods of teaching and pattern of assessment in the local (SSC) system of education. The study was specifically focused on: (1) to compare and analyze the aims and objectives of teaching mathematics at SSC and GCE (O- Level); (2) to compare the contents of textbooks and question papers of SSC and GCE mathematics courses; (3) to critically compare the effectiveness of approaches and teaching methods applied in both systems; (4) to compare and analyze the assessment patterns in both systems.The population of the study was comprised of teachers, students, prescribed text books of mathematics taught at SSC and GCE (O- Level) and question papers of the examination boards of both systems. The overall size of the sample was of 300 teachers, 200 students and 20 subject experts. The sample included 180 teachers, 120 students and 10 subject experts from the SSC system whereas 120 teachers, 80 students and 10 subject experts from GCE system. An interview protocol and questionnaires were designed and administered. A content analysis was made to compare the contents of textbooks and question papers of the last 20 years (1994-2013) of Board of Secondary Education Karachi (BSEK) and Cambridge International Examinations (CIE). The quantitative data were analyzed using t-test.It was concluded that the implementation of mathematics curriculum is relatively more effectivein GCE (O-Level) than in SSC curriculum although no significant difference has been found in the methods of teaching in both systems. The key factors traced out as major contributors in this difference of effectiveness were: GCE teachers were found clear and well-informed about the expected aims and objectives of their curriculum while SSC teachers were not clear because they did not have access to the expected aims and objectives of their curriculum; GCE textbooks were found aligned with the expected aims and objectives of its curriculum while contents in SSC textbooks were not found in support of some very important expected outcomes of curriculum such as logical thinking and systematic reasoning; the approach of GCE teachers regarding organization of the contents for teaching was found to some extent concentric (spiral) while SSC teachers were found adopting a topical approach; the focus of GCE system was found on depth in knowledge through rigorous practice while the focus of SSC system was found on memorization of factual and procedural knowledge through practice; GCE system was found using formative assessment (assessment for learning) more systematically than SSC system where focus was on summative assessment (assessment of learning), during internal school assessments; GCE system was more focused on application of knowledge versus dispensation of knowledge however SSC system was focused more on constant dispensation of knowledge than its application. The foundation of difference between the two systems was found in their methods of assessment. The question papers of GCE mathematics were based on the overall expectations of the curriculum whereas SSC papers coveredthe expectation of factual and procedural knowledge only. GCE papers consisted of application based questions with no question exactly the same as the ones in the textbooks whereas SSC papers were comprised of exactly same as the textbook questions; GCE papers have been found with no sectioning on the basis of topics whereas SSC papers were sectioned on the basis of different topics;no pattern of repetition has been found in GCE papers whereas in SSC papers, a clear pattern of repetition was found; it was found that whole syllabus is required to be done inorder to attempt the GCE paper completely, whereas the SSC paper could be completed even after skipping many topics from the syllabus. No discontinuation of mathematics has been found at school level in GCE system whereas in SSC system,a suspension of mathematics teaching for one complete year (during grade IX) has been observed. In the light of these conclusions, concrete recommendations were made.CERTIFICATE OF APPROVALThis is to certify that Muhammad Akhtar has successfully completed his research study entitled: “A Comparative Analysis of the Effectiveness of Mathematics Curriculum Taught at GCE (O-Level) and SSC Systems of Schools in Karachi”, under my supervision. He has completed his study by his own research and is not a copy of any other thesis on the subject. I have viewed the dissertation; it meets the standards of Hamdard Institute of Education and Social Sciences (HIESS), Hamdard University Karachi.Name and Signature ofDate: January,2014the Research SupervisorACKNOWLEDGEMENTSI thank Almighty Allah for giving me courage and determination, as well as guidance in conducting this study, despite all difficulties.I extend my heartiest gratitude to my supervisor professor Dr. Ahmad Saeed. In fact,it was Dr. Ahmed Seed’s substantial and courteous supervision that has made me able to undergo this research work. His inspiring and concrete assistance provided me clarity and showed light when everything was looking vague and dark.He always remained very tolerant and determined to see me through.I would like to express my profound thankfulness to the Dean and Director (HIESS), Dr.Syed Abdul Aziz for extending his moral and academic support and to all my professors especially to Dr. Zaira Wahab, whose proactive guidance provided me the hands-on experience of research.I would like to present my highest gratitude to all participants of the study for their benevolentcooperation and especially to Anushay Zainab Abbasi for her wonderful proofreading of the dissertation.I am obliged to my parents for their enduring and precious prays to Allah for me.I am grateful to my younger sister Saira Asghar, younger brother Kamran Shahzad Asghar Kang and my wife Nadia Akhtar for providing me every kind of support and cooperation during this study.I am also thankful to my children Nawal Akhtar, Muhammad Areeb Akhtar Kang, Muhammad Bilal Akhtar Kang, Muhammad Saaim Akhtar Kang and Aaizah Akhtar for sacrificing their fun moments with me due to my engagement in research work.TABLE OF CONTENTSAbstractiCertificate of ApprovaliiiAcknowledgmentsivTable of ContentsvList of TablesxList of GraphsxixList of AbbreviationsxxCHAPTER 1: INTRODUCTION BACKGROUND11.2 OBJECTIVES OF THE STUDY61.3 RESEARCH QUESTIONS 71.3.1Subsidiary Research Questions71.4 SIGNIFICANCE OF THE STUDY 81.5 SCOPE OF THE STUDY91.6DEFINITIONS OF KEY TERMS91.7BASIC ASSUMPTIONS10CHAPTER 2: REVIEW OF RELATED LITERATURE2.1IMPORTANCE OF MATHEMATICS112.2 AIMS OF TEACHING MATHEMATICS13Objectives of Education142.3ROLE OF EDUCATIONAL OBJECTIVES 142.4 CHARACTERISTICS OF EDUCATIONAL OBJECTIVES 152.5 TYPES OF EDUCATIONAL OBJECTIVES152.5.1Cognitive Domain162.5.2Affective Domain21Psychomotor Domain272.6 PRINCIPLES OF CURRICULUM CONSTRUCTION 282.6.1 Principle of Utility282.6.2 Principle of Preparation292.6.3 Principle of Discipline/Training292.6.4 Principle of cultural Value292.6.5 Principle of flexibility292.6.6 Principle of suitability302.6.7 Principle of Interest302.6.8 Principle of Correlation302.6.9NCTM Guiding Principles302.7APPROACHES OF ORGANIZING THE CURRICULUM CONTENTS322.7.1Topical Approach322.7.2Spiral or Concentric Approach322.7.3Epistemological Approach322.7.4Constructivist’s Approach322.8 ROLE OF TEXTBOOKS IN MATHEMATICS EDUCATION332.9 APPROACHES OF TEACHING MATHEMATICS352.9.1Learner-Focused Approach 352.9.2Content-Focused Approach, (With emphasis on understanding)352.9.3Content-Focused Approach,(With emphasis on performance)362.9.4Class-Room Focused Approach372.10METHODS OF TEACHING MATHEMATICS 372.10.1Lecture Method 372.10.2Dogmatic Method372.10.3Inductive-Deductive Method372.10.4Heuristic Method382.10.5Analytic-Synthetic Method382.10.6Laboratory Method382.10.7Project Method382.10.8Topical Method382.10.9Concentric Method392.10.10Problem Solving Method392.11PRINCIPLES AND STANDARDS FOR INSTRUCTIONAL PROCESS IN MATHEMATICS392.11.1 Principles 392.11.2 Standards 402.12 ASSESSMENT IN MATHEMATICS412.12.1 Purposes of Assessment442.12.2 Principles of Assessment442.12.3Types of Assessment 462.13STRUCTURE OF SCHOOL EDUCATION IN PAKISTAN472.13.1Secondary School Certificate (SSC) Education 482.13.2 Mathematics Education in SSC System 492.13.3Mathematics Education in GCE System 502.13.4 Examination Boards542.14 GCE (O-Level) MATHEMATICS (CIE)552.14.1 Mathematics (Syllabus D) (4024/4029)552.14.2 Additional Mathematics (4037) 562.14.3 IGCSE Mathematics 562.15DFFERENCE IN CONTENTS AND ASSESSMENT BETWEEN GCE & IGCSE MATHEMATICS COURSES582.16AN OVERVIEW OF MATHEMATICS EDUCATION IN ASIAN COUNTRIES582.16.1 Singapore592.16.2 China 612.16.3 Japan 63CHAPTER 3: RESEARCH METHODOLOGY 3.1 RESEARCH STRATEGY653.2POPULATION653.3SAMPLE663.3.1 Sample of Schools (SSC / GCE)663.3.2 Sample of Teachers (SSC / GCE)673.3.3 Sample of Students (SSC / GCE)673.3.4 Sample of Subject Experts (SSC / GCE)683.4RESEARCH INSTRUMENTS683.4.1Pilot Study693.5DATA COLLECTION703.5.1Ethical Consideration713.6DATA ANALYSIS713.7DELIMITATION OF THE STUDY71CHAPTER 4: DATA ANALYSISSECTION I: COMPOSITION OF THE SAMPLE73SECTION II:ITEM BY ITEM ANALYSIS OF DATA764.1Analysis of the Responses of SSC and GCE Teachers764.2Analysis of the Responses of SSC and GCE Students1364.3Analysis of the Responses of Experts1944.3.1Summary, Discussion and Conclusions202SECTION III:CONTENT ANALYSIS2064.4Analysis of the Contents of Textbooks and Question Papers2064.4.1Summary, Discussion and Conclusions246CHAPTER 5: SUMMARY, FINDINGS, CONCLUSIONS AND RECOMMENDATIONS5.1 SUMMARY2485.2SECTION WISE RESULTS OF DATA ANALYSIS2495.3FINDINGS 2715.3.1 Section I: (Significance, Aims, Objectives, Curriculum)2715.3.2Section II:(Contents / Textbooks)2765.3.3Section III:(Approaches and Methods)2795.3.4Section IV:(Assessment and Evaluation)2855.4CUMULATIVE FINDINGS2895.5CONCLUSIONS 2955.6RECOMMENDATIONS 2975.7FURTHER RESEARCH 299REFERENCES 300APPENDICES 313Appendix I: Questionnaire for Teachers313Appendix II: Questionnaire for Students319Appendix III:Interview Protocol for Subject Experts325Appendix IV:Interview (Responses of the Subject Experts)328Appendix V:Pilot Testing (Computation of Pearson’s ‘r’)348Appendix VI:Syllabus SSC Mathematics 352Appendix VII:Syllabus GCE Mathematics356Appendix VIII:Outline of Mathematics Paper (BSEK)364Appendix IX:Outline of Mathematics Paper (CIE)366Appendix X:List of Schools in the Sample369Appendix XI:List of Subject Experts376LIST OF TABLESTableTitlePage1The affective domain in mathematics education 262 Comparison of traditional and modern concepts of assessment433Stages of Matriculation system of school sducation 484Stages of Cambridge system of school education 515Number of schools (SSC/GCE) in the sample from each district of Karachi666Teachers (SSC/GCE) in the sample from each district of Karachi677Students (SSC/GCE) in the sample from each district of Karachi678Subject experts (SSC/GCE) in the sample from each district of Karachi689Particulars about the teachers7310Particulars about the students7411Particulars about the subject experts7512Mathematics is one of the most important subjects in the school curriculum7613(a)Comparison of reasons for giving importance to mathematics 7614The aim of mathematics education is to train or discipline the mind7915The aim of mathematics education is to transfer knowledge for its application in real life8016The aim of mathematics education is to develop problem solving skills8017The aims of mathematics education are convincing8118The aims of mathematics education are achievable8119The aims of mathematics education can be translated into small objectives8220The objectives of current curriculum are derived from real aims ofmathematics education8221The objectives of mathematics education are well defined8322The objectives of mathematics education are clearly transmitted to teachers8323The current curriculum prepares students for practical life8424The curriculum prepares for future vocations8425The focus of curriculum is on the needs of future education8526The curriculum is comparable withother countries of the region8527The curriculum is correlated with other subjects8628The curriculum is flexible8629The curriculum reflects state-of-the-art8730The curriculum leads towards the set aims of mathematics education8731Contents of the textbooks are properly sequenced8832Contents of the textbooks develop interest 8833Contents incite the sense of enquiry8934Language of the textbooks is simple8935The contents cover an appropriate proportion of sums on application of abstract principles of mathematics in real life problems9036Worked examples in the textbooks provide sufficient guidance to solve all the problems given for exercise on that topic9037(a)Comparison of the domains of intellect developed by the contents of textbooks 9138The contents are in accordance with the intellectual level of students9339The contents contain problems that can be solved by personal investigation without having aprior method to solve them9440The contents include a proper proportion of mathematical representations(Graphs, diagrams, figures and tables)9441The contents include an appropriate proportion of activities for mental exercise (puzzles/riddles)9542The contents are balanced in terms of key areas (number operation, geometry, algebra, measurement, data analysis and probability)9543Pictures and colorful presentations in the textbooks put a positive effect on conceptual understanding9644The number of problems given on a certain topic affects conceptual understanding9645Chaining (bit by bit addition of new material in the sums) on a certain topic in the text books put a positive effect on conceptual understanding9746Contents of the textbooks are properly chained9747(a)Comparison of the approaches of mathematics teaching9848(a)Comparison of the practices of teachers in their classes10049Students should solve problems by teacher’s explained method only10450Additional material is usually used for deeper understanding of concepts10451Additional material is usually used for rigorous drill of learned material10552Mostly previous exam papersare used as an additional material10553Previous papers are solved as a rehearsal for the actual exam paper10654Past papers are solved because questions of previous papers are considered important10655Past papers are solved because questions from previous papers often repeat in the new papers10756Past papers are solved to understand the pattern of questions coming in the recent papers10757Teacher-constructed problems are presented in the class10858Students are allowed to construct and present their own problems in the class10859Procedures of doing a problem are explained but not the reason for the selection of that procedure10960There are some topics in the textbooks that are always left untaught as no questioncomes in the paper from these topics10961 Homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in class11062Completion of a topic means that the teacher has explained the topic and students have done the sums in their copies11063Emphasis is given on neat and tidy written work11164Homework is assigned and checked regularly11165Topics are not explored in depth; only the procedure of doing a sum is explained11266Unexplained short-cuts are told to solve certain problems11267Derivation of the formula is not clarified, only the method of its application is explained11368Usually students avoid checking answers11369Usually students try to skip graph questions11470Teachers do not emphasize checking of answers by students11471Teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of the class11472Mathematics has a significant application in other subjects11573Teachers’ true role is to generate a question in the mind of a child before it is answered11674Both posing and answering of questions by a teacher produce shallow understanding11675Students can communicate mathematical ideas, reasoning and results11776Students take teaching of mathematics as a pleasant activity11777Students exhibit courage in facing unfamiliar problems11878Students express tolerance in solving difficult problems11879Retention of learned material in the memory becomes stronger with repetition11980Repetition of learned material may attach meaningful relationships among the fragments of knowledge11981Tests/Exams are conducted to assess the level of achievement of the instructional objectives12082Tests/Exams are conducted to categorize students into successful and unsuccessful groups12083The verbal/written remark of teacher on the basis of assessment is evaluation12184Assessment helps both teacher and learner in the process of teaching and learning12185The fear of assessment motivates students to work hard12286The fear of final examinations is actually the fear of being insulted on its results12287A teacher is always engaged in the process of assessing his/her students during the class12388The encouraging remarks of a teacher after assessment produce positive effect on the performance of students12389The discouraging remark of a teacher produces a negative effect on the performance of students12490Methods of assessment should enable students to reveal what they know, rather than what they do not know12491Students take mathematics assessments confidently12592The main purpose of assessment is to improve teaching and learning of mathematics12593The exam papers assess the objectives of teaching mathematics 12694The exam papers are balanced in terms of content areas12695The exam papers (SSC/GCE) assess the actual educational objectives of teaching mathematics12796The system of checking papers is fair12797Examinations are conducted under strict vigilance12898Use of unfair means in the paper of mathematics is common12899Grading system of SSC/ GCE is appropriate129100Teachers’ assessment during class is as important as the final examination129101Students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior grades130102Final examinations assess the factual and procedural knowledge of mathematics only130103Questions in the exam papers are given according to a set pattern131104Questions are given from the textbooks in SSC/GCE papers131105Questions are given from past papers in SSC/GCE papers132106Some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paper132107On the basis of previous papers some questions can be predicted for the upcoming paper133108Assessment is done to distinguish students for the improvement of learning133109Test items of SSC/GCE papers cover all objectives of the curriculum134110Sections of SSC/GCE papers are designed in such a way that questions from particular chapters always come in specific sections134111The entire teaching and learning process in the class is designed and implemented to pass the final examinations135112Mathematics is an interesting subject136113I feel pleasure in doing mathematics136114I do mathematics because teachers emphasize its importance137115I do mathematics because it is a compulsory subject at schoollevel137116Mathematics demands rigorous practice138117Mathematics requires concentration138118High achievers in mathematics argue strongly139119High achievers in mathematics are good analysts139120High achievers in mathematics raise more questions 140121School gives a special emphasis on mathematics over other subjects140122(a)Comparison of perspectives of students about mathematics141123High achievers in mathematics also achieve high grades in other science subjects143124Doing mathematics means doing mental exercise144125Correct solution to a problem gives a feeling of achievement144126(a)Comparison of the factors for which students give importance to mathematics145127Mathematics is a scoring subject147128Textbooks of mathematics have an attractive look148129Language used in the textbooks is clear148130Language of textbooks is difficult because excessive mathematical terminologies are used 149131All topics in the textbooks are taught completely for the preparation of final examination149132Methods to solve different types of problems are explained through worked examples in the textbooks150133Textbooks are illustrated with concept-related pictures from real life150134Pictures in the textbooks facilitate in comprehending the concepts151135Diagrams are the frightening element of the textbooks 151136I can study a new topic through worked examples provided in the textbook152137I study the topic from the textbook first before it is explained by the teacher in class152138I have questions in mind before starting a new lesson 153139Only the contents explained by the teacher should be studied153140(a)Comparison of components of the contents that have to be learnt in Mathematics154141Contents of the textbooks are in accordance with the intellectual levelsof students156142Language of the textbooks is in accordance with the language proficiency of students157143Getting afraid of a problem in the first look makes it very difficult to solve157144Doing important topics is better than doing all the topics in order to getgood marks158145The last questions (star questions) of the exercises are generallyleft unsolved158146(a)Comparison of the domains of thinking process during the solution of a problem159147Most of the teachers emphasize solving the sums using their explained methods only161148There is more than one method to solve a problem162149Most of the teachers emphasize neat and tidy work162150(a)Comparison of the remarks of students for questions involving graphs163151Additional material (worksheets/workbooks etc.) is used to get further practice of the sums164152Teacher-constructed problems are presented in the class166153Separate activities are done for low achievers in the class166154Teachers arrange activities to engage high achiever students to help their low achiever class fellows167155In a mathematics class of 40 minutes, students normally ask less than 5 questions167156In a mathematics class of 40 minutes, teachers normally explain for less than 15 minutes168157Students mostly ask ‘HOW’ type questions in the class168158‘WHY’ type questions are rarely posed by students169159Teachers do not encourage ‘WHY’ type questions in the class169160Procedure of solving a problem is explained but not the reason for the selection of that procedure170161Some topics of the textbooks are never taught170162Homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in class171163Completion of a topic means that teacher has explained the topic and students have done the sums in their notebooks171164Homework is assigned and checked regularly by the teachers 172165Classwork of students is checked regularly by the teachers 172166Topics are not explored in depth; only the procedures of solving sums areexplained173167Short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explained173168Derivation of formula is not explained, only the method of its application is told174169The activities of a mathematics class are largely doing repetition of similar sums174170Reference books are taken from the library to explore the topics in depth175171(a)Comparison of experiences of students in the class about the teaching of their teachers175172(a)Comparison of attributes of a good teacher from students’ perspective178173Assessments help in confidence building182174Assessments help in identifying and reducing mistakes183175Assessments help in the preparation for final examinations183176Quizzes (short tests based on calculations without using calculators) are conducted regularly in the class184177Speed tests are conducted regularly in the class184178Positive remarks of the teacher on student’s assessment produce better results185179Negative remarks by a teacher on student’s assessment produce demoralization185180I am well aware of the pattern of SSC/GCE paper186181Students study seriously under the pressure of tests/examinations186182Teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paper187183Questions in SSC/GCE papers are given according to a fixed pattern187184Questions are taken from textbooks in SSC/GCE paper188185Questions are taken from past papers in SSC/GCE paper188186Some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper189187Some questions can be predicted for the upcoming papers on the basis of previous papers189188(a)Comparison of methods used for revision before taking a test/ examination190189In junior grades (VI – VIII); the final paper is set from the whole syllabus192190In junior grades (VI – VIII); the final paper is set from the topics covered in the final term only193191In junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term193192 Comparison of Responses of the Experts194193 Content Analysis206193(a)Sets206193(b) System of Real Numbers, Indices and Radicals211193(c) Algebra217193(d)Matrices232193(e)Statistics234193(f) Geometry238194 Section Wise Results of Data Analysis249194(a) Aims / Objectives249194(b) Contents / Textbooks252194(c) Approaches / Methodology257194(d)Assessment / Evaluation263LIST OF GRAPHSGraphTitlePage1Comparison of the reasons for the importance of mathematics 792Comparison of the domains of intellect developed by the contents of textbooks 933Comparison of the approaches of mathematics teaching1004Comparison of the practices of teachers in their classes1035Comparison of the students' perspectives about mathematics 1436Comparison of the factors for which students give importance to mathematics1477Comparison of components of the contents that are to be learnt in mathematics 1568Comparison of the domains of thinking process in solving a problem1619Comparison of the remarks of students on questions involving graphs 16510Comparison of experiences of students in the class about the teaching methods of their teachers17811Comparison of the attributes of a mathematics teacher from students’perspective 18212Comparison of methods used for revision before taking a test/ examination192LIST OF ABBREVIATIONSASERAnnual Status of Education ReportBSEKBoard of Secondary Education KarachiBTECBusiness Technology Education CouncilCIE Cambridge International ExaminationsEILEEdexcel International London ExaminationGCE (A-Level)General Certificate of Education Advanced LevelGCE (O-Level) General Certificate of Education Ordinary LevelGCSEGeneral Certificate of Secondary EducationHSC High School CertificateHSSC Higher Secondary School CertificateICEInternational Certificate of EducationIGCSEInternational General Certificate of Secondary EducationNCERTNational Council of Educational Training and ResearchNCTMNational Council of Teachers of MathematicsNEPNational Education PolicyPISAProgramme for International Student AssessmentSSC Secondary School CertificateTIMSSTrends in International Mathematics and Science StudyTSLNThinking Schools Learning NationUCLES University of Cambridge Local Examination SyndicateULEACUniversity of London Examination and Assessment CouncilCHAPTER ONEINTRODUCTIONBACKGROUNDSecondary school education is an important stage in the overall educational career of students. It provides a strong base for entering into higher secondary education with appropriate knowledge and skills or act as a terminal stage for those seeking employment. Quality secondary education is therefore vital for a successful future.It is a doorway to social and economic development both at an individual and national level. (OECD, 2011).Historically, secondary education has been witnessed as a neglected area especially in developing countries. However, in the 21st century, its worth has been acknowledged all over the world (World Bank, 2013). In this regard, the importance of mathematics as a compulsory subject at school level is also well acknowledged internationally. It is considered as one of the most important subjects in the secondary school education. It is due to the reason that this subject fulfills the utilitarian, vocational, disciplinary, intellectual, cultural, and social objectives of education (Sharma (2008); Ediger & Rao, 2000). A number of educational authorities in various countries of the world, even in the developing countries,have been highlighting the importance of this subject at different times. The reports of these authories have placed a strong emphasis on the value of mathematics education in the school curriculum. They all recommended improving the ways of its teaching. Cockcroft Report (1982) emphasized that mathematics contributes to the development of human cognitive, affective and psychomotor faculties but the extent to which it does so, depends on the way it is taught. In the subcontinent in 1937, Zakir Hussain Committee recommended that mathematics should be an essential part of school curriculum. The Secondary Education Commission in India (1952) emphasized the need of teaching mathematics as a compulsory subject in schools. India’s most outstanding commission on education (Kothari Commission, 1964) also put an overwhelming emphasis on the teaching of mathematics (as cited in Rani, 2008; Sharan and Sharma, 2008; Sidhu, 2008). Another very prominent government board on education and training in India, in one of its reports ‘Curriculum for the Ten Year School’, highlighted that advancement in the fields of science and technology in this century has made it more essential to give special attention to the study of mathematics (NCERT, 2006).Sharif Commission (1959) examined the condition of education especially science and mathematics education in Pakistan andrecommended that teaching of mathematics should be given special importance at school level (Government of Pakistan, 1959, p.122).Asian countries of the region like China, Japan, Korea and Singapore have acknowledged the worth of teaching this subject. They have been showing a special interest in mathematics education since the last three decadeds of the 20th century. All these countries have developed a centralized national system of education with extraordinary emphasis on mathematics education (Becker et al., 1990). Moreover,they are improving the methods of its teaching day by day. One of the salient features of mathematics education in these countries is the placement of equal focus on the process of doing (problem solving) and the product (learning the contents). In addition, theyuse both intrinsic and extrinsic motivation of students (Leung, 2004; Zhang et al., 2004). As a result of this special attentionto mathematics, students of these countries have been attaining top positions in the international studies for the last 20 years (TIMSS, 1995, 1999, 2003, 2007 & 2011; PISA, 2009, 2012).Singapore has developed acentralized,world-class system of mathematics education.The framework of Singapore’s mathematics education is highly logical with detailed and consistent implementation procedures. Kaur (2004) reported that in Singapore, the core subject of school curriculum is mathematics. Singaporean government revolutionized mathematics education in 1997 by taking three initiatives, one of which was the ‘Thinking Skills Initiative’. They announced their vision to face the challenges of the new century which was‘Thinking Schools, Learning Nation’. They launched this program in all schools to ensure that the young generation can think for themselves and can find solutions to all the problems they face in the future themselves. Thinking Program entailed teaching eight core thinking skills embedded in mathematics which is a core subject at both elementary and secondary level in Singapore. As a result,Singaporean students of grade 4 and grade 8 have outperformed their counterparts worldwide in successive international studies (TIMSS, 1995, 1999, 2003, 2007 & 2011; PISA, 2009, 2012).In addition to this outstanding performance in the international studies in mathematics, their systems of education are contributing in boosting the economies by producing thinking brains and skilled hands. These countries are now some of the world's largest and most prosperous economies i.e. China, Japan, Hong Kong, Taiwan and South Korea (ISR, 2011, p.54).The studies conducted in Pakistan reveal thatmathematics is not taught properly in our schools. The students’ achievement level in mathematics is low as compared to other subjects. Moreover students perform better on those items in which memorization of facts are required whereas their performance is poor on the items requiring comprehension and skills of problem solving (Das, 2006). Mostly teachers transfer knowledge of facts and procedures in mathematics. Textbookcontents are taught to students and theirprecise replication is assessed throughexaminations taken in a fixed pattern (Amirali & Halai, 2010; Warrick& Reimers, 1995).Tayyba (2010) examined the achievement level of lower secondary students in mathematics. She attempted to study the variation in the achievement level across students and schools when different curriculum frameworks are applied. The results of her study reveal that students are able to pass those items which require simple mathematical skills and low rigor level.Arif (2010) conducted a research on the analysis of mathematics curriculum for grade IX in the province of Punjab. He revealed that curriculum does not produce higher order thinking skills in students and the class activities are not linked with curriculum objectives. A number of content areas are also skipped by the teachers (Perveen, 2009). There is dissatisfaction among students, teachers and experts of the subject about mathematics education in our secondary schools (Arif, 2010; Naeemullah, 2007).Sheerazi (2000) in his study found that mathematics is the least understood subject at school level in Pakistan. He further stated that it is generally taught by untrained or semi-trained (trained in general pedagogical aspects) but not by teachers trained for mathematics education. He recommended that comprehensive subject specific training programs for teachers, especially for mathematics teachers should be arranged. Tahir (2005) in his study specified that mathematics education in Pakistan is lacking in qualitative developments. Textbooks display the contents in a well-organized and smart way but these textbooks are taught in isolation with the world of work. As a result instead of understanding the concepts and the inquiry process, students start memorizing the contents.Secondary School Certificate (SSC) is the local system of education in Pakistan. There are two boards of examinations for SSC (the local board / federal board). There is a difference in the schemes of assessment in the local boards and the Federal Board of Secondary Education. In Karachi, Agha Khan University Board of Secondary Education also conducts examinations for SSC. The examination and assessment pattern of this board is remarkably different from other boards.General Certificate of Education (GCE) is a prestigious and internationally recognized qualification. In 1951England abandoned its old School Certificate (SC) and Higher School Certificate (HSC) system of education and introduced a new system in Wales and Northern Ireland. The replacements for SC and HSC levels in GCE system are Ordinary Level (O-Level) and Advanced Level (A-Level) respectively (Umbreen, 2008). GCEprogram has been functioning in Pakistan in some institutions since 1959. A number of institutions offer GCE (O-Level) these days but 432 schools are registered in the British Council, out of which 130 are located in Karachi (The British Council, 2012). GCE (O-Level) and SSC systems are running parallel in Pakistan. It is a common perception thatthe curriculum of GCE mathematics, its teaching and assessment methods are signicantly different and more effective than the SSC curriculum. Thus, these two systems are creating a clear discrimination between the students. The GCE system is expensive and children of privileged class of society can only opt for it. The SSC system on the other hand, is affordable and providing education to the children of under-privileged classes of the society. A number of comparative studies have been conducted in different areas of teaching and learning of mathematics at the international level. These studies provide opportunities to share the experiences and to learn from each other (Mundy & Schmidt, 2005). But no substantial research work has been conducted on the comparative effectiveness of mathematics curriculums of GCE (O-level) and SSC systems of education in Pakistan. Arif (2010) in his study also pointed out that comparative studies of SSC and GCE (O-Level) systems for the physics, chemistry and biology curricula have been conducted but that of mathematics curriculum has not beentaken up yet. He has suggested carrying out such kind of comparative study for the curriculum of mathematics as well.This study has been conducted toprobe the issue at large.OBJECTIVES OF THE STUDYGeneral Objective The overall objective of the study was to analyze the effectiveness of mathematics curriculum taught at General Certificate of Education GCE (O- Level) and SSC systems of schools in Karachi.Specific Objective The study was specifically focused onTo compare and analyze the aims and objectives of teaching mathematics at SSC and GCE (O- Level).To compare the contents of textbooks and Exam papers of SSC and GCE mathematics courses.To critically compare the effectiveness of approaches and teaching methods applied in both the systems.To compare and analyze the assessment patterns in both the systems.RESEARCH QUESTIONS The following research questions would encompass the statement of the problem.What are the projected aims of teaching mathematics in SSC and GCE (O-Level) systems of education?How far are the objectives of teaching mathematics aligned with the anticipated aims of mathematics education in both the systems?What are the similarities and dissimilarities in the contents of instruction and assessment in the two systems?What is the difference between the approaches of teaching mathematics in these systems?What teaching methods are being used to teach mathematics at SSC and GCE level?What are the patterns of assessments in SSC and GCE systems?Subsidiary Research QuestionsWhat are the similarities and dissimilarities in the learning experiences of students in both the systems?What are the attitudes of students towards mathematics in these systems?How far are students aware of the patterns of assessment in the two systems?How far contents of both the courses are suitable for the students in their concept building?What are the differences and commonalities in the study patterns of students in these systems?What are the attributes of a good mathematics teacher from the perspective of students of both the systems? SIGNIFICANCE OF THE STUDY The study was expected to yield the following benefits.The findings of the study would provide guidelines to the curriculum planners, managers and experts in redefining the objectives of the secondary school mathematics curriculum. It would facilitate the course developers to design the mathematics course according to the international standards. The educational planners and administrators may consider subject specific professional training programs for mathematics teachers. The study would provide teachers the view point of students about teaching and assessment in mathematics.It would help teachers to know about the concerns and difficulties of students. It may help teachers teach the subject effectively. The study would help improve the prevailing pattern of assessment in mathematics.The findings of this study may help investigate the shortcomings in the SSC mathematics course in order to improve itsquality in Pakistan.The study would help in the advancement of knowledge.The study may help the concerned authorities in taking suitable actions to make the curriculum effective. SCOPE OF THE STUDY The study was limited to the comparison of effectiveness of mathematics curriculumat all educational institutes engaged in teaching of mathematics curriculum at GCE (O-Level) and SSC (Matriculation) Level in Karachi. The comparison of the two courses was specifically based on their educational objectives, contents of the textbooks, question papers, teaching methods and the patterns of assessment. DEFINITIONS OF THE KEY TERMSAnalysis: A comprehensive investigation to distinguish between facts, to recognize the relationships, to diagnose the organizational parative Analysis: Analysis by comparing two or more comparable alternatives such as contents, methods, approaches etc.Effectiveness: The level to which something is productive in yielding anticipated results. Comparative analysis of the effectiveness: The extent to which two curricular programs and their implementation is producing productive outcomes for students in accordance with the expected outcomes of the curriculum. Mathematics: The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. Curriculum: A course of study in one subject at a school or college (Oxford Dictionary).Mathematics Curriculum: The educational objectives, contents under study, its ways of instruction and the patterns of its assessment would be considered as mathematics curriculum.GCE: General Certificate of Education (O-Level).SSC: Secondary School Certificatecourse of studies also known as matriculation.Karachi: It is the largest city of Pakistan with an estimated population of 21 million. It is situated in the South of Pakistan on the coastline of the Arabian Sea. Due to a high cultural and ethnic diversity in its population, it is often called as ‘Mini-Pakistan’.Exam papers:Examinations of mathematics taken at the end of an academic period. These include both internal school examinations of junior grades and the final examinations of SSC (BSEK) and GCE (CIE). Past Papers:Papers of previous years of SSC mathematics course (Board of Secondary Education Karachi) and GCE mathematics course (Cambridge International Examinations).BASIC ASSUMPTIONSMathematics is a compulsory subject both at GCE and SSC level.Hundreds of teachers and thousands of students have been engaged in teaching-learning process of mathematics.Prescribed textbooks of mathematics are used both at GCE and SSC level.CHAPTER TWOREVIEW OF THE RELATED LITERATURE2.1 IMPORTANCE OF MATHEMATICSAlthough educationists view mathematics from different philosophical standpoints, yet they have a complete agreement on the significance of its teaching at school level. It is therefore; taken as a compulsory subject in the school curriculum.The educational outcomes of mathematics education dependlargely on the ways it is taught. Several educational bodies in the world have acknowledged its value and recommended to improve the methods of its teaching.According to Cockcroft Report (1982) mathematics is an important subject for the utility of its arithmetic skills at home and work place. It provides basis for scientific development and modern technology. It is a management tool in commerce and industry and has a vast application in other fields of knowledge .It is also a concise, powerful and unambiguous means of communication.Zakir Hussain Committee in the subcontinent, The Secondary Education Commission in India , Kothari Commission andIndian National Policy on Education had all put an overwhelming emphasis on teaching of mathematics in the school curriculum (as cited in Rani, 2008; Sharan and Sharma, 2008; Sidhu, 2008). India’s most outstanding body on Educational Research and Training also emphasized that revolution in the fields of science and technology in this century has made it more essential to pay a special attention to the study of mathematics in our schools (NCERT, 2006).Sharif Commission (1959) recommended that an extraordinary devotion should be given to theteaching of science and mathematics in our schools (Government of Pakistan, 1959, p.122). The aim of education is to enable a person lead a valuable life in the society but simply enabling to function in the society is only a narrow aim of education. The higher aim of education is to develop an independent personality with all human potentials (Bruhlmeier, 2010; Sharma, 2007; Taneja, 1990). According to Sidhu (2008), there is a clear reason for giving mathematics the core position in the school curriculum all over the world. He declares it the subject that fulfills both narrow and higher aims of education. Also there is no dispute among educationists, industrialists and business leaders on the values attached with mathematics in school education (Sullivan, 2011). Generally, it is believed that the chief target of mathematics education is to produce thinking skills among students but there are many ways of thinking. According to an outstanding Indian government board on education, the primary goal of mathematics education is to develop thinking habits to tackle abstractions and to produce problem solving skills (NCERT, 2006). Although the study of mathematics contribute to the development of human cognitive, affective and psychomotor faculties but the extent to which it does so depends on the way in which this subject is taught (Cockcroft, 1982). Many nations in the world had recognized the educational values connected to the teaching of mathematics and had taken different measures to improve the education of this subject. Singapore is the best example in this regard.Singaporean students of grade 4 and grade 8 outperformed their counterparts worldwide in successive international studies. The results of last 20 years of International Studies (TIMSS) and (PISA) reveal the triumph of Singaporean students in the world (TIMSS, 1995, 1999, 2003, 2007 and 2011; PISA, 2009, 2012). This outstanding performance is due to a strong education system with a prime focus on the teaching of mathematics. The students of China, Japan, Korea, Taiwan and Hong Kong have also been attaining top positions in these studies for last 20 years (TIMSS, 1995, 1999, 2003, 2007 & 2011; PISA, 2009, 2012). The fundamental thing common in the education systems of these countries is a strong emphasis on mathematics education in the school curriculum.Theother important factor common in these countries is also positively corelted with the system of education and it is a successful economy. These are some of the world's largest and most prosperous economies i.e. China, Japan, Hong Kong, Taiwan and South Korea (ISR, 2011,p.54). Teaching of mathematics as a compulsory subject in the school curriculum has certain aims. These aims are like ideals and are taken in a broader perspective. These aims may be common to different subjects. Knowledge of these aims is very important for a teacher. Aimlessness can harmfully affect the values and the purposes of teaching. A very well planned and organized educational scheme is required to acquire these aims (Mishra, 2008; Sharan and Sharma, 2008).2.2 AIMS OF TEACHING MATHEMATICSThe ideological aims of teaching mathematics areTo provide the learner functional knowledge of mathematics inorder to meet the increasing demands of sophisticated workforce. To train or discipline the mind for overall personality development. To enable the child understand the organization and maintenance of our social structure as a society, which is the inter-relation of individuals and various groups.To prepare the child for further studies in different fields like science, commerce, information technology etc.To develop the cognitive, affective and psychosomatic faculties of child into powers (Mishra, 2008; Sidhu, 2008; Sharan and Sharma, 2008).2.2.1 Objectives of EducationTo achieve the aims, large educational activities are divided into smaller units and one by one after the completion of these units, the projected aims are attained. Therefore to attain an educational aim of teaching a certain subject, every small thing that we do, is said to be an objective. These are short-term targets that can be achieved within a limited time period under a certain classroom setting (Ediger et al., 2010). No subject can be taught properly without clear aims and objectives of its teaching in the mind. They guide the teachers and learners in the desired direction. These objectives must be well balanced among cognitive, affective and psychomotor domains(Rao, 2006).The objectives should be precise, specific and attainable (Sharan and Sharma, 2008; Cartor, 1982).2.3 ROLE OF EDUCATIONAL OBJECTIVES Educational objectives give the framework of our expectations from the students. Objectives are helpful in the following ways.Instruction can be focused on a particular point.Provide us guidelines for learning and instruction.Enable the teacher to assess students’ performance objectively.Help the teacher evaluate his/her own performance.The most important role of objectives is that they are derived from the actual aims and goals of a subject. Thus, they are helpful in achieving the true aims of education (Gronlund and Bookhart, 2009; Sharan and Sharma, 2008, Sidhu, 2008). CHARACTERISTICS OF EDUCATIONAL OBJECTIVES2.4.1 Specific PerformanceAn objective always states what a learner is expected to be able to do and/or produces to be considered competent. For example: to factorize, to construct, to draw, to prove, to evaluate, etc.ConditionsAn objective describes the important conditions under which the behavior is to occur. For example: after doing this exercise, after doing this activity, etc.Criterion or StandardAn objective describes the criteria of acceptable performance. For example find the volume of a cube correct to the nearest litre, find the area correct to three significant figures etc (Gronlund and Bookhart, 2009; Mager, 1997).Description of instructional objectives should encompass all the characteristics of an objective. In this regard, Heinichet al.,(1999) presented a model that is known as ABCD model. A for Audience, B for Behavior, C for Condition and D is for Degree. Another model for writing objectives is SMART Model (Drucker, 1954; Doran, 1981) which again characterizes an objective. S for Specific, M for Measurable, A for Attainable, R for Result-Oriented and T is for Time-Bound.2.5 TYPES OF EDUCATIONAL OBJECTIVESA professor of Chicago University, Dr. B.S. Bloom, and his colleagues, categorized the human behavior into three parts which represent the intended outcomes of the educational process. Cognitive Domain Affective Domain Psychomotor Domain Cognitive Domain This domain is concerned with mental abilities of a learner and it deals largely with information and knowledge. Most of the educational objectives in the current practice of teaching belong to this domain (Mustafa, 2011).This domain is further divided into six major categories of which first three are called lower mental functions and the last three are known as higher mental functions (Bloom & Krathwohl, 1956).KnowledgeKnowledge objectives emphasize most of the psychological processes of remembering.Remembering and recalling of basic facts, symbols and specific details (factual knowledge).Holding of information about classifications and categories, principles and their relationships (conceptual knowledge).The memorization and retrieval of certain methods and procedures on demand (procedural Knowledge).Knowledge of his/her own knowledge. This means to know when and where a particular strategy or technique can produce better results. It is the knowledge about possible errors and the ways to tackle them in problem solving (meta-cognitive knowledge) (Anderson et al., 2001).The instructional objectives in this category are to develop assimilation among these four types of knowledge. The solution of any problem requires a background of some factual knowledge. The first step of instructional objectives is to provide the knowledge about basic facts of mathematics e.g. signs, symbols, notations, rules, principles etc. This factual knowledge is of a great importance as it is the basis of mathematical language. A learner cannot communicate mathematically without this knowledge. The knowledge about routes is very helpful before starting a journey therefore the knowledge of techniques and methods to solve a problem in advance is of great value. The procedural knowledge is associated with conceptual knowledge. The relationships among different ideas or phenomenon are considered to be developed by procedural knowledge. On the other hand conceptual (relational) knowledge may direct towards new methods and techniques (Hiebert, 1986; Leung, 2004). Meta-cognitive knowledge includes knowledge of general strategies and techniques, the knowledge of appropriate situation where and when to apply these strettegies and the knowledge of the effectiveness of these strategies (Pintrich et al., 2000). Meta-cognitive knowledge is considered as the basis of the problem-solving approach in mathematics (Schoenfeld, 1992).Comprehension This is the lowest level of understanding i.e. the ability to use the provided material or the idea being communicated.The ability to examine, understand and draw relative information from a given situation.The capability to interpret and obtain meanings from the given information or situation.The competence to translate the obtained meanings to problem solving.The capacity to extrapolate on the basis of certain statistics (Bloom & Krathwohl, 1956). The instructional objectives at this level are to enable the students to use mathematical language appropriately i.e. use the terminologies, symbols, notations and mathematical vocabulary; read, understand and give meaning to mathematical representations, graphs, charts, tables, diagrams, geometrical figures and models; communicate mathematical ideas, reasoning and results properly and interpret their understanding and can predict a possible solution of problem at the early stage.ApplicationThe ability to use information i.e. to use abstract knowledge in concrete situations is called application.The ability to apply knowledge to new situations other than those where the knowledge was gained.The ability to construct one’s own knowledge from the knowledge gained in a different setting (Bloom & Krathwohl, 1956). It is the students’ ability to comprehenda problem situation and apply their abstract mathematical knowledge to solve that problem. If the application of a formula or procedure isrequired to solve similar problems (sums), this would be the lowest level of application. If the student applies abstract knowledge to a real-life situation that is completely new to him/her, this would be the highest level of application. This activity is always integrated with previous levels of the cognitive domain. Retrieval of factual and procedural knowledge from memory and the use of meta-cognitive knowledge at every stage of problem solving is a part of the application process. Analysis The ability to break down information into parts in order to clarify the communicated message or to organize it to express its properties is called analysis.The ability to divide information into its constituent parts.The ability to distinguish between facts and interpretations.The ability to recognize the relationships among the elements of given information.The ability to diagnose the organizational principles of a given set of data (Bloom & Krathwohl, 1956). Synthesis The ability to put pieces together to form a whole i.e. putting together ideas, arranging and combining them to form a new idea or product that was not clear before.The ability to generalize from the facts.The ability to deduce, foresee and draw conclusions.The capability to produce new information using old ideas (Bloom & Krathwohl, 1956). Evaluation The ability to make judgments about the value of materials and methods is called evaluation.The ability to compare and contrast information.The ability to assess the value of ideas and procedures.The ability to select on the basis of argument.The ability to prove the worth of certain evidence (Bloom & Krathwohl, 1956). Analysis of a given situation is always a fundamental part of problem solving process in mathematics education. It is the basis on which the solution of a problem depends. Therefore the development of the faculty of analysis as a domain of overall intellectual development is a major target of mathematics education. The ability to synthesize scattered data and to produce new knowledge from it, to infer on the basis of acquired knowledge and arguments and to evaluate the value of certain evidence are also the vital areas of mathematics education. Gagne (1977) and Gagne & Briggs (1979) suggested that the most important area of school learning is the cognitive domain of learning. Gagne (1985) described five categories of human behavior that can be observed as the outcomes of learning. These are thinkingskills, communication skills, cognitiveapproaches, physical faculties and attitudes. Gagne focused his attention on the cognitive domain (thinking skills, communication skills, and cognitive approaches) and within the cognitive domain he focused on the thinking skills (Martin & Briggs, 1986). Instructional Objectives of Cognitive DomainThe major area of instructional objectives of the current practice of teaching is of cognitive domain. Some of the possible instructional objectives of this domain are given below.Students comprehend given information and can transform it into mathematical language. Use mathematical language appropriately i.e. they can use the terminologies, symbols, notations and mathematical vocabulary.Read, understand and give meaning to mathematical representations, graphs, charts, tables, diagrams, geometrical figures and municate mathematical ideas, reasoning and results properly.Hold basic factual information of the procedures and formulae to solve certain types of problems.Form relationships among different ideas or phenomena.Have knowledge of general strategies and techniques and the appropriate situation where and when to apply them.Apply abstract knowledge to solve practical life problems.Construct new knowledge from the knowledge gained in a different setting.Analyze a set of data by breaking it into parts.Reason, anticipate and draw conclusions.Evaluate the worth of ideas and procedures.Affective DomainReceivingThis is the level where the learner feels that there is a stimulus that wants attention. After realization of the presence of stimulus,the learner decides to pay attention towards it.Consciousness: The mental alertness of the learner towards a certain thing, phenomenon or issue.Readiness: The inclination of the learner either to pay attentionor to avoid the stimulus.Selected Attention: The ability to have a control over attention in order to select the preferred stimulus out of a number of stimulating distractors (Krathwohl, Bloom & Masia, 1964).Responding This is the level where the learner actively attends, participates and responds to a certain phenomenon or activity and enjoys it. Consent in Response: The response of the learner in which the need of that response is not fully acknowledged by him.Readiness to Respond: The inclination of the learner to respond voluntarily.Gratification in Response: The feeling of satisfaction or pleasure enjoyed by the learner in that response (Krathwohl, Bloom & Masia, 1964).Valuing It is the value given by a learner to a particular thing, phenomenon, or behavior. The range of this level is from simple acceptance to commitment.Acceptance: This is the lowest level of valuing where the learner accepts a phenomenon, behavior etc. but has a low degree of conviction.Preference: At this level the learner not only accepts a behavior but goes further and has intent to pursue and attain mitment: This is the highest degree of belief where the learner has a true commitment for a certain reason and he also tries to convince others of the same (Krathwohl, Bloom & Masia, 1964).Organization At this level,the learner who has internalized some values, compare these values to determine a relationship between them in order to make a personal value system. The prime focus at this level is on comparing the values, finding relationships and on the fusion of these values into a system (Krathwohl, Bloom & Masia, 1964).Conceptualization: At this level the learner attain an ability to conceptualize a value related to those values that have been already internalized or the new values he or she is going to anization of value: This is the level where the learner organizes and puts in order his or her own value system (Martin & Briggs, 1986).Characterization by a value or by set of values At this level, the learner’s behavior comes completely under control of his/her adapted value system and this control persists for a long time. At this stage, the learner’s personality is characterized by the same behavior (Krathwohl, Bloom & Masia, 1964). A number of studies conducted in the recent past have focused on the affective issues in teaching of mathematics and highlighted the significance of beliefs, values and attitudes of students towards mathematics and the implications of these affective issues on performance (Grootenboer, 2007; Leder & Forgasz, 2006; Ma, 2003, McLeod, 1992). Affective issues (beliefs, values, attitudes and emotions) play a key role in mathematics education. Beliefs are understandings, premises, or propositions about the world that are felt to be true (Richardson, 1996, p.103). McLeod (1992) has mentioned four types of beliefs: Beliefs about self, beliefs about mathematics teaching, beliefs about social context and beliefs about mathematics. McLeod (1992) is of the view that these beliefs may change with age but some of them may have a strong anchor and cannot be easily changed by routine instruction. Values are often taken in the same meaning as that of beliefs but there is a clear distinction between them. This distinction has been identified by Clarkson, Fitzsimons and Seah (1999, p.3). According to this division,“values are only shown in the form of actions whereas beliefs can be expressed through verbal expressions and it is not necessary that a person expresses his/her beliefs in the form of observable actions”. Attitudes are observed as either negative or positive. They are developed in two ways; either by experiencing a repeated emotional reaction or by attaching a new attitude to an already existing attitude. For example, if a student has an attitude of dislike towards graphs, he may attach the same attitude towards geometrical transformations (Grootenboer, 2007; McLeod, 1992). Research on attitudes suggests that there is no direct relation between attitude and achievement in mathematics but rather this relation is complex in nature (Ma, 2003, McLeod, 1992). Instructional Objectives of Affective DomainAccording to Sharan (2008), the instructional objectives of affective domain of mathematics education can fall into two categories: appreciation objectives and interest objectives.Some of the possible instructional objectives are as suggested below.Appreciation ObjectivesThe pupil appreciates the role of mathematics in other disciplines of science.Appreciates the symmetry and balance in geometrical figures and solids.Enjoys the patterns of relationships among numbers.Appreciates the use of basic knowledge of mathematics in various aspects of real life.Takes teaching of mathematics as a pleasant activity (Sidhu, 2008).Interest ObjectivesThe student takes interest in solving problems of mathematics.Pays proper concentration in solving mathematical riddles and puzzles.Pays attention to the teacher during the instruction.Does class activities with enthusiasm and homework with rigor.Checks answers with curiosity after solving every problem.Exhibits neatness in his/her works (Sidhu, 2008).Attitude ObjectivesThe student likes his/her mathematics teacher.Enjoys the company of those who are good at mathematics.Helps the weak students in their difficulties willingly.Enjoys taking mathematics assessments.Shows composure during the solution of several similar mathematical problems for practice.Exhibits courage in facing unfamiliar problems and expresses tolerance from the start of problem till its result (Sidhu, 2008).Table 1: The affective domain in mathematics educationCategoryExamplesBeliefs AboutNature of MathematicsOwn PersonalityTeaching of MathematicsAttitudesEmotionsMathematics is a study of rules and proceduresMathematics is a mean to discipline the mindI am a good problem solverTeaching is dispensation of knowledgeReluctance in solving graphical problemsPleasure in solving geometrical problemsInclination towards discovery learningEnjoyment or annoyance in solving non-routine problems.Aesthetic responses to mathematicsAdapted from(McLeod (1992, p, 578)Psychomotor DomainImitation The learner observes an activity and attempts to repeat it, or sees a finished product and attempts to replicate it while attending to a model (Dave, 1967).Manipulation The learner performs an activity or produces a product by following written or verbal instructions without observing the model (Dave, 1967).PrecisionThe learner can independently perform the activity or produce the product without written or oral instructions and without observing a model (Dave, 1967).Articulation At this stage, the learner attains the ability to perform the activity or produce the product to new situations with accuracy and speed (Dave, 1967).Naturalization At this stage, the learner becomes able to perform the activity with ease and the work becomes a routine (Dave, 1967). The learner can perform the activity with a less physical and mental vigor (Huitt, 2003; Dave, 1967). 2.5.3.6 Instructional Objectives of Psychomotor DomainA careful consideration is required for psychomotor objectives in teaching of mathematics as these objectives provide the opportunity to practice the learned material. Practice (drill) is very important in mathematics education as retention of learned material in the memory becomes stronger with repetition. It has also been observed in studies on mathematics instruction that using fragments of knowledge that has already been learned repeatedly may attach meaningful relationships among them but meaningless repetition is not recommended (Rao, 2006; Leung, 2004). Some of the possible psychomotor objectives in teaching of mathematics are as underDrawing a locus or a geometrical figure (line segment, circle, triangle etc.) from the level of imitation to naturalization.Drawing a graph or sketching a diagram by following written or verbal instructions till drawing diverse geometrical and spatial figures autonomously.Application of the formulae and procedures of abstract concepts with accuracy and speed.Order, organization and articulation of the solution of a problem.Demonstration of learned concepts through models or charts.Learning and presenting the concepts using technological resources.Efficient use of electronic devices such as calculators, computers etc. 2.6 PRINCIPLES OF CURRICULUM CONSTRUCTIONMathematics is a very vast subject. It is very difficult to cover all of its areas in the school curriculum.Thus, selection of suitable contents for its teaching is a very important issue. The principles of selecting the content for school curriculum are as follows.2.6.1 Principle of UtilityThere are certain areas of mathematics that are indispensable to learn for every person. Topic of every day mathematics i.e. profit and loss, ratio and proportion, simple and compound interest, hire purchase, exchange rate, estimation and approximation etc. are very important for every educated person. The utilitarian value of these topics demands that they should be the essential part of mathematics curriculum at school level (Sidhu, 2008; Mishra, 2008).2.6.2 Principle of PreparationThe selection of contents should be made in such a way that the learned contents can provide a preparatory ground to the learner for the future. The purpose of these contents in the curriculum is to prepare the child for the future. There are two ways to prepare the children for the futurePreparation for future vocations.Preparation for higher education.(Sidhu, 2008)2.6.3 Principle of Discipline/TrainingOne of the aims of mathematics education is to discipline or train the mind. Therefore, a suitable proportion of topics should be consisted of such activities. The contents of this type sometimes do not have any utilitarian value but in order to achieve the disciplinary aim of education, this type of content i.e. puzzles, riddles, crosswords etc. should be a part of the curriculum (Sidhu, 2008; Mishra, 2008; Sharan, 2008).2.6.4 Principle of cultural ValueTopics that can develop the characteristics of patience, tolerance, consistency, containment and appreciation are very important along with problem solving. Therefore, the problems should be posed by incorporating these values in them (Sidhu, 2008).2.6.5 Principle of flexibilityThe curriculum should be flexible so that old and outdated contents can be eradicated and new updated contents can be incorporated (Sharan, 2008, Noyes, 2007).2.6.6 Principle of suitabilityAccording to this principle contents should be selected in accordance with the age and level of the students. The suitability of the contents for certain age and level depends primarily on the difficulty level of the contents. It also depends upon the sequential arrangement of the topics (Noyes, 2007).2.6.7 Principle of InterestThisprinciple focuses on the concerns of the pupils who often seem to complain about the uninteresting curriculum contents of mathematics. The topic should be selected in such a way that they can catch the interest of students at different grade levels (Noyes, 2007).2.6.8 Principle of CorrelationThis principle demands that topics in mathematics curriculum should be correlated with the topics of other subjects especially with physics and chemistry. Therefore, the curriculum of mathematics will directly or indirectly support other subjects and this is the inter-disciplinary aim of mathematics education (Sharan, 2008).2.6.9 NCTM Guiding PrinciplesThe National Council of Teachers of Mathematics (NCTM) in USA is concerned with quality in mathematics education. This organization produced a number of valuable publications regarding mathematics curriculum. The following guiding principles are adapted from prominent NCTM publications.Focus on Coherence There are different areas of mathematics such as arithmetic, algebra and geometry. All these areas are highly interconnected. The coherence in the curriculum means to organize and integrate important concepts within these areas logically and effectively. The purpose of this focus and coherence is to develop a rich understanding of and proficiency in problem solving. Focus on Importance The focus of curriculum should be on those contents and procedures that are important and are worthy of both teachers’ and students’ time and attention. The reasons for this importance may be their usefulness in developing other mathematical concepts, in relating different domains of mathematical knowledge and in making students able for higher education and asadroit personnel. Focus on Articulation Learning mathematics involves integrating the learned concepts to the new ones in the hierarchy of ideas and to develop a clear understanding of the relationship among these. A well- articulated mathematics curriculum can provide the teachers an opportunity to guide students towards gradually increasing sophistications and depths of knowledge.Focus on Depth over Breadth The emphasis of mathematics curriculum should be on depth rather than breadth. Curriculum must focus on the essential ideas and processes of mathematics in depth rather than expanding the content areas. But an important care in this regards is the avoidance of unnecessary repetition of topics.2.7 APPROACHES OF ORGANIZING THE CURRICULUM CONTENTSThere are two basic approaches used to arrange the contents in a ical ApproachThe topical approach is a way of organizing the contents topic wise. When one topic is finished, the next topic starts. This approach is narrower in focus (Sidhu, 2008; Hurwitz, 2007).Spiral or Concentric ApproachAccording to the spiral approach, each topic is revisited in a systematic way in a more detailed and complex manner each time. This means that covering the same topics several years in a row and advancing them slightly on each pass. Thus, a child will solve the problems of the same topic in successive years of his education with an increase in the difficulty level of the problems (Bruner, 1960).Epistemological Approach According to this approach, the contents should be differentiated on the basis of epistemological structure and simple, formal and advanced ways of knowing mathematics should be the basis of organizing the contents(Noddings, 1985).Constructivist’s Approach According to this approach, the contents are organized on the basis of students’ interests and needs. In this approach, the teacher does not have to cover certain topics in a sequence but the role of teacher is to arouse the interest of the students and facilitate them in their own construction of knowledge. Therefore, in this approach, when the teacher succeeds ininciting the curiosity of learners in a certain area, the learning material related to that area is presented and vice versa. The order of contents in this approach is completely dependent on students’ interests and needs (Ball & Kuhs, 1986).2.8 ROLE OF TEXTBOOKS IN MATHEMATICS EDUCATIONTextbooks are the most important feature of mathematics education all over the world, especially in developing countries.These are taken as the epicenter of mathematics teaching. According to Mahmood (2010a), textbooks are the only available learning material in schools. The availability of additional teaching and learning material like school libraries, audio/video aids, computer, internet etc. is rare in Pakistan. Textbooks are an important and primary source of teaching and learning activities (Kajander, 2009; Schmidt et al., 2001; Tanner, 1988). In mathematics the sequencing and ordering of learning material is very important.Therefore, teachers mostly use the textbooks as an organized source of contents and as a curriculum guide (Mahmoodet al., 2009; Freeman & Porter, 1989). Teachers usually teach the topics which are present in mathematics textbooks and the topics that are not included in the textbooks are generally not explored (Freeman & Porter, 1989). Sheldon (1988) identified three reasons for the extensive use of textbooks in schools.Designing personal content for teaching is an extremely difficult task for teacher.Teachers have very limited time available in schools in which they cannot develop their own teaching material. Due to some external pressures on teachers they cannot do this task.Teachers use textbooks to achieve a uniformity of instruction among different classes.They also use them to give students an organized set of problems for further practice at home (Pepin, 2001). On the other hand, students use textbooks to revise their conceptual and procedural knowledge as they believe that solved examples in the textbooks help them in solving new problems (Reyset al., 2004; Tyson & Woodward, 1989). The findings of some international studies conducted after the high performance of students’ of Asian countries in TIMSS, revealed that there is a positive correlation of high degree between textbooks and achievement of students (Fan & Zhu, 2004; Haggarty & Pepin, 2002; Li, 2000; Valverde et al., 2002). Yeap (2005) indicated through his study that textbooks having colorful pictures and presentations put a positive effect on students’ conceptual understandings. He also argued that the number of problems on a certain topic given in the textbook affect conceptual understanding positively.Ginsburg, Leinwand, Anstrom & Pollock (2005) in a comparative study of textbooks revealed that Singaporean mathematics textbooks contain in-depth information of mathematical topics compared to American textbooks. He declared it one of the reasons for the Singaporean students’ deep understanding of concepts. A number of similar studies have been conducted to analyze the textbooks of school mathematics in Asian and European countries (Fan, 2007; Pepin, 2001; Schmidtet al., 2001; Li, 2000; Stevenson et al., 1986). Mahmood (2010b) found that in Pakistan, there is a serious lack of consistency in approved textbooks of mathematics by different publishers at elementary levels. He identified the internal non-linearity and non-integration of topics within a set of series of books of more than three publishers. He also recognized inconsistency with respect to contents and identified that some approved textbooks of mathematics do not cover the required national curriculum content areas. He mentioned that approved textbooks of mathematics have a reasonable level of vertical integration but a very little horizontal integration has been found.2.9 APPROACHES OF TEACHING MATHEMATICS According to Ball and Kuhs (1986), the following four approaches of teaching mathematics are used in the classrooms.Learner-Focused Approach Learner-focused approach (Ball and Kuhs, 1986) emphasizes the need to focus the entire instructional activities on the interests and needs of the learner. This is the constructivist’s approach of teaching (Piaget, 1977). Learning is a process of developing understanding by methods of inquiry (Cobb & Steffe, 1983).The role of teacher in this approach is to facilitate the learners’ construction of knowledge by stimulating their thoughts, administering the learning process by posing thought provoking problems and asking inciting questions. The role of the teacher is to help the students and he/she can help them by listening, examining, accommodating, reaffirming, encouraging and providing counter examples (Dienes, 1972). The focus of teaching always remains on concept building. The teacher niether have a sequenced set of activities to donor he/she has to cover an organized set of topics in the class, instead the teacher has to arouse the interests of the learners. As this approach focuses on individuals rather than the contents therefore the organization and presentation of the material depend on the areas of interests of the students and their needs.Content-Focused Approach ( with emphasis on understanding) According to this approach (Ball and Kuhs, 1986), the prime focus of teachers lies on the content but with a stress on the development of understanding of concepts and operations. Skemp (1976) stated that it is not enough for students to understand how to execute different mathematical tasks (relational understanding). He claimed that for a complete understanding, they should be aware of why the concepts and their relationships work as they do (instrumental understanding). As the focus in this approach is on both content and understanding, the expectations from the teacher become high. The teacher has a little authority to organize the learning content in this approach contrary to learner-focused approach where the organization and presentation of content rests on needs and interests of the learner. The dilemma for teachers with this approach is that on one hand they want to explore the topic deeply to get a complete understanding which requires alternate instructional strategies and is quite time consuming but on the other hand they are given a limited time within which they have to complete the prescribed contents as well.Content-Focused Approach (with emphasis on performance) This approach (Ball and Kuhs, 1986) is taken from a psychological viewpoint rather than a disciplinary viewpoint. The contents are presented in a sequence to students and this organization of content is based on a hierarchy of concepts and skills. The ordering of material is done before presenting it to students. This sequencing is based on the maxims of content organization. The material is presented in an expository style with the explanations of difficult terminologies, concepts and procedures. The teacher asks convergent questions from the students so that they can draw a conclusion about a certain matter. The focus of this approach remains on doing the problems from the textbooks and gaining expertise by practice. The performance of students on these tasks is taken as learning in the subject.Class-Room Focused ApproachWith a class-room focused approach (Ball and Kuhs, 1986), the teacher is an active instructor who presents material effectively, explains efficiently and makes students involve in the teaching-learning process avoiding interruptions from inside or outside of the class. The role of the teacher is a continuous monitoring of the students’ class-work, home-work and giving them feedback. The maintenance of continuous flow of planned activities and students’ interest in the lesson by minimizing the disruptions is the prime responsibility of the teacher in this approach. Five possible components especially for the teaching of mathematics in this approach could be: daily revision, class-work, home-work, weekly revision and monthly revision of skills and concepts.METHODS OF TEACHING MATHEMATICSSidhu (2008) described the following methods of teaching for mathematics.Lecture Method This is the method of imparting knowledge through speech. In this method, the teacher delivers a planned lecture in front of students who have to listen to it attentively. This method is not suitable for teaching mathematics in its purest form.Dogmatic Method In this method, the teacher provides the details of formulae and procedures to students and they have to follow and practice it. In this method, the emphasis lies on accuracy.Inductive-Deductive Method Inductive method is based on induction which means to generalize or taking it as a principle after testing its results on a number of occasions. It leads from concrete to abstract and from examples to formula. Deductive method is opposite to inductive method in which we have to proceed from abstract to concrete and from formula to examples.Heuristic Method In this method,the learner has to discover knowledge by his/her own effort. The teacher does not have to impart knowledge in this method. The teacher can guide and assist his/her students in a gradual manner so that they can discover the knowledge easily.Analytic-Synthetic Method Analytic method proceeds from unknown to known. In this method, the problem is broken into its constituent parts so that a relationship can be found between these parts and an already known piece of knowledge. Synthetic method is converse of analytic method in which the learner proceeds from known to unknown. This is a method of putting isolated bits of knowledge together to reach the point where one can conclude or get a new piece of knowledge.Laboratory MethodIt is a method in which students use concrete material (practical equipment) to develop mathematical concepts. It becomes more interesting when applied in lower grades with computer games. The construction of geometrical figures involves the use of geometrical instruments such as protractor, compass, set squares etc. so it is like laboratory work.Project Method This method is based on the fact that knowledge is individual and is a method of spontaneous and accidental teaching. The students have to work on a project and as the project progresses, the learner or group of learners start gathering the bits of knowledge encountered by them on the ical Method It is the converse of concentric method. In this method, a topic is taken as a unified whole or as an unbreakable unit and is taught till its end without any intervention of any other topic in between.Concentric Method In this method, a certain topic is studied over a long period of time, starting from foundation level of the concept widening its circle and by adding more contents in it during the subsequent years. Problem Solving Method This method was first introduced by Polya (1957). In this method students are provided a problem for which they do not have an immediate answer. Moreover, they do not know a specific procedure that can be directly applied to solve it (Rani, 2008; Schoenfeld, 1992). They have to study the problem in depth and after analyzing the given information, they have to design their own strategy to solve it. The problems given to students should be interesting, well-structured and based on completely new situations that are unfamiliar to the student previously (NCTM, 2000).PRINCIPLES ANDSTANDARDS FOR INSTRUCTIONAL PROCESS IN MATHEMATICS NCTM in USA published a document ‘Principles and Standards of School Mathematics’, which provides guidelines for instructional process in mathematics (NCTM, 2000).The principles are statements that reflect basic perceptions essential for an effective instructional process in mathematics. 2.11.1 Principles Equity: All students can learn mathematics if instructed properly. Therefore every student should be accommodated in the process, terms of access and attainment. For this, necessary arrangements should be made.Curriculum: A curriculum is not a series of activities, it is more than that. It should be coherent, practical and well planned.Teaching: Teaching is a task to develop understanding of mathematics by assimilating factual, procedural and conceptual knowledge under the umbrella of meta-cognitive knowledge making students competent and confident to solve problems.Learning: Development of conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition (Kilpatrick et al., 2001).Assessment: Assessment should inform about the worth of instruction and learning. It should guide both teachers and students to improve their performance.Technology: The use of technology is very important in mathematics education because it enhances students’ conceptual learning (NCTM, 2000).2.11.2 Standards The standards are metaphors about how instruction should be imparted to achieve an optimum level of knowledge and understanding in students. These principles and standards are very helpful to mathematics teachers and educators, who can take guidance to improve their instruction.2.11.2.1 Content Standards A possible national curriculum for a country should include the following key content areas in mathematics.Number and OperationsAlgebraGeometryMeasurementData Analysis and Probability (NCTM, 2000). Process StandardsProblem Solving: It means to engage the students in those well-structured problems for which they do not have any direct method to solve. They imply their existing knowledge to design a strategy to solve these problems and thus construct their own knowledge.Reasoning and Proof: It is the basic aim of mathematics to reason logically by evolving thoughts, reconnoitering phenomena, rationalizingresults, and using mathematical inferences in all content areas. Communication: Communication of ideas in mathematical language in both written and verbal formis very important as it helps build one’s own understanding and helps others in clearing their concepts.Connections: Mathematics is an interrelated field where every topic is connected to some other. The instructional processes in which the connections within some mathematical ideas or branches are emphasized become more meaningful for students because in this way, they learn the practical use of mathematics.Representations:Mathematical ideas can be represented in a number of ways such as figures, diagrams, tables, graphs, notations with letter symbols etc. The proficient use of representations enables students to translate, interpret and model complex mathematical phenomena (NCTM, 2000).2.12 ASSESSMENT IN MATHEMATICSThe process of collecting information about the effectiveness of teaching and learning is called assessment (Hanna & Dettmer, 2004). Evaluation is considered as the determination of worth of the results of assessment data. The history of formal assessment on students’ academic achievements is very old (Siu, 2004). There are two basic concepts of assessment.Traditional Concept In ancient times the concept of assessment was to judge the knowledge of the students on certain topics. The traditional concept of assessment is still prevailing in different forms in mathematics. In the traditional method, students are assessed by routine sums present in their textbooks on certain topics from their syllabus. The items of these assessments usually assess lower order thinking skills of the students i.e. mainly factual and procedural knowledge. These tests are usually time-bound (limited period of time, e.g. 1 period tests /3-hours exams), instrument-bound (paper-and-pencil and/or with calculators), and venue-bound (within classrooms/ board level) tests. These tests are of two types; internal (organized by school) and external (organized by an external examination board). The fundamental purpose of these assessments is to mark students on the basis of their performance and to categorize them on the basis of their grades (Lianghuo, 2004).Modern Concept According to modern concept of assessment which is much broader, mathematics education cannot be assessed only on the basis of routine written tests. It goes beyond it, emphasizing how students are assessed and what, why and when are they assessed(Lianghuo, 2004). According to this concept, assessment is the collection of evidence about students’ knowledge (factual, procedural and conceptual); their skills to use mathematics and their dispositions towards mathematics. The collection of evidence is to assist teaching-learning process in multiple ways. According to Singapore Ministry of Education’s Assessment Guide, taking tests, devising mark scheme and giving marks is not students’ assessment. Assessment should be on going, an integral part of teaching-learning process and its chief purpose should be the improvement of mathematics education (Lianghuo, 2004, p.3).Table 2: Comparison of traditional and modern concepts of assessmentMathematics AssessmentTraditional ConceptModern ConceptWhat (Contents)Cognitive DomainKnowledge and Lower Order SkillsFocus on product of learningBoth Cognitive and Affective DomainsKnowledge (Factual, Conceptual, Procedural), Skills, Aptitudes and dispositions.Focus on both product and process.Where (Location)Within ClassroomsWithin and/or Outside ClassroomsWhen (Time)Summative (at the end of a term, quarter, year etc.)Formative (on going during instruction) and SummativeHow (Method)Conventional (paper-pencil) written tests within a given time duration (one period test, 3 hours test, etc.)Both Conventional and Alternative (observing students, annotated records, student’s work-folios etc.)Why (Purpose)Single purpose (mainly grading and reporting students’ level of learning).Multiple Purposes(Principally improvement of teaching and learning). Adapted from (Lianghuo, 2004, p.4)2.12.1 Purposes of Assessment According to NCTM (1995) assessment standard document the four broad purposes for the assessment of mathematics are as followsMonitor students’ progressTo promote progressMaking instructional decisionsTo improve instructionEvaluate students’ achievement To recognize achievementEvaluate programs To modify programs2.12.2 Principles of AssessmentDe Lange (1999, p.10) in his report, ‘Framework for Classroom Assessment in Mathematics’, has made the following list of principles for assessment.The highest purpose of assessment is to distinguish students for the improvement of learning (Gronlund, 1968; Black & William, 1998).Methods of assessment should disclosethe level of achievement of students learning rather than quantifying their unlearning (Cockcroft, 1982).A balanced assessment plan includes various formats and it provides students opportunities to express and document their performance in variety of ways (Wiggins, 1992).Assessment items should encompass all the expected objectives of the curriculum.Mark scheme should be accessible to students and should be strictly followed. It should also provide examples of marking on previous assessments.The overall process of assessment should be clear to students.A genuine feedback on the performance of students is also an important and essential part of assessment.The quality of a test should not be measured by reliability and validity in the traditional sense but reliability and validity should be measured in the light of the above principles (De Lange, 1999, p.10). According to the Australian association of mathematics teachers, the learning of mathematics should be measured under the following guidelines.Practices of assessing mathematical learning should be appropriate Assessments should match the purposes for which they are conducted, i.e. either the assessment is for learning opportunities (formative) which should be conducted on a regular basis or it is an assessment of learning (summative), which should be conducted on key stages of schooling.Assessments should encompass the full range of learning objectives. Use of different strategies (written reports, group presentations, teachers’ observations etc.) should be adopted to ensure this task.Assessment should match the published national curriculum.Assessment should be consistent with the educational objectives and aims of mathematicseducation (The AAMT, 2008).Assessment should be fair and inclusive Students should be fully aware of the nature of tasks and criteria for grading their performances.Assessment should be inclusive on the basis of gender or culture, and it should consist of a variety of tasks that gives students the opportunity to disclosetheir level of achievement of learning. Moreover,assessment should be conducted in a way that its processes become clear and transparent to students.Assessment should be done with planned means (assessment rubrics, marking schemes etc.) to reduce the chances of subjective judgments.It should be ensured that students at school level mathematics assessment should be familiar with what (genres of items) might be expected of them (The AAMT, 2008).Assessment should inform learning and action Teachers should give genuine feedback to students on the information gathered through assessment about their learning and use it to improve their future instruction.Teachers should provide constructive feedback to students and their parents so that they can improve their performance.Teachers should view the assessment of students as a single event performed at a particular time only (The AAMT, 2008).2.12.3 Types of Assessment There are three types of assessments: diagnostic, formative and summative (Hanna & Dettmer, 2004).2.12.3.1 Diagnostic AssessmentDiagnostic assessment helps the teacher to identify the current level of skills and concepts of students, which in turn helps the teacher plan future teaching keeping in view the strengths and weaknesses of the students.Types of Diagnostic AssessmentsSmall-scale written/oral pre-test.Oral questioning prior to start instruction.Brief interviews before starting class.2.12.3.2 Formative Assessment It is known as assessment for learning; it is an ongoing assessment of students during the instructional process. Formative assessment also provides feedback to teachers about the usefulness of instruction and guides the teacher to improve instruction by highlighting students’ misconceptions. It helps us improve our teaching by providing feedback day by day throughout the year (Hanna & Dettmer, 2004).Types of Formative Assessments: Observation of students’ work during the lesson.Unstructured questioning during class.Blackboard presentations.Inspection of students’ written home-work.Small-scale written test during instruction.Listening to students2.12.3.3 Summative Assessment It is known as assessment of learning; it takes place at the end of a formal teaching and learning program. It provides information and feedback about the overall effectiveness of the instructional program. Usually it takes place biannually or at the end of an academic year (Hanna & Dettmer, 2004).Types of Summative Assessment: Terminal examinations (monthly, quarterly, half-yearly etc.)Annual examinationsSTRUCTURE OF SCHOOL EDUCATION IN PAKISTAN There are two major systems of formal school education in Pakistan (NEP, 2008). Majority of the students attend the national SSC (matriculation) system of education. The GCE system of education is also available and is expanding rapidly. The structure of school education (SSC) in Pakistan consists of the following stages.Table 3: Stages of Matriculation system of school educationPre-School(3-5 years)Playgroup - Nursery- KGPrimary School(6-10 years)Class I – VMiddle School(11-13 years)Class VI – VIIIHigh School(14-15 years)Class IX (SSC part I)+Class X (SSC part II)= (Matriculation)(ASER, 2012)2.13.1 Secondary School Certificate (SSC) Education High school education in Pakistan is comprised of grade IX (SSC: part-I) and grade X (SSC: part-II). The courseincludes a combination of eight subjects including optionals (such as Biology, Chemistry, Computer Science, Physics, Economics, Geography, Civics, Education etc.) as well as compulsory subjects (such as Mathematics, English, Urdu, Islamiyat and Pakistani Studies). The subjects are selected in two groups, Science Group or General Group. In Science Group students have only one choice; either they have to select biology or computer science. Chemistry, physics and mathematics are compulsory science subjects. In General Group, students have to select four optional subjects from the humanities group of subjects. There are two boards of examinations for SSC, one is the local board and the other is federal board. There is a difference in the schemes of assessments in local boards and the Federal Board of Secondary Education. In Karachi, a third emination board, Agha Khan University Board of Secondary Education is also available. The examination and assessment pattern of this board is remarkably different from other boards. 2.13.1.1 Board of Secondary Education Karachi (BSEK) The students appearing in SSC Part-I (Science Group) under this board have to take five exams/subjects (English, Pakistan Studies, Sindhi, Chemistry and Biology/ Computer Science).In Part-II, they take English, Islamiyat, Urdu, Mathematics and Physics.General Group candidates take English, Pakistan Studies, Sindhi, General Mathematics and an optional subject from humanities group in SSC Part-I. English, Urdu, Islamiyat and two optional subjects are taken in Part-II.2.13.1.2 Federal Board of Secondary Education This board is available to candidates all over Pakistan and even from UAE and Saudi Arabia. This board, like other boards of the Punjab Province, takes examinations of all the subjects at both grade IX and grade X levels. The contents of each subject have been divided into two equal parts and students are assessed for first part of each subject in grade IX and for the second part in grade X.2.13.2 Mathematics Education in SSC System Mathematics is a compulsory school subject in SSC system. India (Rani, 2008; Sharan, 2008), China (Li, 2008; Fan, 2004), Singapore (Soh, 2008) and Japan (Yoshikawa, 2008) are the countries in the region where mathematics is the focal point of school curriculum. Unfortunately this subject has not yet attained the required attention of the concerned educational authorities in Pakistan.Under Board of Secondary Education Karachi (BSEK), the students of SSC Part-I (General Group) have to take a compulsory paper of General Mathematics of 100 marks whereas the students of Science Group do not take any mathematics paper in SSC Part-I. Science Group students take their mathematics paper of 100 marks in SSC Part-II. The same book is used by students in both groups with some topics deleted for general group. Candidates appearing under Federal Board of Secondary Education take two papers, one paper in SSC part-I(75 marks) and the other in part-II(75 marks).2.13.3 Mathematics Education in GCE System GCE mathematics is a compulsory course to be taken for all students of this system. It consists of two papers, paper-I(80 marks) in which use of calculator is not allowed and a paper-II (100 marks) in which scientific calculators are allowed. A very special attention is given to this subject in this system. The focus of teaching in this system remains on the application of mathematics in practical situations. The students generally take examination of mathematics in May/June but they can also appear in October/November for the improvement of grade if they want. Cambrige International Examination (CIE) is the board that takes the examination with the help of British Council Pakistan.Table 4: Stages of Cambridge system of school educationCambridge Primary(5-11 years)Cambridge PrimaryCambridge Primary CheckpointCambridge ICT StartersCambridge Secondary 1(11-14 years)Cambridge Secondary 1Cambridge CheckpointCambridge ICT StartersCambridge Secondary 2(14-16 years)Cambridge IGCSECambridge O LevelCambridge ICECambridge Advanced(16-19 years)Cambridge International AS and A LevelsCambridge AICECambridge Pre–U()2.13.3.1 GCE (O-Level) GCE (O-Level) examination is an international school-leaving certificate. It is an international qualification equivalent to the UK’s General Certificate of Secondary Education (GCSE). The GCE (O-Level) has been replaced by (GCSE) in U.K since 1986 but still it is widely taken all over the world, especially in the countries that were formerly British colonies including Pakistan (Umbreen, 2008). The GCE (O-Level) curriculum is a comprehensive and balanced study program witha wide range of subjects as a course of study. The curriculum targets the development of creative thinking, enquiry and problem solving skills of the learners and is organized in sucha way that students attain both functionaland theoretical knowledge and skills (CIE, 2008). Candidates have to select their subjects of study from a wide range of options. A candidate may take as many subjects as he/she wants to take depending on the availability and qualification of staff for different subjects in the institution where the candidate is studying. In Pakistan a candidate has to take 5 compulsory subjects: Mathematics, English Language, Urdu Language, Pakistan Studies and Islamiyat. Apart from these compulsory subjects, candidates have to select 4 optional subjects. Different institutions provide this option in different ways to students according to their available resources and faculty qualifications. Usually institutions offer subjects in groups of four such as Commerce group, Business Studies group or Science group. For example, in science group, a candidate has to take Physics, Chemistry, and Biology but for the fourth subject an option is given to select a subject such as Additional Mathematics/English Literature etc. Those students, who want to take more subjects than those offered by the institution, can take them privately. Generally, candidates take their O-Level examinations for 2 subjects, Islamiyat and Pakistan Studies, in grade-10 (age 15+). The other 7 subjects are taken in grade-11(age 16+).There are two sessions for O-Level examination in a year: May/June and October/November. Results are given out in August and February respectively (). Grade A* (A-star) is allotted on highest performance in O-Level, and grade E is allotted to a minimum satisfactory performance. The British Council is an international organization of U.K for educational and cultural relations with other countries. The GCE (O-Level) examinations in Pakistan are organized and supervised by the British Council in Pakistan.2.13.3.2 General Certificate of Secondary Education GCSE GCSE is a British certificate of education for secondary school students of an age of fifteen-sixteen in UK, Wales and Northern Ireland. In 1986, the GCE (O-Level) and CSE were replaced by General Certificate of Secondary Education (GCSE) in UK. GCSE emphasizes more on course-work and places less emphasis on final (summative) assessments ().2.13.3.3 International General Certificate of Secondary Education (IGCSE) IGCSE was developed by CIE formerly called UCIE in 1985 for candidates outside the United Kingdom. The examination board Edexcel has also developed its own version of ‘Edexcel IGCSE’ since 2009. IGCSE is not a certificate of education that usually comprises of a combination of some subjects. It is a program based on distinct subjects of study, i.e. a candidate of IGCSE can get this qualification in just one subject or as many subjects as he/she can. For this reason, students of the same school take different number of IGCSE papers from all over the world. IGCSE is primarily exam-based, it resembles GCE (O-Level) rather than GCSE. The IGCSEgrades are from A* to G with a grade "U" (Ungraded). The “U” grade is equivalent to “Failed” in SSC system. A* grade was not awarded before 1994. GCSE added this grade to recognize the very top end of achievement ().2.13.3.4 Cambridge International Certificate of Education (ICE) Cambridge ICE is the group award of the International General Certificate of Secondary Education (IGCSE). To get an ICE, a candidate has to pass at least seven subjects, selecting from five different groups of subjects. These groups are comprised of a wide range of subjects from different curriculum areas. These groups are:Group I: LanguagesGroup II: Humanities and Social SciencesGroup III: SciencesGroup IV: MathematicsGroup V: Creative, Technical and Vocational The candidate has to select two languages from group I (First language, Second language), one subject each from group II, III, IV and V. The seventh subject may be selected from any group().2.13.4 Examination BoardsThere are mainly two examination boards which conduct O-Level examinations in Pakistan ().Cambrige International Examinations (CIE)Edexcel Cambridge International Examinations (CIE) UCLES is a department of University of Cambridge and Cambridge International Examination (CIE) is a part of UCLES. CIE is the largest assessment agency of Europe and is a part of Cambridge Assessment. It is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES) which is a non-teaching department of the University of Cambridge and a nonprofit organization. CIE is responsible for setting and assessing a large number of examinations within the United Kingdom and on international level (). It was established in 1998 to provide internationally recognized qualifications to meet the needs of modern world of employment and education. CIE qualifications are accepted and recognized all over the world (Brophy, 1999). In Pakistan, O-Level examinations are conducted by UCLES and the process of designing the question papers and the assessment is done by CIE. CIE operate in 160 countries across 6 regions: America, Asia Pacific, Europe, the Middle East and North Africa, South Asia, and Southern Africa. In some countries, such as Singapore, Cambridge examinations are the state qualification for students in secondary school. In other parts of the world, such as Botswana, Namibia and Swaziland, it works with governments to reform education systems and helps to localize examinations by training officials, teachers, markers and examiners in curriculum development and assessment ().Edexcel Edexcel is another board of examinationfor O-level and A-Level. It was formed in 1996 by the merging two boards of examinations i.e. BTEC and ULEAC. The Business and Technology Education Council (BTEC) was the board of examination for vocational qualifications and the University of London Examination and Assessment Council (ULEAC) was one of the major examination boards in UK. Edexcel International examinations provide qualifications at the level of GCE (O-Level and A-Level) and had started an International General Certificate of Secondary Education (IGCSE), available outside UK, since 2009().?2.14 GCE (O-Level) MATHEMATICS (CIE)2.14.1 Mathematics (Syllabus D) (4024/4029) Mathematics is a compulsory subject at GCE (O-Level), IGCSE and ICE levels. The GCE (O-Level) Mathematics is called Syllabus D, and has the syllabus code 4024/4029. The syllabus code 4029 is specific only for Mauritius. The course 4024 is examined in both May/June and October/November sessions while 4029 is examined in October/November session only. The aims of mathematics syllabus‘D’ according to Cambridge International Examinations (CIE) are to arouse intellectual curiosity, develop mathematical knowledge and skills for utilitarian value, appreciation and for further studies. Development of mathematical language for verbal and symbolic communication and emphasis on problem-solving skill and efficient use of calculators in computation are some other salient features of this syllabus (CIE, 2008). GCE mathematics consists of two papers, containing questions on any part of the syllabus. Moreover, questions are not essentially limited to a single topic. Paper 1 contains approximately 25 short answer questions. All questions needs to be attemted without using calculators. Paper 2 has structured questions across two sections. Section A contains approximately six to seven questions without any choice. Section B contains five questions from which four questions have to be attempted, giving students a choice one question (CIE, 2013).2.14.2 Additional Mathematics (4037) This course is planned for those students who are good at mathematics and want to take up mathematics in their higher studies. The O-Level Additional Mathematics syllabus enables them to extend their mathematical skills, knowledge and understanding. The syllabus contains most of the contents on Pure Mathematics which enables learners to acquire a suitable foundation for further study in mathematics().2.14.3 IGCSE Mathematics Cambridge IGCSE Mathematics provides two options; either to select syllabus codes 0580 (without coursework) or 0581 (with coursework). In both courses, there are two further choices of Mathematics (core) or Mathematics (extended). In mathematics (core) grades are awarded from C-G whereas in extended mathematics, grades are from A*-E. All the papers in IGCSE have no choice of questions and the use of calculators is allowed ().2.14.3.1 IGCSE Mathematics (0580-without coursework)Mathematics (core) Students have to take two papers in mathematics (core): paper 1 and paper 3. Paper 1 contains short questions with a time limit of 1 hour. Paper 3 consists of structured questions to be done within 2 hours. Mathematics (extended)Mathematics (extended) consists of paper 2 and paper 4. Time duration for paper 2 is 1.5 hours and 2.5 hoursfor paper 4 (CIE, 2013).2.14.3.2 IGCSE Mathematics (0580-with coursework)Mathematics (core)This includes three papers: paper 1, paper 3 and paper 5 in which the first two papers are same except for their weightage of marks. Paper 5 is coursework that carries a weightage of 20%. The first two papers are weighted as 30% and 50% respectively.Mathematics (extended)This includes three papers in it as well: paper 2, paper 4 and paper 6 (coursework). The weightage of marks is 30%, 50% and 20% respectively (CIE, 2013).2.15 DFFERENCE IN CONTENTS AND ASSESSMENT BETWEEN GCE & IGCSE MATHEMATICS COURSESFor IGCSE mathematics, candidates have an option of doing coursework if they want whereas for O-Level mathematics there is no coursework. IGCSE mathematics has two options: core /extended. In Core grades C to G and in Extended grade A* to E are awarded respectively. GCE (O-Level) has grades from A* to E. In O-Level mathematics paper 1, calculators are not allowed whereas in IGCSE mathematics, calculators are allowed in both papers. The total time duration for both papers is 4.5 hours for O-Level mathematics whereas it is 3 hours for IGCSE mathematics (core) and 4 hours for IGCSE mathematics (extended). There is no choice in questions in IGCSE mathematics, while in O-Level mathematics; there is a choice of 1 question in section B of Paper 2 ().2.16 AN OVERVIEW OF MATHEMATICS EDUCATION IN ASIAN COUNTRIESThe results of some international studies conducted during the last 20 years show some interesting results. TIMSS is an international study to assess the knowledge in mathematics and science of fourth and eighth grade students from all over the world. Singapore, China, Japan, Korea, Taiwan and Hong Kong are among those Asian countries that have been attaining top positions in international studies on students’ achievement in mathematics and science. The outstanding performance of these countries in mathematics is the success of their education systems. Therefore, it is worthwhileto analyze the ways mathematics is taught in these countries. A number of international research studies have been conducted to study the education systems of these countries. A review of these studies is presented to find some of the common characteristics of the way mathematics is taught in these countries.2.16.1 Singapore Singaporean students of 8th grade got first positions in mathematics in the first three consecutive studies held during 1995, 1999 and 2003 respectively. Their position in the fourth study (2007) was third and they have achieved second position in the fifth study (2011). In the 4th grade category, Singapore stood first in the 1995 and 2003 studies (TIMSS, 1995, 1999, 2003, 2007 and 2011). Program for International Students Assessment (PISA) is another international study conducted by the Organization for Economic Co-operation and Development (OECD) that evaluates education systems throughout the world after every three years. Students of 15 years of age are assessed in key subjects: reading, mathematics and science. In PISA (2009) assessment out of 65 countries, Singapore again achieved second position in mathematics (PISA, 2009).Kaur (2004) reported that in 1997, before the start of 21st century, Singaporeans’ announced their vision to face the challenges of the new century. The vision consisted of four words: “Thinking Schools, Learning Nation”. Hence, they launched a thinking program in all schools. The aim of this program was to ensure that the young generation can think to find solutions of their problems especially the new problems they will face in the 21st century. Thinking Program was to teach these eight thinking skills embedded in mathematics which is a core subject in both elementary and secondary level in Singapore.Collection of Facts, Remembering, Concentrating, Organizing, Analyzing, Evaluating, Creating, and Assimilating. (Kaur, 2004) The primary goal of Singaporean school mathematics curriculum is the intelligent and creative use of mathematics as a means for problem solving (Soh, 2008). The attainment of this mathematical ability depends on five inter-related components: concepts, skills, processes, attitudes and metacognition (Ministry of Education Singapore, 2007). The most common approach (Stacey, 2005; Lesh & Zawojewski, 2007) used by the Singaporean teachers is: learning the routine contents thoroughly, formulating strategies for problem solving and finally applying these strategies with the development of useful metacognitive skills. Ginsburg et al., (2005), in an exploratory study conducted by American Institute of Research, titled, “What the United States can Learn from Singapore’s World-Class Mathematics System”, admitted that Singaporean students are more capable than the US in mathematics. The study pointed out that the following components of Singapore mathematics education make it superior to the US mathematics education.Highly logical national mathematics frameworkHigh quality problem-based mathematics textbooksStrong assessment systemHighly qualified and trained teachersAlternative framework for weak student The study identified the weaknesses in the U.S. mathematics program and indicated that US students never go much beyond learning the mechanics of applying definitions and formulas to routine, simple, one-step problems. It was concluded with the recommendation that United States needs in overall, the sound features of the Singapore mathematics system.2.16.2 China Li (2008) reported that after the establishment of Peoples Republic of China in 1949, the Soviet Union model of education was imported and all school textbooks were adapted from them. In 1952, within three years, a national unified textbook policy was adopted. After 1958, Chinese curriculum developers developed their own mathematics curriculum according to their own conditions. Although the influence of Soviet Union’s system remained in terms of characteristics like integrity, coherence, focus and rigor, China succeeded in developing an indigenous national system governed by ministry of education. Tu (2010) analyzed the system of mathematics education in China and highlighted the following guiding principles.Emphasis on ‘The Two Basics’ (Basic Knowledge and Basic Skills).Focus on development of mathematical thinking skills (Chinese take mathematics as aerobics of mind).Preservation of heuristic method of teaching proposed by Confucius (Not to intervene or answer until and unless the student have made an effort or have raised a question).Influence of Dewey’s theory (1910) ‘learning by doing’and Polya’s theory (1957) of ‘how to solve problems’ on Chinese mathematics teachers. The salient characteristics of Chinese Mathematics Education are its explicit learning objectives with four operational levels (knowing, understanding, grasping and active application). There is a famous Chinese proverb, “Insight comes out of familiarity”. Chinese believe that until they know something well, they cannot be able to innovate it. The meaning taken by this proverb in China is to apply the basic knowledge in problem solving and do rigorous practice. Similarly, it means to memorize and understand a piece of knowledge and practice basic skills until efficacy in application is achieved. By this they don’t mean to practice meaninglessly, in fact they believe in attaining understanding by analogy and comprehension through connections (Tu & Shen, 2010; Zhang et al., 2004). Lim (2007) studied the characteristics of mathematics teaching in China and summarized them as follows.Variation in teaching (use of different kinds of examples).Revision of previous work before starting new lessonSummarization of the taught concepts at the end of each lesson.Regular homeworkSerious and orderly discipline in classesStrict format of writing (precise and unambiguous language).Use of ICT such as Power Point and multimedia presentations.A close teacher-student relationship (encouraging in nature).2.16.3 Japan Yoshikawa (2008) reported that Japan, after implementing new curriculum in 2002, reduced the contents so that the topics can be studied in depth. The four elements in their objectives of teaching mathematics are: knowledge, skills, ability to think mathematically and interests in mathematics, willingness to learn mathematics and attitudes towards mathematics. Mastrull (2002) studied the Japanese system of mathematics education in comparison with United States. She examined the reasons for outstanding performance of Japanese students in mathematics and viewed the following features accountablefor the superiority of Japanese students over US students.Japanese parents especially mothers take in part in the education of their children.Japan has a nationally standardized school curriculum and textbooks.Mathematics is given a special status in the school curriculum and classes of mathematics are normally held during first periods of the day.Teachers usually adopt problem-solving approach and involve students in group work.A normal Japanese mathematics class starts with the review of previous work and ends with a summarization of key points by the teacher.Regular home assignments and their assessment by the teacher in class.Preference to mental calculation by both teachers and parents. Therefore the use of calculators in elementary level is prohibited and a minimum use at secondary level. Skiba (2001) stated that the Japanese parents give every first grader student a math set wrapped in a beautiful way like wedding gifts. The gift includes mathematical instruments and stationery that the student needs during his/her primary mathematics education. Teachers enjoy a high social status in Japanese society. They have a higher number of periods per week than the teachers in the United States yet they are more committed andpersuaded. Professional development of teachers is extremely important in Japan. The economic status of teachers in Japan is also very impressive. In addition to salary, they are rewarded with a variety of allowances including living allowance, housing allowance and traveling allowance, as well as three bonuses in a year. There are some common characteristics among the education systems of these Asian countries: a centralized national system, extraordinary emphasis on mathematics education (Becker et al., 1990), equal focus on the process of doing mathematics (problem solving) and learning the contents of mathematics using both intrinsic and extrinsic motivation of students (Leung, 2004; Zhang et al., 2004). A substantial attention on teacher’s training and provision of facilities for them is another important common factor. The reviewed literatureportrays a broader picture of mathematics education in the school curriculum. Firstly, it exhibits the significance of mathematics teaching on philosophical grounds, its expected aims and objectives; principles of the content selection and assessment. Secondly, on an operational level, it reveals the educational objectives of mathematics within cognitive, affective and psychomotor domains; approaches of selection and organization of the contents; approaches and methods of teaching assessment. Thirdly, the literature presents the overall structure of SSC and GCE systems of education with a focus on the mechanism of mathematics education. Lastly, the literature displays the key features of mathematics education of those countries whose students are performingoutstandingly in the international studies conductedduring the last twenty years. The overall literature review provides a strong foundation to compare and analyze the effectiveness of the mathematics curriculum taught at SSC and GCE systems of education in Karachi, Pakistan. CHAPTER THREERESEARCH METHODOLOGY The majorobjective of this study was to analyze the effectiveness of mathematics curriculum taught at General Certificate of Education GCE (O- Level) and SSC system of schools in Karachi by comparing the objectives of teaching, course contents, methods of teaching and the assessment patterns in the two systems.The study is descriptive in nature in which mixed method approach of research has been applied. The survey method was used to collect data from a randomly selected sample. Questionnaires were used to collect data from teachers and students of both the systems. The data from subject experts were collected through semi-structured interviews. A criterion of minimum 15 years of experience in teaching mathematics was developed for the subject experts of both systems. RESEARCH STRATEGYThe research was aimed to make a comparative study of the Secondary SchoolCertificate (SSC) and the General Certificate of Education GCE (O-level), Mathematics Course in Karachi. The strategy of research was a mixed research approach. POPULATIONThe population of the study was comprised of teachers, students and prescribed text books of mathematics taught at 5812 (public/private) secondary schools (Board of Secondary Education Karachi, 2012) registered in the SSC systemand 130 schools (The British Council, 2012)registered in the GCE (O-Level) system. The question papers of previous yearsof both SSC (Board of Secondary Education Karachi / BSEK) and O-Level (Cambridge International Examination / CIE) mathematics course were also part of the population.SAMPLE Sudman (1976) suggested that a minimum of 100 elements is needed for each major group or subgroup in the sample and for each minor subgroup, a sample of 20 to 50 elements is necessary. The overall sample size in this study was of 300 teachers, 200 students and 20 subject experts. Karachi city is administratively divided into five districts (District South, District East, District Central, District West and District Malir). Numbers of schools in each district were not evenly distributed. The density of GCE (O-Level) schools in the District South was much higher than the other districts. On the other hand District West and District Malir had a much lower number of GCE (O-Level) schools. To get a fair representation from each district in the sample, stratified random sampling design along with purposive sampling design was adopted. There were 432 registered institutions, offering GCE (O-Level) in Pakistan, out of which 130 were located in Karachi (The British Council, 2012).3.3.1 Sample of Schools (SSC / GCE)A detailed summary of SSC and GCE schools in the sample from each district of Karachi is presented in the following table.Table 5: Number of schools (SSC/GCE) in the sample from each district of KarachiDistrictsSchools (SSC)Schools (GCE)TotalSouth6040100East502070Central501060West100010Malir100010Total180702503.3.2 Sample of Teachers (SSC / GCE)A detailed summary of SSC and GCE teachers in the sample from each district of Karachi is presented in the following table.Table 6: Teachers (SSC/GCE) in the Sample from each District of KarachiDistrictsTeachers (SSC)Teachers (GCE)TotalMaleFemaleMaleFemaleSouth38224530135East3020251388Central3020050257West0604000010Malir0604000010Total1107075453003.3.3 Sample of Students (SSC / GCE)A detailed summary of SSC and GCE students in the sample from each district of Karachi is presented in the following table.Table 7: Students (SSC/GCE) in the sample from each district of KarachiDistrictsStudents (SSC)Students (GCE)TotalMaleFemaleMaleFemaleSouth2515252085East2015151060Central1510050535West0505000010Malir0505000010Total705045352003.3.4 Sample of Subject Experts (SSC / GCE)A detailed summary of SSC and GCE subject experts in the sample from each district of Karachi is presented in the following table.Table 8: Subject experts (SSC/GCE) in the sample from each district of KarachiDistrictsExperts (SSC)Experts (GCE)TotalMaleFemaleMaleFemaleSouth0301050110East0201020106Central0101010003West0000000000Malir0100000001Total07030802203.4 RESEARCH INSTRUMENTSQuestionnaires were developed on the basis of objectives of study in the light of related literature and the works of previous researchers (Kiyani (2002, p.291; Naeemullah, 2007, p.175; Umbreen 2008, p.185 &Naeem, 2011, p.226). A questionnaire comprising of 100 items was used to collect data from teachers of both the systems (Appendix I). The data from students were collected through a questionnaire containing 80 items (Appendix II). An Interview Protocol containing 14 open-ended items was designed and administered from the Subject Experts of both the systems (Appendix III).3.4.1 Pilot Study A small sample of 14 teachers and 14 students was drawn from the actual sample of the study for pilot testing. Questionnaires developed for teachers were first distributed among 14 teachers, 7 questionnaires were given to the teachers of SSC system and 7 were given to the teachers of GCE system. Similarly questionnaires developed for the students were distributed among 14 students, taking 7 students from each system. The researcher approached each respondent in person and requested them to enquire about whatever confusion they had in responding to any item of the questionnaire. The respondents made some queries about different items. The researcher took the opinion of the respondents to make those items more clear. The items of the questionnaires were reexamined on the basis of the opinions of the respondents. Items that were enquired about due to the use of certain terminology or difficult words were changed and items were reconstructed using simple terminologies and words.The collected data were then analyzed for a measure of the linear correlation(dependence) between two variables through Pearson product-moment correlation coefficient (sometimes referred to as the PPMCC or PCC or Pearson's ‘r’).The value of Pearson’s ‘r’ found is given below.Teachers’ Questionnaire = 0.834 (Appendix IV)Students’ Questionnaire = 0.763 (Appendix IV)3.5 DATA COLLECTION The prime objective of this study was the comparative analysis of the effectiveness of mathematics curriculum of SSC and GCE. Data were collected through questionnaires to get the views of teachers on objectives of teaching, course contents, approaches/methods of teaching and their stances on prevailing assessment patterns of both the systems. The views of teachers were supplemented by administering an interview protocol for the subject experts of both the systems. Information on students’ outlook about mathematics, their attitude towards the contents of textbooks, their learning and assessment experiences being studied in two different systems were obtained by another questionnaire. Besides data collection through questionnaires, the content analysis of both curricula was conducted. For this, data were collected from the published records available as well as through internet resources. To compare the patterns of assessment, a comparison of annual papers of the last 20 years (1994-2013) of both SSC and GCE was done. For this purpose published materials as well as internet resources were used. After collecting data for the pilot study, data collection was started in February, 2013. The session of SSC was ending and students of grade X (SSC), after undergoing their mathematics curriculum, were ready to appear for their annual examination. These students could answer questions better than those students who had not completed their course of study. Therefore, data from SSC students and teachers were collected first. After this, data from GCE teachers and students were collected before the end of their academic session. Finally, interviews from subject experts were conducted. The whole process of data collection took 4 months and was completed in May, 2013.3.5.1 Ethical ConsiderationThe participants were well informed about the research study. There consent was taken by informing them about the nature of the study. It was confirmed that the data will be kept confidential.To avoid disclosure of personal information, names of the participants are not displayed with the data collected from them. 3.6 DATA ANALYSISAfter the collection of data, it was tabulated, analyzed and interpreted in the light of the objectives of the study and research questions using the t-test. The questionnaires developed for teachers and students were analyzed at five-point rating scale:(i) Strongly Agree (ii) Agree (iii) Undecided (iv) Disagree (v) Strongly Disagree. The items designed for the interview of the subject experts were all open ended. The responses of experts were summarized in the tables mentioning the frequency of the respondents against each response. The suggestions from the experts were also included in conclusions and recommendations. The content analysis of the text books and question papers of GCE and SSC was made.Finally, conclusions were drawn and recommendations were made on the basis of analyzed responses of teachers, students, experts and in the light of content analysis.3.7 DELIMITATION OF THE STUDY Due to limited time and resources available to the researcher, the study was delimited to the responses of teachers and students of grade X only from SSC system and grade XI (O-Level) only from GCE system.CHAPTER FOURDATA ANALYSISThe specific objective of this study was to compare the mathematics curriculum of the SSC (Matriculation) and GCE (O-Level) in order to find the differences in terms of strengths and weaknesses of educational objectives, contents of the textbooks, approaches of teaching, methods of teaching and assessment systems so that the effectiveness of key factors involved in these courses can be determined. The analysis of data collected through research instruments is presented in the following pages.This chapter is divided into following three sections.SECTION I: COMPOSITION OF THE SAMPLESECTION II: ITEM BY ITEM ANALYSIS OF THE DATAAnalysis of the responses of teachersAnalysis of the responses of studentsAnalysis of the responses of subject expertsSECTION III: CONTENT ANALYSIS4.4Analysis of the contents of textbooks and question papersSECTION I: COMPOSITION OF THE SAMPLETable 9 shows details of particulars about the teachers in the sample.Table 9: Particulars about the teachersDetailsFrequencySSCGCEGenderMale (110)Female (70)Male (75)Female (45)Marital StatusMarried (88)Unmarried (92)Married (80)Unmarried (40)AgeLess than 30 years (74)30 to 34 years (40)35 to 39 years (18)40 to 44 years (18)45 to 49 years (12)50 years or above (18)Less than 30 years (36)30 to 34 years (38)35 to 39 years (24)40 to 44 years (10)45 to 49 years (6)50 years or above (6)AcademicQualificationsB.Sc. (38)B.A / / B.E (40)M.Sc. (62)M.A / M.B.A (40)B.Sc. (22)B.A / / B.E (16)M.Sc. (70)M.A / M.B.A (12)Professional QualificationsPTC (2), C.T (2)B.Ed. (42), M.Ed. (10)Other Short Courses (4)B.Ed. (14)M.Ed. (8)PGCC (16)ExperienceLess than 5 years (70)5 to 9 years (50)10 to 14 years (26)15 to 19 years (10)20 years or above (24)Less than 5 years (44)5 to 9 years (32)10 to 14 years (26)15 to 19 years (12)20 years or above (6)Control ofInstitutionPrivate / GovernmentPrivate (165)Government (15)Private (120)Government (0)(Contd…….)Monthly IncomeLess than 40 thousands (147)40 to 60 thousands (23)60 to 80 thousands (0)80 to 100 thousands (1)100 thousands plus (2)Did not mention (7)Less than 40 thousands (64)40 to 60 thousands (32)60 to 80 thousands (8)80 to 100 thousands (2)100 thousands plus (10)Did not mention (4)Table 10: Particulars about the studentsDetailsFrequencySSCGCEGenderMale (70)Female (50)Male (45)Female (35)GradeX (120)(Matriculation)XI (80)(O-Level-Final year)Age14 years (11)15 years (25)16 years (68)17 years (16)15 years (13)16 years (45)17 years (16)18 years (6)Qualification of FatherGraduate (75)Undergraduate (39)Did not mention (6)Graduate (69)Undergraduate (7)Did not mention (4)Qualification of MotherGraduate (44)Undergraduate (70)Did not mention (6)Graduate (54)Undergraduate (22)Did not mention (4)Table 11: Particulars about the subject expertsDetailsFrequencySSCGCEGenderMale (7)Female (3)Male (8)Female (2)DesignationsH.M (3)HOD (4)Senior Teachers (3)H.M (0)HOD (4)Senior Teachers (6)AcademicQualificationsB.Sc. (2)M.Sc. (8)B.Sc. (1)M.Sc. (9)Professional QualificationsB.Ed. (3)M.Ed. (6)Nil (1)B.Ed. (4)M.Ed. (1) PGCC (2), Nil (3)Experience(in years)15-20 (2)21-25 (2)26-30 (3)31-35 (2)36-40 (0)41-45 (1)15-20 (7)21-25 (2)26-30 (0)31-35 (1)Control of InstitutionPrivate / GovernmentPrivate (9)Government (1)Private (10)Government (0)SECTION II: ITEM BY ITEM ANALYSIS OF DATA4.1 ANALYSIS OF THE RESPONSES OF TEACHERS Table 12: Mathematics is one of themost important subjects in the school curriculumH0:There will be no significant difference between SSC and GCE teachers on the statement that mathematics is one of themost important subjects in the school curriculumRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1 = 4.500.7360.0870.345GCE(O-Level)120x2 = 4.470.766df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table ‘12’we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.345. Hence H0 is accepted, which leads us to the conclusion that there is no significant difference between SSC and GCE system of schools on the statement that mathematics is one of the most important subjects in the school curriculum.Table 13(a): Comparison of the reasons for giving importance to mathematics ReasonsH0:There will be no significant difference between the reasons of SSC and GCE teachers for giving importance to mathematics1. It is largely applied in practical lifeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.610.6480.0822.804GCE(O-Level)120x2= 4.380.738(Contd…….)2.It is largely applied in other subjectsSSC(Matriculation)180x1 = 4.300.8410.0831.325GCE(O-Level)120x2=4.410.5913.It develops power of intellect SSC(Matriculation)180x1 = 4.470.6210.0710.282GCE(O-Level)120x2=4.450.5944.It develops desirable habitsSSC(Matriculation)180x1 = 3.630.9760.1110.631GCE(O-Level)120x2=3.700.9075.It develops desirable attitudesSSC(Matriculation)180x1 = 3.481.0190.1180.593GCE(O-Level)120x2= 3.550.998df =298 tabulated ‘t’ value at 0.05 = 1.960ConclusionsIt is largely applied in practical life Referring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.804. Hence,H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the reason that mathematics is important at school level due to its practical application.It is largely applied in other subjectsReferring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 1.325. Hence,H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding the reason that mathematics is important at school level due to its application in other subjects.It develops the power of intellectReferring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 0.282. Hence,H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding the reason that mathematics is important at school level as it develops intellectual powers.It develops desirable habitsReferring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 0.631. Hence,H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding the reason that mathematics is important at school level as it develops desirable habits among students.It develops the desirable attitudesReferring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 0.593. Hence,H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding the reason that mathematics is important at school level as it develops desirable attitudes among students.13(b): Graph 1*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 14: The aim of mathematics education is to train or discipline the mindH0:There will be no significant difference between SSC and GCE teachers on the statement that the aim of mathematics education is to train or discipline the mindRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=4.200.8350.0971.546GCE(O-Level)120x2=4.050.852df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 14, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.546. Hence,H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding the statement that the aim of mathematics education is to train the mind.Table 15: The aim of mathematics education is to transfer knowledge for its application in real lifeH0:There will be no significant difference between SSC and GCE teachers on the statement that the aim of mathematics education is to transfer knowledge for its application in real lifeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=4.330.8610.0910.549GCE(O-Level)120x2=4.380.715df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 15, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.549. Hence,H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the aim of mathematics education is to transfer knowledge for its application in real life.Table 16: The aim of mathematics education is to develop problem solving skillsH0:There will be no significant difference between SSC and GCE teachers regarding the statement that the aim of mathematics education is to develop problem solving skillsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=4.350.8110.0811.975GCE(O-Level)120x2=4.510.596df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 16, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 1.975. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themregarding the statement that development of problem solving skills is the aim of mathematics education.Table 17: The aims of mathematics education are convincingH0:There will be no significant difference between SSC and GCE teachers on the statement that the aims of mathematics education are convincingRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.371.1760.1125.982GCE(O-Level)120x2=4.040.768df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 17, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.982. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that aims of mathematics education are convincing.Table 18: The aims of mathematics education are achievableH0:There will be no significant difference between SSC and GCE teachers on the statement that the aims of mathematics education are achievableRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=4.020.9350.1060.283GCE(O-Level)120x2=4.050.890df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 18, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.283. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that aims of mathematics education are achievable.Table 19: The aims of mathematics education can be translated into small objectivesH0:There will be no significant difference between SSC and GCE teachers on the statement that the aims of mathematics education can be translated into small objectivesRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.740.8150.0970.618GCE(O-Level)120x2=3.800.839df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 19, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.618. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that the aims of mathematics education can be translated into small objectives.Table 20: The objectives of current curriculum are derived from real aims of mathematics educationH0:There will be no significant difference between SSC and GCE teachers on the statement that objectives of current curriculum are derived from actual aimsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.820.9940.1091.848GCE(O-Level)120x2=3.580.892df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 20, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.848. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them in their beliefs that the objectives of current curriculum are derived from actual aims.Table 21: The objectives of mathematics education are well definedH0:There will be no significant difference in the opinions of SSC and GCE teachers that objectives of mathematics teaching are well definedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.730.9570.1051.428GCE(O-Level)120x2=3.880.861df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 21, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.428.Hence, H0 is accepted, which leads us to the conclusion that there is no significant difference in the opinions of SSC and GCE teachers that the objectives of teaching mathematics are well defined.Table 22: The objectives of mathematics education are clearly transmitted to teachersH0:There will be no significant difference between SSC and GCE teachers regarding the statement that objectives of mathematics education are clearly transmitted to teachersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.471.1100.1992.261GCE(O-Level)120x2=3.920.161df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 22, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 2.261. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themregarding the statement that objectives of mathematics education are clearly transmitted to teachers.Table 23: The current curriculum prepares students for practical lifeH0:There will be no significant difference between SSC and GCE teachers on the statement that the current curriculum prepares students for practical lifeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.841.1500.1102.363GCE(O-Level)120x2=4.100.764df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 23, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.363. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the current curriculum prepares students for practical life.Table 24: The curriculum prepares for future vocationsH0:There will be no significant difference between SSC and GCE teachers regarding the statement that curriculum prepares for future vocationsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.701.0380.0992.323GCE(O-Level)120x2=3.930.685df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 24, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.323. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that curriculum prepares for future vocations.Table 25: The focus of curriculum is on the needs of future educationH0:There will be no significant difference between SSC and GCE teachers for the statement that focus of the curriculum is on the needs of future educationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.681.0660.1043.846GCE(O-Level)120x2=4.080.748df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion: Referring to table 25, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.846. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them with respect to the statement that focus of the curriculum is on the needs of future education.Table 26: The curriculum is comparable with the curricula of other countries of the regionH0:There will be no significant difference between SSC and GCE teachers regarding the statement that the curriculum is comparable with the curricula of other countries of the regionRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.141.1760.1206.333GCE(O-Level)120x2=3.900.915df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion: Referring to table 26, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.333. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that the curriculum is comparable with the curricula of other countries of the region.Table 27: The curriculum is correlated with other subjectsH0:There will be no significant difference between SSC and GCE teachers regarding the statement that the curriculum is correlated with other subjectsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.680.9200.1022.843GCE(O-Level)120x2=3.970.843df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 27, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.843. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that the curriculum is correlated with other subjects.Table 28: The curriculum is flexibleH0:There will be no significant difference between SSC and GCE teachers in stating the current curriculum flexibleRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.511.0410.1033.981GCE(O-Level)120x2= 3.920.765df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 28, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.981. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them in stating the current curriculum flexible.Table 29: The curriculum reflects state-of-the-artH0:There will be no significant difference between SSC and GCE teachers regarding the statement that curriculum reflects state of the artRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.041.0370.1154.869GCE(O-Level)120x2= 3.600.942df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 29, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.869. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that curriculum reflects state-of-the-art.Table 30: The curriculum leads towards the set aims of mathematics educationH0:There will be no significant difference between SSC and GCE teachers on the statement that the curriculum leads towards the set aims of mathematics educationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.621.1370.1133.539GCE(O-Level)120x2= 4.020.813df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 30, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.539. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the curriculum leads towards the set aims of mathematics education.Table 31: Contents of the textbooks are properly sequencedH0:There will be no significant difference between SSC and GCE teachers on the statement that contents of the textbooks are properly sequencedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.661.0620.1121.250GCE(O-Level)120x2= 3.800.879df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 31, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.250. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that contents of the textbooks are properly sequenced.Table 32: Contents of the textbooks develop interest H0:There will be no significant difference between SSC and GCE teachers on the statement that contents develops interest in studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.551.0710.1150.608GCE(O-Level)120x2= 3.620.922df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 32, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.608. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that the content develops interest in students.Table 33: Contents incite the sense of enquiryH0:There will be no significant difference between SSC and GCE teachers on the statement that contents incite the sense of enquiryRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.361.1240.1103.090GCE(O-Level)120x2= 3.700.888df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 33, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.090. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that contents incite the sense of enquiry.Table 34: Language of the textbooks is simpleH0:There will be no significant difference between SSC and GCE teachers on the statement that language of the textbooks is simpleRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.900.9640.0931.720GCE(O-Level)120x2= 4.060.642df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 34, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.720. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that language of the textbooks is simple.Table 35: The contents coveran appropriate proportion of sums on application of abstract principles of mathematics in real life problemsH0:There will be no significant difference between SSC and GCE teachers on the statement that the contents cover application of abstract principles in real life problemsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.341.0920.1163.275GCE(O-Level)120x2= 3.720.922df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 35, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.275. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the contents cover application of abstract principles in real life problems.Table 36: Worked examples in the textbooks provide sufficient guidance to solve all the problems given for exercise on that topicH0:There will be no significant difference between SSC and GCE teachers on the statement that worked examples in the text books provide sufficient guidance to solve all the problems given for exercise on that topicRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.551.0610.1173.846GCE(O-Level)120x2= 4.000.938df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 36, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.846. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that worked examples in the text books provide sufficient guidance to solve all the problems given for exercise on that topic.Table 37(a): Comparison of the domains of intellect developed by contents of the textbooks Domains ofIntellectH0:There will be no significant difference between SSC and GCE teachers that contents of the textbooks develop these domains of intellect1. Logical ReasoningRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=3.611.1080.1045.192GCE(O-Level)120x2=4.150.6852.Analytical and Critical ThinkingSSC(Matriculation)180x1= 3.461.0290.1045.961GCE(O-Level)120x2=4.080.7663.Problem-Solving SkillsSSC(Matriculation)180x1=3.860.8810.0932.043GCE(O-Level)120x2=4.050.7234.Spirit of Exploration and DiscoverySSC(Matriculation)180x1=3.291.0940.1232.764GCE(O-Level)120x2=3.631.0085.Power of ConcentrationSSC(Matriculation)180x1=3.441.0540.1101.636GCE(O-Level)120x2=3.620.846df =298 tabulated ‘t’ value at 0.05 = 1.960ConclusionsLogical reasoningReferring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.192. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that contents of textbooks develop logical reasoning.Analytical and Critical ThinkingReferring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.961. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that contents develop analytical and critical thinking.Problem-Solving SkillsReferring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.043. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that contents develop problem-solving skills.Spirit of Exploration and DiscoveryReferring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.764. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that contents develop spirit of exploration and discovery.Concentration PowerReferring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.636. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding the reason that contents develop concentration power.37(b): Graph 2*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 38: The contentsare in accordance with intellectual level of studentsH0:There will be no significant difference between SSC and GCE teachers that the contents are in accordance with intellectual level of studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.471.0190.1153.913GCE(O-Level)120x2= 3.920.944df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 38, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.913. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the contents are in accordance with intellectual level of students.Table 39: The contents contain problems that can be solved by personal investigation without having aprior method to solve themH0:There will be no significant difference between SSC and GCE teachers on the statement that content covers problems whose solutions can be found by personal investigation onlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.221.0570.1036.311GCE(O-Level)120x2= 3.870.724df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 39, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.311. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the content covers problems that can be solved by personal investigation only.Table 40: The contents include a proper proportion of mathematical representations (graphs, diagrams, figures and tables)H0:There will be no significant difference between SSC and GCE teachers on the statement that content covers a proper proportion of mathematical representationsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.970.8930.0911.758GCE(O-Level)120x2= 4.130.676df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 40, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.758. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that the content covers a proper proportion of mathematical representations.Table 41: The contents include an appropriate proportion of activities for mental exercise (puzzles/riddles)H0:There will be no significant difference between SSC and GCE teachers on the statement that the contents include an appropriate proportion of activities to develop the habit of thinking among studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.001.2890.1305.231GCE(O-Level)120x2= 3.680.958df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 41, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.231. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that the contents include an appropriate proportion of activities to develop the habit of thinking among students.Table 42: The contents are balanced in terms of key areas (number operation, geometry, algebra, measurement, data analysis and probability).H0:There will be no significant difference between SSC and GCE teachers on the statement that the contents are balanced in terms of key areasRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.690.9790.1014.752GCE(O-Level)120x2= 4.170.763df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 42, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.752. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the content is balanced in term of key areas.Table 43: Pictures and colorful presentations in the textbooks put a positive effect on conceptual understandingH0:There will be no significant difference between SSC and GCE teachers on the statement that the pictures and colorful presentations help in conceptual understandingRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.671.1610.1134.071GCE(O-Level)120x2= 4.130.873df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 43, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.071. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the pictures and colorful presentations help in conceptual understanding.Table 44: The number of problems given on a certain topic affects conceptual understandingH0:There will be no significant difference between SSC and GCE teachers on the statement that the number of problems given on a certain topic affects conceptual understandingRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.561.0180.1113.963GCE(O-Level)120x2= 4.000.883df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 44, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.963. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that the number of problems given on a certain topic affects conceptual understanding.Table 45: Chaining (bit by bit addition of new material in the sums) on a certain topic in the text books put a positive effect on conceptual understandingH0:There will be no significant difference between SSC and GCE teachers on the statement that chaining of sums put a positive effect on conceptual understandingRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.611.0570.1133.451GCE(O-Level)120x2= 4.000.883df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 45, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.451. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the statement that chaining of sums put a positive effect on conceptual understanding.Table 46: Contents of the textbooks are properly chainedH0:There will be no significant difference between SSC and GCE teachers with respect to the statement that the content is properly chainedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.371.1660.1633.987GCE(O-Level)120x2= 4.020.833df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 46, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.987. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them with respect to the statement that the content is properly chained.Table 47(a): Comparison of the approaches of mathematics teachingApproachesH0:There will be no significant difference between the SSC and GCE teachers in the selection of an approach for mathematics teaching1. Learner-FocusedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=4.250.5910.1181.445GCE(O-Level)120x2= 4.130.7692.Content-Focused with an emphasis on conceptual understandingSSC(Matriculation)180x1= 4.100.8490.0863.256GCE(O-Level)120x2= 4.380.6403.Content-Focused with an emphasis on performance SSC(Matriculation)180x1=3.930.9580.1141.140GCE(O-Level)120x2=3.800.9714.Classroom-FocusedSSC(Matriculation)180x1=4.080.8790.1163.103GCE(O-Level)120x2=3.721.043df =298 tabulated ‘t’ value at 0.05 = 1.960ConclusionsLearner-FocusedReferring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.445. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them in their choice for learner-focused approach.Content-Focused (with an emphasis on conceptual understanding)Referring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.256. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themin their choice for content-focused approach with an emphasis on understanding.Content-Focused (with an emphasis on performance)Referring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.140. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them in their choice for content-focused approach with an emphasis on performance.Classroom-FocusedReferring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.103. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them in their choice for classroom-focused approach.47(b): Graph 3Table 48(a): Comparison of the practices of teachers in their classesPracticesH0:There will be no significant difference between the reasons of SSC and GCE teachers regarding the role of a teacher in the class1. Solving all the sums on the board for studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1=2.641.2570.1522.434GCE(O-Level)120x2=2.271.313(Contd…….)2.Solving few sums and letting students do the remainingSSC(Matriculation)180x1=4.290.7820.5870.443GCE(O-Level)120x2=4.031.0083.Explaining important points and encourage students to solve the sumsSSC(Matriculation)180x1=3.731.1880.1371.605GCE(O-Level)120x2=3.951.1414.Letting students solve the sums independently and helping them on their demand onlySSC(Matriculation)180x1=3.641.2740.1440.625GCE(O-Level)120x2=3.551.1855. Making groups of students and facilitating them findingsolutions of the given sumsSSC(Matriculation)180x1=3.921.1040.1402.285GCE(O-Level)120x2=3.601.233df =298 tabulated ‘t’ value at 0.05 = 1.960ConclusionsTeacher solves all the sums Referring to table 48(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.434. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that solving all the sums on a topic is teachers’ routine in their classes.Teacher solves some of them and let students to solve the remainingReferring to table 48(a), we find that the tabulated ‘t’ value = 1.960, at α= 0.05 with df= 298 is smaller than the computed ‘t’ value = 0.443. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that teachers’ usual class practice is to solve a few sums on the board and letstudents do the remaining.Teacher explains important points and encourage students to solve the sumsReferring to table 48(a), we find that the tabulated ‘t’ value = 1.960, at α= 0.05 with df= 298 is smaller than the computed ‘t’ value = 1.605. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that explaining important points and encouragingstudents to solve the sums is teachers’ normal routine in the class.Teacher let students solve the sums independently and provide help on demand onlyReferring to table 48(a), we find that the tabulated ‘t’ value = 1.960, at α= 0.05 with df= 298 is smaller than the computed ‘t’ value = 0.625. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that letting students solve the sums independently and providing help on their demand only is teachers’ usual routine in the class.Teacher facilitates the students working in groups to solve the sums by mutual understandingReferring to table 48(a), we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 2.285. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that facilitating students solving sums in groups is teachers’ usual practice in their classes.48(b): Graph 4Table 49: Students should solve problems by teacher’s explained method onlyH0:There will be no significant difference between SSC and GCE teachers on the statement that students should solve problems by teacher’s explained method onlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 2.76 1.3600.1462.328GCE(O-Level)120x2= 2.421.154df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 49, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed‘t’=2.328. Hence, H0 is rejected, which leads us to the conclusion that there is a significant difference between SSC and GCE teachers on the statement that students should solve problems by teacher’s explained method only.Table 50: Additional material is usually used for deeper understanding of conceptsH0:There will be no significant difference between SSC and GCE teachers on the statement that additional material is usually used for deeper understanding of concepts.RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.180.8560.1201.750GCE(O-Level)120x2= 3.971.119df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 50, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.750. Hence, H0 is accepted, which leads us to the conclusion that there is no significant difference between SSC and GCE teachers on the statement that additional material is usually used for deeper understanding of concepts.Table 51: Additional material is usually used for rigorous drill of learned materialH0:There will be no significant difference between SSC and GCE teachers on the statement that additional material is usually used for rigorous drill of learned materialRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.730.9460.1140.088GCE(O-Level)120x2= 3.720.940df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 51, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.088. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that additional material is usually used for rigorous drill of learned material.Table 52: Mostly previous exam papers are used as an additional materialH0:There will be no significant difference between SSC and GCE teachers on the statement that additional material is mostly previous exam papersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.381.1570.1351.259GCE(O-Level)120x2= 3.551.411df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion: Referring to table 52, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.259. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that additional material is mostly previous exam papers.Table 53: Previous papers are solved as a rehearsal for the actual exam paperH0:There will be no significant difference between SSC and GCE teachers on the statement that previous papers are solved as a rehearsal for the actual exam- paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.980.8610.0921.630GCE(O-Level)120x2= 4.130.724df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion: Referring to table 53, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.630. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that previous papers are solved as a rehearsal for the actual exam paper.Table 54: Past papers are solved because questions of previous papers are considered importantH0:There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions of previous papers are considered importantRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.361.1150.1370.803GCE(O-Level)120x2= 3.471.199df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 54,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.803. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that past papers are solved because questions of previous papers are considered important.Table 55: Past papers are solved because questions from previous papers often repeat in the new papersH0:There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions from previous papers often repeat in the new papersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.471.1730.1472.313GCE(O-Level)120x2= 3.131.294df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 55, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.313. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that past papers are solved because questions from previous papers often repeat in the new papers.Table 56: Past papers are solved to understand the pattern of questions coming in the recent papersH0:There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved to understand the pattern of questions coming in the recent papersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.190.8190.9300.108GCE(O-Level)120x2= 4.180.770df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 56, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.108. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that past papers are solved to understand the pattern of questions coming in the recent papers.Table 57: Teacher-constructed problems are presented in the classH0:There will be no significant difference between SSC and GCE teachers on the statement that teacher-constructed problems are presented in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.311.0260.1150.957GCE(O-Level)120x2= 3.200.947df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 57, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.957. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that teacher-constructed problems are presented in the class.Table 58: Students are allowed to construct and present their own problems in the classH0:There will be no significant difference between SSC and GCE teachers on the statement that students are allowed to construct and present their own problems in the class RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.930.9090.1192.605GCE(O-Level)120x2= 3.621.075df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 58, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.605. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that students are allowed to construct and present their own problems in the class.Table 59: Procedures of doing a problem are explained but not the reason for the selection of that procedureH0:There will be no significant difference between SSC and GCE teachers on the statement that procedures of doing a problem are explained but not the reason for the selection of that procedureRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.231.1320.0207.500GCE(O-Level)120x2= 3.081.225df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 59, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 7.500. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that procedures of doing a problem are explained but not the reason for the selection of that procedure.Table 60: There are some topics in the textbooks that are always left untaught as no question comes in the paper from these topicsH0:There will be no significant difference between SSC and GCE teachers on the statement that there are some topics in the textbooks that are always left untaught as no question comes in the paper from these topicsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.171.3090.1443.125GCE(O-Level)120x2= 3.081.165df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 60, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.125. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that there are some topics in the textbooks that are always left untaught as no question comes in the paper from these topics.Table 61: Homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in classH0:There will be no significant difference between SSC and GCE teachers on the statement that homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.631.8460.1750.914GCE(O-Level)120x2= 3.471.185df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 61, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.914. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in class.Table 62: Completion of a topic means that the teacher has explained the topic and students have done the sums in their copiesH0:There will be no significant difference between SSC and GCE teachers on the statement that completion of a topic means that the teacher has explained the topic and students have done the sums in their copiesRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.811.1010.1412.695GCE(O-Level)120x2= 3.431.267df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 62, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.695. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that completion of a topic means that the teacher has explained the topic and students have done the sums in their copies.Table 63: Emphasis is given on neat and tidy written workH0:There will be no significant difference between SSC and GCE teachers on the statement that emphasis is given on neat and tidy written workRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.220.6990.0984.796GCE(O-Level)120x2= 3.750.914df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 63, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.796. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that Emphasis is placed on neat and tidy written work.Table 64: Homework is assigned and checked regularlyH0:There will be no significant difference between SSC and GCE teachers on the statement that homework is assigned and checked regularlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.250.9060.1183.220GCE(O-Level)120x2= 3.871.049df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 64, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.220. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that homework is assigned and checked regularly.Table 65: Topics are not explored in depth; only the procedure of doing a sum is explainedH0:There will be no significant difference between SSC and GCE teachers on the statement that topics are not explored in depth; only the procedure of doing a sum is explainedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.191.2070.1404.000GCE(O-Level)120x2= 2.631.178df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 65, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.000. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that topics are not explored in depth; only the procedure of doing a sum is explained.Table 66: Unexplained short-cuts are told to solve certain problemsH0:There will be no significant difference between SSC and GCE teachers on the statement that unexplained short-cuts are told to solve certain problemsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.231.1710.1341.268GCE(O-Level)120x2= 3.061.118df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 66, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.268. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that unexplained short-cuts are told to solve certain problems.Table 67: Derivation of the formula is not clarified, only the method of its application is explainedH0:There will be no significant difference between SSC and GCE teachers on the statement that derivation of the formula is not clarified, only the method of its application is explainedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 2.671.0810.1400.214GCE(O-Level)120x2= 2.701.253df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 67, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.214. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that derivation of the formula is not clarified, only the method of its application is explained.Table 68: Usually students avoid checking answersH0:There will be no significant difference between SSC and GCE teachers on the statement that generally students avoid checking answersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.141.1760.1420.070GCE(O-Level)120x2= 3.151.218df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 68, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.070. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that Usually students avoid checking answers.Table 69: Usually students try to skip graph questionsH0:There will be no significant difference between SSC and GCE teachers on the statement that generally students try to skip graph questionsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.371.0960.1290.930GCE(O-Level)120x2= 3.251.187df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 69, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.930. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that usually students try to skip graph questions.Table 70: Teachers do not emphasize checking of answers by studentsH0:There will be no significant difference between SSC and GCE teachers on the statement that teachers do not emphasize checking of answers by studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.111.2230.1292.774GCE(O-Level)120x2= 2.731.118df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 70, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.774. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that teachers do not emphasize checking of answers by students.Table 71: Teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of the classH0:There will be no significant difference between SSC and GCE teachers on the statement that teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 2.561.2730.1420.563GCE(O-Level)120x2= 2.481.157df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 71, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.563. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of the class.Table 72: Mathematics has a significant application in other subjectsH0:There will be no significant difference between SSC and GCE teachers on the statement that mathematics have a significant application in other subjectsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.170.8380.0801.375GCE(O-Level)120x2= 4.280.555df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 72, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.375. Hence, H0 is accepted which leads us to the conclusion that there is no significant difference between SSC and GCE teachers on the statement that mathematics has a significant application in other subjects.Table 73: Teachers’ true role is to generate a question in the mind of a child before it is answeredH0:There will be no significant difference between SSC and GCE teachers on the statement that teachers’ true role is to generate a question in the mind of a child before it is answeredRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.290.7230.0883.750GCE(O-Level)120x2= 3.960.758df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 73, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.750. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that teachers’ true role is to generate a question in the mind of a child before it is answered.Table 74: Both posing and answering of questions by a teacher produce shallow understandingH0:There will be no significant difference between SSC and GCE teachers on the statement that both posing and answering of questions by a teacher produce shallow understandingRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.790.8670.1100.091GCE(O-Level)120x2= 3.800.971df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 74, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.091. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that both posing and answering of questions by a teacher produce shallow understanding.Table 75: Students can communicate mathematical ideas, reasoning and resultsH0:There will be no significant difference between SSC and GCE teachers on the statement that students can communicate mathematical ideas, reasoning and resultsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.84o.8060.0873.218GCE(O-Level)120x2= 4.120.690df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 75, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.218. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that students can communicate mathematical ideas, reasoning and results.Table 76: Students take teaching of mathematics as a pleasant activityH0:There will be no significant difference between SSC and GCE teachers on the statement that students take teaching of mathematics as a pleasant activityRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.730.9690.1181.780GCE(O-Level)120x2= 3.521.033df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 76, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.780. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that students take teaching of mathematics as a pleasant activity.Table 77: Students exhibit courage in facing unfamiliar problemsH0:There will be no significant difference between SSC and GCE teachers on the statement that students exhibit courage in facing unfamiliar problemsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.590.9350.0962.917GCE(O-Level)120x2= 3.870.724df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 77, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.917. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that students exhibit courage in facing unfamiliar problems.Table 78: Students express tolerance in solving difficult problemsH0:There will be no significant difference between SSC and GCE teachers on the statement that students express tolerance in solving difficult problemsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.690.9670.1081.296GCE(O-Level)120x2= 3.550.872df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 78, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.296. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that students express tolerance in solving difficult problems.Table 79: Retention of learned material in the memory becomes stronger with repetitionH0:There will be no significant difference between SSC and GCE teachers on the statement that retention of learned material in the memory becomes stronger with repetitionRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.070.6490.0920.109GCE(O-Level)120x2= 4.080.849df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 79, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.109. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that retention of learned material in the memory becomes stronger with repetition.Table 80: Repetition of learned material may attach meaningful relationships among the fragments of knowledgeH0:There will be no significant difference between SSC and GCE teachers on the statement that repetition of learned material may attach meaningful relationships among the fragments of knowledgeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.160.7170.0840.476GCE(O-Level)120x2= 4.120.715df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 80, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.476. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that repetition of learned material may attach meaningful relationships among the fragments of knowledge.Table 81: Tests/Exams are conducted to assess the level of achievement of the instructional objectivesH0:There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to assess the level of achievement of the instructional objectivesRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.370.4840.0792.532GCE(O-Level)120x2= 4.170.763df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 81, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.532. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that tests/exams are conducted to assess the level of achievement of the instructional objectives.Table 82: Tests/Exams are conducted to categorize students into successful and unsuccessful groupsH0:There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to categorize students into successful and unsuccessful groupsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.731.1680.1444.035GCE(O-Level)120x2= 3.271.260df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 82, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.035. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that tests/exams are conducted to categorize students into successful and unsuccessful groups.Table 83: The verbal/written remark of a teacher on the basis of assessment is evaluationH0:There will be no significant difference between SSC and GCE teachers on the statement that the verbal/written remark of a teacher on the basis of assessment is evaluationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.870.9260.1070.654GCE(O-Level)120x2= 3.800.898df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 83, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.654. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the verbal/written remark of a teacher on the basis of assessment is evaluation.Table 84: Assessment helps both teacher and learner in the process of teaching and learningH0:There will be no significant difference between SSC and GCE teachers on the statement that assessment helps both teacher and learner in the process of teaching and learningRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.360.6410.0841.071GCE(O-Level)120x2= 4.270.756df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 84, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.071. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that assessment helps both teacher and learner in the process of teaching and learning.Table 85: The fear of assessment motivates students to work hardH0:There will be no significant difference between SSC and GCE teachers on the statement that the fear of assessment motivates students to work hardRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.280.6870.0864.318GCE(O-Level)120x2= 3.900.752df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 85, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.318. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that the fear of assessment motivates students to work hard.Table 86: The fear of final examinations is actually the fear of being insulted on its resultsH0:There will be no significant difference between SSC and GCE teachers on the statement that the fear of final examinations is actually the fear of being insulted on its resultsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.771.0710.1293.798GCE(O-Level)120x2= 3.281.106df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 86, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.798. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that the fear of final examinations is actually the fear of being insulted on its results.Table 87: A teacher is always engaged in the process of assessing his/her students during the classH0:There will be no significant difference between SSC and GCE teachers on the statement that a teacher is always engaged in the process of assessing his/her students during the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.010.9770.1030.583GCE(O-Level)120x2= 4.070.799df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 87, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.583. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that a teacher is always engaged in the process of assessing his/her students during the class.Table 88: The encouraging remarks of a teacher after assessment produce positive effect on the performance of studentsH0:There will be no significant difference between SSC and GCE teachers on the statement that the encouraging remarks of a teacher after assessment produce positive effect on the performance of studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.430.7040.0700.000GCE(O-Level)120x2= 4.430.647df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 88, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.000. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the encouraging remarks of a teacher after assessment produce positive effect on the performance of students.Table 89: The discouraging remark of a teacher produces a negative effect on the performance of studentsH0:There will be no significant difference between SSC and GCE teachers on the statement that the discouraging remark of a teacher produces a negative effect on the performance of studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.000.8480.0960.729GCE(O-Level)120x2= 4.070.799df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 89, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.729. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the discouraging remark of a teacher produces a negative effect on the performance of students.Table 90: Methods of assessment should enable students to reveal what they know, rather than what they do not knowH0:There will be no significant difference between SSC and GCE teachers on the statement that methods of assessment should enable students to reveal what they know, rather than what they do not knowRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.810.9700.1042.115GCE(O-Level)120x2= 4.030.822df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 90, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.115. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that methods of assessment should enable students to reveal what they know, rather than what they do not know.Table 91: Students take mathematics assessments confidentlyH0:There will be no significant difference between SSC and GCE teachers on the statement that students take mathematics assessments confidentlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.511.1140.1280.469GCE(O-Level)120x2= 3.451.064df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 91, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.469. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that students take mathematics assessments confidently.Table 92: The main purpose of assessment is to improve teaching and learning of mathematicsH0:There will be no significant difference between SSC and GCE teachers on the statement that the main purpose of assessment is to improve teaching and learning of mathematicsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.270.6990.0871.609GCE(O-Level)120x2= 4.130.769df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 92, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.609. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the main purpose of assessment is to improve teaching and learning of mathematics.Table 93: The exam papers assess the objectives of teaching mathematicsH0:There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the objectives of teaching mathematicsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.990.8680.0881.364GCE(O-Level)120x2= 3.870.650df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 93, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.364. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the exam papers assess the objectives of teaching mathematics.Table 94: The exam papers are balanced in terms of content areasH0:There will be no significant difference between SSC and GCE teachers on the statement that the exam papers are balanced in terms of content areasRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.060.8260.0790.127GCE(O-Level)120x2= 4.050.539df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 94, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.127. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the exam papers are balanced in terms of content areas.Table 95: The exam papers (SSC/GCE) assess the actual educational objectives of teaching mathematicsH0:There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the actual educational objectives of teaching mathematicsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.900.8350.0870.230GCE(O-Level)120x2= 3.920.671df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 95, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.230. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the exam papers assess the actual educational objectives of teaching mathematics.Table 96: The system of checking papers is fairH0:There will be no significant difference between SSC and GCE teachers on the statement that the system of checking papers is fairRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.641.3010.1165.259GCE(O-Level)120x2= 4.250.704df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 96, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.259. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that the system of checking papers is fair.Table 97: Examinations are conducted under strict vigilanceH0:There will be no significant difference between SSC and GCE teachers on the statement that examinations are conducted under strict vigilanceRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.631.3450.1176.752GCE(O-Level)120x2= 4.420.671df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 97, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.752. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that examinations are conducted under strict vigilance.Table 98: Use of unfair means in the paper of mathematics is commonH0:There will be no significant difference between SSC and GCE teachers on the statement that use of unfair means in the paper of mathematics is commonRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.531.2400.1466.712GCE(O-Level)120x2= 2.551.241df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 98, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.712. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that use of unfair means in the paper of mathematics is common.Table 99: Grading system of SSC/ GCE is appropriateH0:There will be no significant difference between SSC and GCE teachers on the statement that grading system of SSC/ GCE is appropriateRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.520.8510.0954.737GCE(O-Level)120x2= 3.970.780df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 99, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.737. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that grading system of SSC/ GCE is appropriate.Table 100: Teachers’ assessment during class is as important as the final examinationH0:There will be no significant difference between SSC and GCE teachers on the statement that teachers’ assessment during class is as important as the final examinationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.090.8380.0861.860GCE(O-Level)120x2= 4.250.654df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 100, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.860. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that teachers’ assessment during class is as important as the final examination.Table 101: Students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior gradesH0:There will be no significant difference between SSC and GCE teachers on the statement that students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior gradesRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.080.8760.0892.359GCE(O-Level)120x2= 4.250.676df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 101, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.359. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior grades.Table 102: Final examinations assess the factual and procedural knowledge of mathematics onlyH0:There will be no significant difference between SSC and GCE teachers on the statement that final examinations assess the factual and procedural knowledge of mathematics onlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.830.9030.1184.237GCE(O-Level)120x2= 3.331.068df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 102, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.237. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that final examinations assess the factual and procedural knowledge of mathematics only.Table 103: Questions in the exam papers are given according to a set patternH0:There will be no significant difference between SSC and GCE teachers on the statement that questions in the exam papers are given according to a set patternRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.801.0750.1302.077GCE(O-Level)120x2= 3.531.125df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 103, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.077. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that questions in the exam papers are given according to a set pattern.Table 104: Questions are given from the textbooks in SSC/GCE papersH0:There will be no significant difference between SSC and GCE teachers on the statement that questions are given from the textbooks in SSC/GCE papersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.381.2320.1357.259GCE(O-Level)120x2= 2.401.092df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 104, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 7.259. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that questions are given from the textbooks in SSC/GCE papers.Table 105: Questions in SSC/GCE papers are given from the past papers H0:There will be no significant difference between SSC and GCE teachers on the statement that questions in SSC/GCE papers are given from the past papers RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.621.2540.1455.448GCE(O-Level)120x2= 2.831.264df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 105, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.448. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that questions in SSC/GCE papers are given from the past papers.Table 106: Some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paperH0:There will be no significant difference between SSC and GCE teachers on the statement that some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.561.1620.1393.813GCE(O-Level)120x2= 3.031.178df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 106, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.813. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paper.Table 107: On the basis of previous papers some questions can be predicted for the upcoming paperH0:There will be no significant difference between SSC and GCE teachers on the statement that on the basis of previous papers some questions can be predicted for the upcoming paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.780.9690.1285.547GCE(O-Level)120x2= 3.071.163df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 107, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.547. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that on the basis of previous papers some questions can be predicted for the upcoming paper.Table 108: Assessment is done to distinguish students for the improvement of learningH0:There will be no significant difference between SSC and GCE teachers on the statement that assessment is done to distinguish students for the improvement of learningRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 4.080.5850.0620.484GCE(O-Level)120x2= 4.050.467df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 108, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.484. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that assessment is done to distinguish students for the improvement of learning.Table 109: Test items of SSC/GCE papers cover all objectives of the curriculumH0:There will be no significant difference between SSC and GCE teachers on the statement that test items of SSC/GCE papers cover all objectives of the curriculumRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.890.8920.1210.248GCE(O-Level)120x2= 3.920.743df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 109, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.248. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that test items of SSC/GCE papers cover all objectives of the curriculum.Table 110: Sections of SSC/GCE papers are designed in such a way that questions from particular chapters always come in specific sectionsH0:There will be no significant difference between SSC and GCE teachers on the statement that sections of SSC/GCE papers are designed in such a way that questions from particular chapters always come in specific sectionsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.990.8000.1174.872GCE(O-Level)120x2= 3.421.109df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 110, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.872. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the statement that sections of SSC/GCE papers are designed in such a way that questions from particular chapters always come in specific sections.Table 111: The entire teaching and learning process in the class is designed and implemented to pass the final examinationsH0:There will be no significant difference between SSC and GCE teachers on the statement that the entire teaching and learning process in the class is designed and implemented to pass the final examinationsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)180x1= 3.871.0830.1191.261GCE(O-Level)120x2= 3.720.958df =298 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 111, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.261. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that the entire teaching and learning process in the class is designed and implemented to pass the final examinations.4.2 ANALYSIS OF THE RESPONSES OF STUDENTSTable 112: Mathematics is an interesting subjectH0:There will be no significant difference between SSC and GCE students on the statement that mathematics is an interesting subjectRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.430.7600.1191.008GCE(O-Level)80x2= 4.310.880df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 112,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.008. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics is an interesting subject.Table 113: I feel pleasure in doing mathematicsH0:There will be no significant difference between SSC and GCE students on the statement that I feel pleasure in doing mathematicsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.971.0600.1570.892GCE(O-Level)80x2= 3.831.009df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 113,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.892. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that I feel pleasure in doing mathematics.Table 114: I do mathematics because teachers emphasizeits importanceH0:There will be no significant difference between SSC and GCE students on the statement that I do mathematics because teachers emphasizeits importanceRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.961.1410.1621.728GCE(O-Level)80x2= 2.681.111df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 114,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.728. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that I do mathematics because teachers emphasizeits importance.Table 115: I do mathematics because it is a compulsory subject at school levelH0:There will be no significant difference between SSC and GCE students on the statement that I do mathematics because it is a compulsory subject at schoolRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.161.0770.1754.689GCE(O-Level)80x2= 3.341.302df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 115,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.689. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that I do mathematics because it is a compulsory subject at school level.Table 116: Mathematics demands rigorous practiceH0:There will be no significant difference between SSC and GCE students on the statement that mathematics demands rigorous practiceRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.430.7630.1060.943GCE(O-Level)80x2= 4.330.725df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 116,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.943. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics demands rigorous practice.Table 117: Mathematics requires concentrationH0:There will be no significant difference between SSC and GCE students on the statement that mathematics requires concentrationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.630.6600.0860.581GCE(O-Level)80x2= 4.680.546df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 117,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.581. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics requires concentration.Table 118: High achievers in mathematics argue stronglyH0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics argue stronglyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.531.1440.1621.728GCE(O-Level)80x2= 3.251.108df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 118,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.728. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that high achievers in mathematics argue strongly.Table 119: High achievers in mathematics are good analystsH0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics are good analystsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.721.0470.1311.221GCE(O-Level)80x2= 3.880.802df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 119,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.221. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that high achievers in mathematics are good analysts.Table 120: High achievers in mathematics raise more questionsH0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics raise more questionsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.200.8940.1443.958GCE(O-Level)80x2= 3.631.059df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 120,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.958. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that high achievers in mathematics raise more questions.Table 121: School gives a special emphasis on mathematics over other subjectsH0:There will be no significant difference between SSC and GCE students on the statement that school gives a special emphasis on mathematics over other subjectsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.641.2820.1760.682GCE(O-Level)80x2= 3.761.172df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 121,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.682. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that school gives a special emphasis on mathematics over other subjects.Table 122(a): Comparison of the perspectives of students about mathematicsStandpointsH0:There will be no significant difference between the SSC and GCE students on their perspectives towards mathematics1. Its contents are useless in daily lifeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=2.421.1850.1660.723GCE(O-Level)80x2=2.301.1302. It is difficult to memorize the formulae/proceduresSSC(Matriculation)120x1=3.021.3750.1803.000GCE(O-Level)80x2=2.491.1583. There isuseless repetition of similar sumsSSC(Matriculation)120x1=2.881.1640.1574.459GCE(O-Level)80x2=2.181.0414. It requires a lot of time for practiceSSC(Matriculation)120x1=3.911.1880.1650.121GCE(O-Level)80x2=3.801.114df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsIts contents are useless in daily lifeReferring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed‘t’=0.723. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics is boring because its contents are useless in daily life.It is difficult to memorize the formulae/proceduresReferring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.000. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that mathematics is boring because it is difficult to memorize formulae.There is useless repetition of similar sumsReferring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.459. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that mathematics is boring because there is useless repetition of similar sums.It requires a lot of time for practiceReferring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.121. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that it requires a lot of time for practice.122(b): Graph 5*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 123: High achievers in mathematics also achieve highgrades in other science subjectsH0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics also achieve highgrades in other science subjectsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.631.1440.1540.779GCE(O-Level)80x2= 3.511.169df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 123,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.779. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that high achievers in mathematics also achieve highgrades in other science subjects.Table 124: Doing mathematics means doing mental exerciseH0:There will be no significant difference between SSC and GCE students on the statement that doing mathematics means doing mental exerciseRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.350.8850.1021.275GCE(O-Level)80x2= 4.480.551df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 124,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.275. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that doing mathematics means doing mental exercise.Table 125: Correct solution to a problem gives a feeling of achievementH0:There will be no significant difference between SSC and GCE students on the statement that correct solution to a problem gives a feeling of achievementRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.450.7380.0931.720GCE(O-Level)80x2= 4.610.582df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 125,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.720. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that correct solution to a problem gives a feeling of achievement.Table 126(a): Comparison of the factors for which students give importance to mathematicsFactorsH0:There will be no significant difference between the SSC and GCE students on the factors for the importance of mathematics1.It trains the mindRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=4.470.6850.0960.0729GCE(O-Level)80x2=4.540.6552. It is a compulsory subject in school curriculum SSC(Matriculation)120x1=4.081.0000.1491.208GCE(O-Level)80x2=3.901.0513.It isan essential part of entry tests for higher educationSSC(Matriculation)120x1=3.631.2010.1641.219GCE(O-Level)80x2=3.891.1024.It is applied in many other subjectsSSC(Matriculation)120x1=4.170.7920.0982.041GCE(O-Level)80x2=4.370.597df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsIt trains the mindReferring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.729. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics is important because it trains the mind.It is a compulsory subject in school curriculumReferring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.208. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics is important because it is a compulsory subject in school curriculum.It is an essential part of entry tests at the higher education levelReferring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.219. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics is important because it is an essential part of entry tests at the higher education level.It is applied in many other subjectsReferring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.041. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that mathematics is important because it is applied in many other subjects. 126(b): Graph 6*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 127: Mathematics is a scoring subjectH0:There will be no significant difference between SSC and GCE students on the statement that mathematics is a scoring subjectRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.570.7070.1021.176GCE(O-Level)80x2= 4.450.709df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 127,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.176. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics is a scoring subject.Table 128: Textbooks of mathematics have an attractive lookH0:There will be no significant difference between SSC and GCE students on the statement that textbooks of mathematics have an attractive lookRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.631.2760.1970.355GCE(O-Level)80x2= 2.561.421df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 128,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.355. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that mathematics textbooks have an attractive look.Table 129: Language used in the textbooks is clearH0:There will be no significant difference between SSC and GCE students on the statement that language used in the textbooks is clearRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.630.9340.1441.111GCE(O-Level)80x2= 3.791.039df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 129,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.111. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that language used in the textbooks is clear.Table 130: Language of textbooks is difficult because excessive mathematical terminologies are usedH0:There will be no significant difference between SSC and GCE students on the statement that language of textbooks is difficult because excessive mathematical terminologies are usedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.121.1320.1594.779GCE(O-Level)80x2= 2.361.082df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 130,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.779. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that language of textbooks is difficult because excessive mathematical terminologies are used.Table 131: All topics in the textbooks are taught completely for the preparation of final examinationH0:There will be no significant difference between SSC and GCE students on the statement that all topics in the textbooks are taught completely for the preparation of final examinationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.361.3850.1595.238GCE(O-Level)80x2= 4.200.892df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 131,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.238. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that all topics in the textbooks are taught completely for the preparation of final examination.Table 132: Methods to solve different types of problems are explained through worked examples in the textbooksH0:There will be no significant difference between SSC and GCE students on the statement that methods to solve different types of problems are explained through worked examples in the textbooksRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.640.9060.1282.734GCE(O-Level)80x2= 3.990.864df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 132,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.734. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that methods to solve different types of problems are explained through worked examples in the textbooks.Table 133: Textbooks are illustrated with concept-related pictures from real lifeH0:There will be no significant difference between SSC and GCE students on the statement that textbooks are illustrated with concept-related pictures from real lifeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.701.1990.1673.832GCE(O-Level)80x2= 3.341.136df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 133,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.832. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that textbooks are illustrated with concept-related pictures from real life.Table 134: Pictures in the textbooks facilitate in comprehending the conceptsH0:There will be no significant difference between SSC and GCE students on the statement that the pictures facilitate in comprehending the conceptsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.611.0230.1530.392GCE(O-Level)80x2= 3.551.089df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 134,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.392. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that the pictures facilitate in comprehending the concepts.Table 135: Diagrams are the frightening element of the textbooksH0:There will be no significant difference between SSC and GCE students on the statement that diagrams are the frightening element of the textbooksRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.591.2260.1562.821GCE(O-Level)80x2= 2.150.982df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 135,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.821. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that diagrams are the frightening element of the textbooks.Table 136: I can study a new topic through worked examples provided in the textbookH0:There will be no significant difference between SSC and GCE students on the statement, “I can study a new topic through worked examples provided in the textbook”.RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.521.2830.1685.774GCE(O-Level)80x2= 2.551.078df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 136,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.774. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement,“I can study a new topic through worked examples provided in the textbook”.Table 137: I study the topic from the textbook first before it is explained by the teacher in classH0:There will be no significant difference between SSC and GCE students on the statement, “I study the topic from the textbook first before it is explained by the teacher in class”.RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=3.831.1280.1651.818GCE(O-Level)80x2= 3.531.158df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 137,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.818. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement, “I study the topic from the textbook first before it is explained by the teacher in class”.Table 138: I have questions in mind before starting a new lessonH0:There will be no significant difference between SSC and GCE students on the statement,“I have questions in mind before starting a new lesson”.RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.781.1170.1561.795GCE(O-Level)80x2= 3.501.055df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 138,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.795. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement, “I have questions in mind before starting a new lesson”.Table 139: Only the contents explained by the teacher should be studiedH0:There will be no significant difference between SSC and GCE students on the statement that only the contents explained by the teacher should be studiedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.951.3400.1765.114GCE(O-Level)80x2= 2.051.135df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 139,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.114. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that only the contents explained by the teacher should be studied.Table 140(a): Comparison of components of the contents that have to be learnt in mathematicsComponentsH0:There will be no significant difference between the SSC and GCE students on memorization of these components of the contents1. FormulaeRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=4.051.0280.1560.897GCE(O-Level)80x2=3.911.1162.Steps of long procedures SSC(Matriculation)120x1=3.581.1350.1610.124GCE(O-Level)80x2=3.601.0983.Definitions SSC(Matriculation)120x1=3.581.1190.1737.514GCE(O-Level)80x2=2.281.2534.Proofs of geometrical theorems SSC(Matriculation)120x1=4.031.1950.1889.148GCE(O-Level)80x2=2.311.365df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsFormulaeReferring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.897. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that formulae are to be memorized in mathematics.Steps of long proceduresReferring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.124. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that steps of long procedures are to be memorized in mathematics.DefinitionsReferring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.514. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that definitions are to be memorized in mathematics.Proofs of theoremsReferring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 9.148. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that proofs of geometrical theorems are to be memorized in mathematics.140(b): Graph 7lefttop*For this comparison, SA & A alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 141: Contents of the textbooks are in accordance with the intellectual levels of studentsH0:There will be no significant difference between SSC and GCE students on the statement that the contents of textbooks are in accordance with the intellectual levels of studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.481.1150.1480.203GCE(O-Level)80x2= 3.510.955df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table141,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.203. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that the contents of textbooks are in accordance with the intellectual levels of students.Table 142: Language of the textbooks is in accordance with the language proficiency of studentsH0:There will be no significant difference between SSC and GCE students on the statement that the language of textbooks is in accordance with the language proficiency of studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.550.8970.1321.016GCE(O-Level)80x2= 3.690.922df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 142,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.016. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that the language of textbooks is in accordance with the language proficiency of students.Table 143: Getting afraid of a problem in the first look makes it very difficult to solveH0:There will be no significant difference between SSC and GCE students on the statement that getting afraid of a problem in the first look makes it very difficult to solveRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.090.9610.1824.945GCE(O-Level)80x2= 3.191.424df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 143,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.945. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that getting afraid of a problem in the first look makes it very difficult to solve.Table 144: Doing important topics is better than doing all the topics in order to get good marksH0:There will be no significant difference between SSC and GCE students on the statement that doing important topics is better than doing all the topics in order to get good marksRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.481.3020.1715.673GCE(O-Level)80x2= 2.511.102df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 144,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.673. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that doing important topics is better than doing all the topics in order to get good marks.Table 145: The last questions (star questions) of the exercises are generally left unsolvedH0:There will be no significant difference between SSC and GCE students on the statement that the last questions (star questions) of the exercises are generally left unsolvedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.481.2090.1720.581GCE(O-Level)80x2= 3.581.178df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 145,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.581. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between themon the statement that the last questions (star questions) of the exercises are generally left unsolved.Table 146(a): Comparison of the domains of thinking process during the solution of a problemDomainsH0:There will be no significant difference between the SSC and GCE students on the domains of thinking process during the solution of a problem1.Retrieval of formula and method from memoryRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=4.061.1620.1341.045GCE(O-Level)80x2=4.200.7362.Development of one’s own strategy to solve the problemSSC(Matriculation)120x1=3.371.2960.1672.515GCE(O-Level)80x2=3.791.0523.Thinking to get an insightSSC(Matriculation)120x1=3.621.1090.1492.215GCE(O-Level)80x2=3.950.9794.Effort to recall the chapter and exercise of the problemSSC(Matriculation)120x1=4.070.9500.1755.943GCE(O-Level)80x2=3.031.359df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsRetrieval of formula and method from memoryReferring to table 146(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.045. Hence, H0 is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that during the solution of a problem they think to retrieve the formula and method from memory.Development of our own strategy to solve the problemReferring to table 146(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.515. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that during the solution of a problem they think to develop their own strategy to solve the problem.Thinking to get an insightReferring to table ‘146(a)’ we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.215. Hence H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that during the solution of a problem they think to get an insight for its solution.Effort to remember the chapter and exercise number of the problemReferring to table ‘146(a)’ we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.943. Hence H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that during the solution of a problem they try to remember from which chapter and exercise number the problem is. 146(b): Graph 8*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 147: Most of the teachers emphasize solving the sums using their explained methods onlyH0:There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize solving the sums using their explained methods onlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.481.1880.1661.386GCE(O-Level)80x2= 3.711.127df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 147,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.386. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that most of the teachers emphasize solving the sums using their explained methods only.Table 148: There is more than one method to solve a problemH0:There will be no significant difference between SSC and GCE students on the statement that there is more than one method to solve a problemRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.330.7900.1011.485GCE(O-Level)80x2= 4.480.636df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 148,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.485. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that there is more than one method to solve a problem.Table 149: Most of the teachers emphasize neat and tidy workH0:There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize neat and tidy workRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.161.0370.1634.172GCE(O-Level)80x2= 3.481.190df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 149,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.172. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that most of the teachers emphasize neat and tidy work.Table 150(a): Comparison of the remarks of students for questions involving graphsRemarksH0:There will be no significant difference between the SSC and GCE students on their remarks for graph questions 1.DifficultRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=3.401.3370.1863.889GCE(O-Level)80x2=2.401.1862.BoringSSC(Matriculation)120x1=3.141.3680.1980.202GCE(O-Level)80x2=3.101.3743.Time ConsumingSSC(Matriculation)120x1=3.671.2180.1911.885GCE(O-Level)80x2=3.311.3834.AnnoyingSSC(Matriculation)120x1=3.041.2460.1921.875GCE(O-Level)80x2=3.401.383df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsDifficultReferring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 3.889. Hence, H0 is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that graph question are difficult.BoringReferring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.202. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that graph questions are boring.Time ConsumingReferring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.885. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that graph questions are time consuming.AnnoyingReferring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.875. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that graph questions are annoying.150(b): Graph 9 *For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 151: Additional material (worksheets/workbooks etc.) is used to get further practice of the sumsH0:There will be no significant difference between SSC and GCE students on the statement that additional material (worksheets/workbooks etc.) is used to get further practice of the sumsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.631.2170.1591.069GCE(O-Level)80x2= 3.801.024df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 151,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.069. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that additional material (worksheets/workbooks etc.) is used for further practice of the sums.Table 152: Teacher-constructed problems are presented in the classH0:There will be no significant difference between SSC and GCE students on the statement that teacher-constructed problems are presented in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.601.0950.1594.717GCE(O-Level)80x2= 2.851.115df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 152,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.717. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that teacher-constructed problems are presented in the class.Table 153: Separate activities are done for low achievers in the classH0:There will be no significant difference between SSC and GCE students on the statement that separate activities are done for low achievers in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.131.1420.1575.668GCE(O-Level)80x2= 2.241.058df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 153,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.668. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that separate activities are done for low achievers in the class.Table 154: Teachers arrange activities to engage high achiever students to help their low achiever class fellowsH0:There will be no significant difference between SSC and GCE students on the statement that teachers arrange activities to engage high achiever students to help their low achiever class fellowsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.251.3170.1852.054GCE(O-Level)80x2= 2.871.257df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 154,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.054. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that teachers arrange activities to engage high achiever students to help their low achiever class fellows.Table 155: In a mathematics class of 40 minutes, students normally ask less than 5 questionsH0:There will be no significant difference between SSC and GCE student on the statement that in a mathematics class of 40 minutes students normally ask less than 5 questionsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.081.1960.1662.892GCE(O-Level)80x2= 2.601.121df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 155,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.892. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that in a mathematics class of 40 minutes students normally ask less than 5 questions.Table 156: In a mathematics class of 40 minutes, teachers normally explain for less than 15 minutesH0:There will be no significant difference between SSC and GCE students on the statement that in a mathematics class of 40 minutes teachers normally explain for less than 15 minutesRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.541.1590.1720.402GCE(O-Level)80x2= 2.831.209df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 156,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.402. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that in a mathematics class of 40 minutes teachers normally explain for less than 15 minutes.Table 157: Students mostly ask ‘HOW’ type questions in the classH0:There will be no significant difference between SSC and GCE students on the statement that Students mostly ask ‘HOW’ type questions in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.230.8770.1100.091GCE(O-Level)80x2= 4.240.679df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 157,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.091. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that students mostly ask ‘HOW’ type questions in the class.Table 158: ‘WHY’ type questions are rarely posed by studentsH0:There will be no significant difference between SSC and GCE students on the statement that ‘WHY’ type questions are rarely posed by studentsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.861.1250.1570.637GCE(O-Level)80x2= 3.761.070df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 158,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.637. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that ‘WHY’ type questions are rarely posed by students.Table 159: Teachers do not encourage ‘WHY’ type questions in the classH0:There will be no significant difference between SSC and GCE student on the statement that teachers do not encourage ‘WHY’ type questions in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.251.1760.1612.112GCE(O-Level)80x2= 3.591.076df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 159,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.112. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that teachers do not encourage ‘WHY’ type questions in the class.Table 160: Procedure of solving a problem is explained but not the reason for the selection of that procedureH0:There will be no significant difference between SSC and GCE students on the statement that procedure of solving a problem is explained but not the reason for the selection of that procedureRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.481.0840.1591.258GCE(O-Level)80x2= 3.681.122df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 160,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.258. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that procedure of solving a problem is explained but not the reason for the selection of that procedure.Table 161: Some topics of the textbooks are never taughtH0:There will be no significant difference between SSC and GCE student on the statement that some topics of the textbooks are never taughtRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.781.0570.1726.221GCE(O-Level)80x2= 2.711.275df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 161,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 6.221. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that some topics of the textbooks are never taught.Table 162: Homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in classH0:There will be no significant difference between SSC and GCE students on the statement that homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.021.0040.1371.168GCE(O-Level)80x2= 3.860.910df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 162,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.168. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in class.Table 163: Completion of a topic means that teacher has explained the topic and students have done the sums in their notebooksH0:There will be no significant difference between SSC and GCE student on the statement that completion of a topic means that teacher has explained the topic and students have done the sums in their notebooksRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.521.2430.1572.357GCE(O-Level)80x2= 3.890.981df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 163,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.357. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that completion of a topic means that teacher has explained the topic and students have done the sums in their notebooks.Table 164: Homework is assigned and checked regularly by the teachersH0:There will be no significant difference between SSC and GCE student on the statement that homework is assigned and checked regularly by the teachersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.691.2680.1789.438GCE(O-Level)80x2= 2.011.183df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 164,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 9.438. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that homework is assigned and checked regularly by the teachers.Table 165: Classwork of students is checked regularly by the teachersH0:There will be no significant difference between SSC and GCE student on the statement that classwork of students is checked regularly by the teachersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.191.3430.1826.319GCE(O-Level)80x2= 2.041.195df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 165,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 6.319. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that classwork of students is checked regularly by the teachers.Table 166: Topics are not explored in depth; only the procedure of solving a sum is explainedH0:There will be no significant difference between SSC and GCE students on the statement that topics are not explored in depth; only the procedure of solving a sum is explainedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.101.2300.1790.223GCE(O-Level)80x2= 3.061.246df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 166,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.223. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that topics are not explored in depth; only the procedure of solving a sum is explained.Table 167: Short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explainedH0:There will be no significant difference between SSC and GCE students on the statement that short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explainedRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.331.1910.1821.374GCE(O-Level)80x2= 3.081.309df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 167,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.374. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explained.Table 168: Derivation of formula is not explained, only the method of its application is toldH0:There will be no significant difference between SSC and GCE students on the statement that derivation of formula is not explained, only the method of its application is toldRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.261.3190.1770.452GCE(O-Level)80x2= 3.181.167df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 168,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.452. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that derivation of formula is not explained, only the method of its application is told.Table 169: The activities of a mathematics class are largely doing repetition of similar sumsH0:There will be no significant difference between SSC and GCE students on the statement that the activities of a mathematics class are largely doing repetition of similar sumsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.701.0330.1430.279GCE(O-Level)80x2= 3.660.967df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion: Referring to table 169,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.279. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that the activities of a mathematics class are largely doing repetition of similar sums.Table 170: Reference books are taken from the library to explore the topics in depthH0:There will be no significant difference between SSC and GCE students on the statement that reference books are taken from the library to explore the topics in depthRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.371.2840.1850.160GCE(O-Level)80x2= 2.531.281df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion: Referring to table 170,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.160. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that reference books are taken from the library to explore the topics in depth.Table 171(a): Comparison of experiences of students in the class about the teaching methods of their teachersMethodsH0:There will be no significant difference between the SSC andGCE students regarding their observations of teaching methods of their teachers1.Teachers explain some problems on a topic from the textbook on the boardRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=4.180.7740.0940.426GCE(O-Level)80x2=4.140.545(Contd…….)2.Explain all the problems on a topic from the textbook on the boardSSC(Matriculation)120x1=2.831.1790.1672.874GCE(O-Level)80x2=2.351.1373. Explainimportant points and procedures and help students in solving the sumsSSC(Matriculation)120x1=3.881.0700.1442.083GCE(O-Level)80x2=4.180.9524.Give sums directly and facilitate students in finding their solutionsSSC(Matriculation)120x1=2.591.2800.1830.328GCE(O-Level)80x2=2.651.264df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsTeachers explain some problems on a topic from the textbook on the boardReferring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.426. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding their experience in the class of mathematics that teachers explain some problems on a topic from the textbooks on the board.Explain all the problems on a topic from the textbook on the boardReferring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.874. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between themregarding their experience in the class of mathematics that teachers explain all the problems on a topic from the textbooks on the board.Explain important points and procedures and help students in solving the sums Referring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.083. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between themregarding their experience in the class of mathematics that teachers explain important points and procedures and help students in solving the sums.Give sums directly and facilitate students in finding their solutionsReferring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.328. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between themregarding their experience in the class of mathematics that teachers give sums directly and facilitate students in finding their solutions.171(b): Graph 10*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 172(a): Comparison of attributes of a good teacher from students’ perspectiveAttributesH0:There will be no significant difference between the SSC and GCE students regarding the attributes of a good teacher1.Starting a new lesson with recapitulationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=4.041.0950.1430.979GCE(O-Level)80x2=4.180.9252.Presenting uninteresting matter in an interesting waySSC(Matriculation)120x1=4.120.9540.1192.689GCE(O-Level)80x2=4.440.726(Continued from the previous page…….)3.Presenting difficult concepts in a simple waySSC(Matriculation)120x1=4.400.7260.0931.827GCE(O-Level)80x2=4.570.5884.Explaining lengthy concepts very conciselySSC(Matriculation)120x1=4.000.9700.1631.349GCE(O-Level)80x2=3.781.2195.Keeping students alert and attentive by creating humorSSC(Matriculation)120x1=4.081.0170.1312.784GCE(O-Level)80x2=4.440.8246.Giving encouraging remarksSSC(Matriculation)120x1=4.190.8230.1063.679GCE(O-Level)80x2=4.580.6717.Engaging the entire class in productive activitiesSSC(Matriculation)120x1=3.041.0210.1532.810GCE(O-Level)80x2=3.821.0858.Finishing a lesson with a summary of the class activitiesSSC(Matriculation)120x1=4.120.9720.1550.194GCE(O-Level)80x2=4.151.137df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsStarting a new lesson with recapitulationReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.979. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding the attribute of a good teacher that he/she starts a new lesson with recapitulation.Presenting uninteresting matter in an interesting wayReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.689. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the attribute of a good teacher that he/she presents uninteresting matter in an interesting way.Presenting difficult concepts in a simple wayReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.827. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding the attribute of a good teacher that he/she presents difficult concepts in a simple way.Explaining lengthy concepts very conciselyReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.349. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding the attribute of a good teacher that he/she explains lengthy concepts very concisely.Keeping students alert and attentive by creating humorReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.748. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the attribute of a good teacher that he/she keeps students alert and attentive by creating humor.Giving encouraging remarksReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.679. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the attribute of a good teacher that he/she gives encouraging remarks.Engaging the entire class in productive activitiesReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.810. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the attribute of a good teacher that he/she engages all class in productive activities.Finishing a lesson with a summary of the class activitiesReferring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.194. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding the attribute of a good teacher that he/she finishes a lesson with a summary of who the class activities.172(b): Graph 11*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 173: Assessments help in confidence buildingH0:There will be no significant difference between SSC and GCE students on the statement that assessments help in confidence buildingRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.240.8300.1261.984GCE(O-Level)80x2= 3.990.893df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 173,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 1.984. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that assessments help in confidence building.Table 174: Assessments help in identifying and reducing mistakesH0:There will be no significant difference between SSC and GCE students on the statement that assessments help in identifying and reducing mistakesRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.340.7390.0950.316GCE(O-Level)80x2= 4.310.608df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 174,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.316. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that assessments help in identifying and reducing mistakes.Table 175: Assessments help in the preparation for final examinationsH0:There will be no significant difference between SSC and GCE students on the statement that assessments help in the preparation for final examinationsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.440.8070.0920.217GCE(O-Level)80x2= 4.460.594df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 175,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.217. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that assessments help in the preparation for final examinations.Table 176: Quizzes (short tests based on calculations without using calculators) are conducted regularly in the classH0:There will be no significant difference between SSC and GCE student on the statement that quizzes (short tests based on calculations without using calculators) are conducted regularly in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.881.3480.1922.135GCE(O-Level)80x2= 3.291.323df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 176,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.135. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that quizzes (short tests based on calculations without using calculators) are conducted regularly in the class.Table 177: Speed tests are conducted regularly in the classH0:There will be no significant difference between SSC and GCE students on the statement that speed tests are conducted regularly in the classRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 2.431.2550.1891.746GCE(O-Level)80x2= 2.761.343df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 177,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.746. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that speed tests are conducted regularly in the class.Table 178: Positive remarks of the teacher on student’s assessment produce better resultsH0:There will be no significant difference between SSC and GCE students on the statement that positive remarks of the teacher on student’s assessment produce better resultsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.090.9260.1720.349GCE(O-Level)80x2= 4.031.343df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 178,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.349. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that positive remarks of the teacher on student’s assessment produce better results.Table 179: Negative remarks by a teacher on student’s assessment produce demoralizationH0:There will be no significant difference between SSC and GCE students on the statement that negative remarks by a teacher on student’s assessment produce demoralizationRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.770.9320.1410.851GCE(O-Level)80x2= 3.891.006df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 179,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.851. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that negative remarks by a teacher on student’s assessment produce demoralization.Table 180: I am wellaware of the pattern of SSC/GCE paperH0:There will be no significant difference between SSC and GCE student on the statement, “I am well aware of the pattern of SSC/GCE paper”RespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.260.8350.1332.105GCE(O-Level)80x2= 3.980.981df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table ‘180’ we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.105. Hence H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement, “I am well aware of the pattern of SSC/GCE paper”.Table 181: Students study seriously under the pressure of tests/examinationsH0:There will be no significant difference between SSC and GCE students on the statement that students study seriously under the pressure of tests/examinationsRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.961.1030.1490.939GCE(O-Level)80x2= 4.100.976df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 181,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.939. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that students study seriously under the pressure of tests/examinations.Table 182: Teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paperH0:There will be no significant difference between SSC and GCE student on the statement that teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.641.0830.1894.974GCE(O-Level)80x2= 2.701.444df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 182,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.974. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paper.Table 183: Questions in SSC/GCE papers are given according to a fixed patternH0:There will be no significant difference between SSC and GCE student on the statement that questions in SSC/GCE papers are given according to a fixed patternRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.110.9510.1737.688GCE(O-Level)80x2= 2.781.340df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 183,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.688. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that questions in SSC/GCE papers are given according to a fixed pattern.Table 184: Questions are taken from the textbooks in SSC/GCE paperH0:There will be no significant difference between SSC and GCE student on the statement that questions are taken from the textbooks in SSC/GCE paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.891.0270.15311.503GCE(O-Level)80x2= 2.131.084df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 184,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 11.503. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that questions are taken from the textbooks in SSC/GCE paper.Table 185: Questions are taken from past papers in SSC/GCE paperH0:There will be no significant difference between SSC and GCE student on the statement that questions are taken from past papers in SSC/GCE paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.880.9540.1638.282GCE(O-Level)80x2= 2.531.232df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 185,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 8.282. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that questions are taken from past papers in SSC/GCE paper.Table 186: Some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paperH0:There will be no significant difference between SSC and GCE student on the statement that some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paperRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.721.1240.1718.070GCE(O-Level)80x2= 2.341.222df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 186,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 8.070. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper.Table 187: Some questions can be predicted for the upcoming papers on the basis of previous papersH0:There will be no significant difference between SSC and GCE student on the statement that some questions can be predicted for the upcoming papers on the basis of previous papersRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 4.170.7810.1547.532GCE(O-Level)80x2= 3.011.227df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 187,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.532. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that on the basis of previous papers some questions can be predicted for the upcoming paper.Table 188(a): Comparison of methods used for revision before taking a test/ examinationMethodsH0:There will be no significant difference between the SSC and GCE students on the methods used for revision 1.Solving all the sums from the textbooksRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1=3.831.1980.1774.972GCE(O-Level)80x2=2.951.2422.Solving different types of sums from the textbooksSSC(Matriculation)120x1=4.240.8090.1302.308GCE(O-Level)80x2=3.940.9593. Solving sums from the past papers (five years)SSC(Matriculation)120x1=4.180.9670.1240.806GCE(O-Level)80x2=4.280.7794.Reading solved sums from the copiesSSC(Matriculation)120x1=3.571.2750.1835.355GCE(O-Level)80x2=2.591.2695. Reading worked examples from the textbooksSSC(Matriculation)120x1=3.571.2140.1774.915GCE(O-Level)80x2=2.701.237df =198 tabulated ‘t’ value at 0.05 = 1.960ConclusionsSolving all the sums from the exercisesReferring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 4.972. Hence, H0 is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that all sums should be solved from the exercises.Solving different types of sums from the exercisesReferring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 2.308. Hence, H0 is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the statement that different types of sums should be solved on a topic from the textbook for revision.Solving sums from the past papers (five years)Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.806. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between themon the statement that sums should be solved from past papers for revision.Reading solved sums from the notebooks (notes maintained in the form of solutions of sums from the textbooks)Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 3.889. Hence, H0 is rejected which leads us to the conclusion that the two groups of students have no significant difference between themon the statement that sums should be read from the notebooks for revision.Reading worked examples from the textbooksReferring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 3.889. Hence, H0 is rejected which leads us to the conclusion that the two groups of students have no significant difference between themon the statement that worked examples from the textbooks should be read for revision.188 (b): Graph 12*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreementTable 189: In junior grades (VI – VIII); the final paper is set from the whole syllabusH0:There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the whole syllabusRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.011.4050.1675.569GCE(O-Level)80x2= 3.940.959df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 189,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.569. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that in junior grades (VI – VIII); the final paper is set from the whole syllabus.Table 190: In junior grades (VI – VIII); the final paper is set from the topics covered in the final term onlyH0:There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the topics covered in the final term onlyRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.481.3280.1747.356GCE(O-Level)80x2= 2.201.118df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 190,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.356. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that in junior grades (VI – VIII); the final paper is set from the topics covered in the final term only.Table 191: In junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next termH0:There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next termRespondentsNMeanSDSEx1-x2t-valueSSC(Matriculation)120x1= 3.081.2470.1645.976GCE(O-Level)80x2= 2.101.051df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 191,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.976. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement that in junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term.ANALYSIS OF THE RESPONSES OF SUBJECT EXPERTSThe responses of experts of both the systems, for each question asked from them, have been compared and presented in the following table.Table 192: Comparison of the Responses of Subject ExpertsQ1. Are you satisfied with the current routine of teaching mathematics at school level? If not, what are your reservations?Responses of Experts (SSC-System)Responses of Experts (GCE-System)Satisfied (3)Unsatisfied (7)Undecided (0)Reservations-There is shortage of resources. (3)-Teachers are untrained. (2)-The objectives of teaching are not coherent with the needs of students and society. (1)-There is a discontinuation of one year, as mathematics is not taught in grade IX. (1)Satisfied (8)Unsatisfied (2)Undecided (0)Reservations-The syllabus is very lengthy. (1)-Increasing trend of private tuitions of this subject is decreasing the interest of students in the class. (1)Q.2 Is teaching of mathematics according to some clear objectives? If yes, then according to your observation, what is the major objective?Responses of Experts (SSC-System)Responses of Experts (GCE-System)Agreed (7)Disagreed (2)Undecided (1)-Syllabus is designed to continue this subject in higher grades. (3)-Enable the students to do basic operations and calculations. (1)(Contd…….)-Objectives are to make students learn the formulae and procedures of solving different kinds of problems. (2)-Objectives are not clear to teachers but in my opinion the only objective is to make student’s memorize the contents and procedures so that they can get good marks by reproducing them in the final examination. (1) Agreed (10)Disagreed (0)Undecided (0)-Objectives are to enhance thinking skills of students. (2)-Prepare students for GCE-Exam. (4)-Prepare students for higher learning giving them first-hand knowledge. (2)-Enable students to think within the horizon before thinking beyond horizon. (1)-Making students able to think and making them good problem solvers. (1)Q.3 Do you agree that these objectives can fulfill the true aims of mathematics education?Responses of Experts (SSC-System)Responses of Experts (GCE-System)Agreed (3)Disagreed (5)Undecided (2)Agreed (9)Disagreed (0)Undecided (1)Q.4 Do you agree that mathematics education in Pakistan is comparable with the other countries of Asia?Responses of Experts (SSC-System)Responses of Experts (GCE-System)Agreed (4)Disagreed (5)Undecided (1)Agreed (7)Disagreed (3)Undecided (0)Q.5 Do you agree that mathematics should be the prime focus of school curriculum as it develops cognitive, affective and psychomotor faculties of an individualResponses of Experts (SSC-System)Responses of Experts (GCE-System)Agreed (9)Disagreed (0)Undecided (0)(Contd…….)-Agreed,butif our teaching touches these domains then, the current focus of teaching is on the contents only. (1)Agreed (10)Disagreed (0)Undecided (0)-------Q.6 Are you satisfied with the contents of textbooks of mathematics used at secondary level?Responses of Experts (SSC-System)Responses of Experts (GCE-System)Satisfied (4)Unsatisfied (4)Undecided (0)-Yes, but problem is not with the contents. It is with the methods of teaching and assessment. (1)-Yes, but some topics like number sequence, probability, etc. should be included. (1)Satisfied (5)Unsatisfied (3)Undecided (0)-Yes, books are not written locally. They serve the needs in terms of contents but it will be better if books are written by local authors. (1)-Yes but the names of persons and places are not familiar to our students. If these are familiar, students can mentally visualize the context of that problem and learning of the concept becomes more concrete. (1)Q.7 What changes would you like to suggest improving these textbooks?Responses of Experts (SSC-System)Responses of Experts (GCE-System)-New topics should be added. (3)-Word problems designed to apply mathematical concepts in real life situations should be increased. (4)-Textbooks should be updated on regularly and periodically. (3)(Contd…….)-Worked examples in the textbooks should be improved. (1)-Textbooks should be activity-based that can develop interest among students. (2)-In lower grades, too many books of different publishers are used and schools frequently change these books. If a series of textbooks is used in one year and next year is replaced by another series, it will affect the logical sequence of contents and vertical integration of concepts. (2)-To cover all the topics of O-Level mathematics syllabus the books have an addendum at the end of each book. It will be better if all the contents given in the addendum are incorporated into the main part of the books. (2)-It is better if the books are written by local authors. (3)-Reference books should be used instead of textbooks keeping in view the needs of students. (4)-Content on number sequence and problem solving should be increased. (1)-Answers of graph and loci questions should be given in the form of constructed graphs and geometrical figures respectively. (1)-A teachers’ manual should be published with each book for their guidance. (2)Q.8 Are you satisfied with the current methods of selection and sequencing of contents? If not, please give your opinion.Responses of Experts (SSC-System)Responses of Experts (GCE-System)Satisfied (2)Dissatisfied (7)Undecided (1)-Sequence of contents is not proper at lower secondary and secondary level. (2)-Selection of contents should be made accordingly with the sequence of the textbooks. (3)-Selection is made taking topics from the three key areas (arithmetic, algebra, geometry) but the prime concern of this selection is to ensure making a balancedquestion paper for terminal/half-yearly examination. (4)(Contd…….)-It is done in a sitting of teachers where the selection, elimination and sequence of contents are made according to their choice and feasibility of completing it within the available time. (3)Satisfied (7)Dissatisfied (3)Undecided (0)-It should be done on logical grounds. (4)-The selection of content should be done on the basis of educational needs of students. (5)-In the process of selection and its sequencing, no special consideration is made on the prerequisites, interests and needs of students. (3)-------Q.9 In your opinion, what changes should be made in the approaches and methods of teaching mathematics?Responses of Experts (SSC-System)Responses of Experts (GCE-System)-Activity-based teaching. (4)-Project-based teaching. (2)-Taking the aid of technology (audio-video aides, internet etc.). (4)-Mathematics should be taught just like a language. (1)-Emphasis is mostly given on the product but the process is also as important as the product. (1)-Teachers should have to address all the cognitive levels in their teaching (knowledge, comprehension, application, analysis, synthesis and evaluation). (1)-Step by step instructions should be given instead of giving the key to open the lock (a method to solve the problem). (2)(Contd…….)-Activity based teaching. (2)-Spend maximum time on basic concepts. (4)-Prefer mental calculations and avoid calculators as much as possible. (3)-Computer Assisted Instruction (CAI) should be introduced. (1)-Instead of teaching a large number of chapters, teach a chapter in depth. (2)-Teach the students to use the (FFF) approach in solving a problem i.e. face it, fight it and finish it. (1)-Make the students confident by rigorous practice. (6)Q.10 Are you satisfied with current system of assessment in mathematics at school level? If not, please suggest some changes.Responses of Experts (SSC-System)Responses of Experts (GCE-System)Satisfied (4)Dissatisfied (6)Undecided (0)-Use formative assessment system. (2)-Discourage rote memorization of contents by giving application based problems as much as possible. (3)-Check understanding of students rather than checking that the student can solve a sum or not. (2)-Don’t give sums directly from the textbook or five year (previous papers). (4)Satisfied (7)Dissatisfied (3)Undecided (0)-Agreed but tests should be held more frequently. (3)-More quizzes and mental maths tests should be administered. (2)-Teachers should construct their own problems rather than taking them from past papers. (3)Q.11 Are you satisfied with the current pattern of the mathematics paper (GCE/SSC)? In your opinion, what improvements should be made in it?Responses of Experts (SSC-System)Responses of Experts (GCE-System)Satisfied (2)Dissatisfied (8)Undecided (0)-Questions should not be taken from textbooks / previous papers. (3)-Pattern of the paper should be such that it discourages guess work and selected study habits. (2)(Contd…….)-Pattern of questions should be such that students can use their skills to solve them (2).-Vigilance system during examination should be improved. (4)-Workshops/Refresher-Courses for papers setters and checkers should be organized.(3)-System of assessing the papers should be improved. (2)Satisfied (7)Dissatisfied (2)Undecided (1)-Agreed but selective learning should be discouraged. (3)-More application based questions should be included. (2)-It should test deep understanding instead of basic knowledge. (1)-------Q.12 What are the major strengths of the current system of teaching and learning mathematics in your opinion?Responses of Experts (SSC-System)Responses of Experts (GCE-System)-It provides strong factual and procedural knowledge of different operations in mathematics. (1)-Enables the students to do computation with knowledge of long procedures and formulae. (1)-Provides strong content knowledge for further studies. (3)-Develops among students, a skill of presenting their learned material in a well-organized and orderly manner. (1)-It develops a habit of doing neat and tidy work in students. (1)(Contd…….)- A sense of responsibility by maintaining the notes (solution of problem in the textbooks) and getting them checked from the teachers regularly. (1)-Fair and unbiased. (1)-It is internationally recognized. (2)-No choice of leaving any topic from the prescribed syllabus. (1)-There is room to incorporate different methods of teaching in this system. (1)-Flexibility of appearing for CIE paper either in May or November, twice a year.-Examinations are conducted under strict vigilance. No chance of using unfair means. (3)- Paper is balanced in terms of calculations done mentally (Paper-I) and using calculators (Paper-II). (1)- A standardized system of assessing the papers. (1)Q.13 What are the major weaknesses in your opinion in the current system of mathematics education?Responses of Experts (SSC-System)Responses of Experts (GCE-System)-There is a discontinuation of one complete year for the study of mathematics in the system. Students after class VIII study mathematics in class X. The suspension of mathematics in grade IX is the biggest weakness of the current system. (2)-Syllabus is too lengthy for a 9-month session. (1)-System of current examinations encourage cramming. (1)- System encourages selected study of some topics, leaving some of the topics completely untouched. (2)-There is a wide gap of standards between SSC and HSC. (1)-Massive use of unfair means. (3)(Contd…….)-This system is very expensive. (4)-Not for majority of the students. (1)-It is based on (2 + 212 ) hour’s performance of students. Learning of students in previous 4 years is to be incorporated. (1)-Excessive use of private tuitions. (2)-Very lengthy syllabus. (2)-------Q.14 What changes would you like to suggest for the overall improvement of mathematics education?Responses of Experts (SSC-System)Responses of Experts (GCE-System)-Training sessions for teachers. (8)-Revision of curriculum. (6)-Eliminating the one year suspension of mathematics during class IX. (2)-Improving the assessment system. (6)-Improving the textbooks. (4)-Making neutral places as centers of examination to curb the problem of cheating. (1)-Coursework should be included along with the final paper. (3)-Increasing the contents that produce thinking skills. (8)-Discouraging the trends of tuitions especially shortcuts (crash-courses) at different private tuition centers. (4)-Increasing the role of school. (5)-Discouraging the increasing trend of the practice of only selected contents at tuition centers. (2)-This system should be in the range of as many students as possible. (2)Summary, Discussion and ConclusionsThe comparative analysis of the responses of the subject experts revealed that in both systems, there is a complete agreement on the significance of mathematics in the school curriculum, but GCE experts showed a comparatively higher satisfaction level than the SSC experts with the current practice of teaching. The issues highlighted by SSC / GCE experts may be summarized and concluded as follows.The clarity of aims and objectives of teaching mathematics, as expected in their corresponding curricula, was found much higher in GCE subject experts than the SSC experts. The aims and objectives of GCE curriculum and its assessment were defined in their curriculum and were easily available on the internet. Moreover, teachers were informed of the aims and objectives in this system. On the SSC side, neither were these easily approachable nor was there a trend of informing teachers of them by school managements.A suspension of mathematics at grade IX level was found on SSC side but no such discontinuity of mathematics educationwas found in GCE system at school level.GCE curriculum was found to be relatively much broader in terms of key areas of the content than that of SSC curriculum.The contents of GCE curriculum were more logically sequenced than the SSC curriculum contents.There was relatively more drill (practice) of the learned material in GCE than SSC system.There was no significant difference in the selection and organization of the contents for instruction but GCE teachers were more inclined towards the concentric approach which was missing on the SSC side.GCE system was focused on ‘depth versus breadth’, while SSC system have focus on ‘breadth versus depth’. It means that teachers of GCE system emphasize proficiency in basic knowledge and skills while on the other side, there is a focus on furthering content knowledge.There was a wide gap of standards in terms of different areas of contents of SSC and HSC, while there wasn’t such a big difference between the course contents of O-Level and A-Level mathematics.Textbooks on GCE side have an internal coherence which is comparatively lower on SSC side. GCE schools use a series of 4 books as the syllabus of O-Level. Almost all schools use these four books from grade VI till XI (O-Level). Students therefore do not face trouble in changing schools. On the other side, schools in the SSC system do not use the same series of books from grade VI till VIII. Moreover, there is a suspension of mathematics for one year in grade IX, after which all the schools have to use the same book of Sindh Textbook Board in grade X.The principle of cultural value has been found in the textbooks of SSC system which is missing on the GCE side because the books used by GCE schools are not written by local authors. GCE students face problems in conceptualizing a given situation when names of persons, places, and objects etc. do not resemble their surroundings.The contents for the development of problem solving skills were quite large in number in GCE course compared to SSC course.The worked examples in the textbooks of GCE system are more self-explanatory and encompass all the procedures that are to be used in the solution of problems on a certain topic. Formative assessment was more systematic on GCE side than SSC system.Formative assessments are done systematically on regular intervals and students’ performance is accumulated in their final exam’s performance. As a result, students take these assessments seriously. SSC system relies only on summative assessments. Moreover, in most SSC schools, there is a terminal system (semester system). They move forward on topical bases. Once a topic is taught and assessed in a term, it does not come in the next term or even in the final examination.There was no difference in the methods of SSC and GCE systems for the preparation of final examination. Both systems emphasize their students to solve previous exam papers for the preparation of final examination.There was a significant difference in the approaches used by GCE and SSC systems to solve previous papers. GCE system emphasizes on providing students with an experience of putting a problem on a topic in different situations in various ways. Moreover, the solution of papers is also done for extra practice and rehearsal of the examination. On the other hand, SSC system does this with the approach of prediction of questions for the upcoming papers.There was a higher trend for selected study on SSC side than GCE side.The pattern of SSC papers is fixed. Questions are taken as they are in textbooks. Questions from certain chapters are always given in specific sections. An ample amount of choice is given to select questions from different sections. As a result, there is a trend of selected study in this system. On GCE side, neither are questions taken from textbooks, nor is there a fixed pattern of questions in specific sections. Moreover, there is a minor choice of just one question in GCE paper. As a result, students have to prepare the entire syllabus.GCE examinations were found to be held under strict vigilance while there is a common observation of the use of unfair means in SSC examinations.There was more flexibility of taking examination on GCE side. Students can appear for the examination twice in a year either in May or in November. On SSC side, there is only one annual examination a student can appear in. However, a supplementary examination is held for those candidates who have not passed their annual examination.The approach of teaching mathematics of GCE teachers was ‘content-focused’but with an emphasis on understanding and performance. The approach of SSC teachers, on the other hand, was also ‘content-focused’ but emphasis is simply on performance. SECTION III: CONTENT ANALYSISAnalysis of the Contents of Textbooks and Question PapersA comparison of the contents of textbooks as well as the patterns of assessment in both systems has been presented in the following tables.Table 193(a): SetsSSCGCESetsBasic operations on SetsUnion, intersection, difference, complementSymmetric difference ( A?B)Use of Venn DiagramPower SetDE Morgan’s LawsCartesian Product & its GraphsFunction and its Types(Sindh Textbook Board Mathematics for IX-X,2012,Ch.1)SetsBasic operation on SetsUnion,intersection,difference,complement-------Use of Venn diagrams-------DE Morgan’s Laws--------------(New Syllabus Oxford Mathematics Book2,Ch.10), (Book3; Addendum,Ch.I)Nature of the ContentsGeneral Objectives-Cognitive *Understand and use set language.*Solve problems involving basic operations on sets.------- (Contd…….) -Psychomotor* Enable students to draw Venn diagrams of given setsGeneral Objectives-Cognitive*Same*Same*Use of Venn diagrams in solving daily life problems.-Psychomotor* Enable students to draw Venn diagrams from the given information in any form.Ingredients of the contents*Methods to operate on sets were explained through worked examples and sets of Real numbers or letters of English alphabet were mostly used.Similar sums were given in further exercises.-------Ingredients of the contents* Methods to operate on sets were explained through worked examples and sets of concrete objects were mostly used. Similar problems were given for further exercises.*Word problems were given, where application of basic operations of sets was required as well as the proper use of Venn diagrams, for their solution.Presentation*Black& white color was used to differentiate among parts of Venn diagrams.Presentation*Different colors were used to differentiate among different parts of Venn diagrams.Sequencing: AppropriateSequencing: AppropriateIntegration with other Topics-------Integration with other TopicsProblems were given in which Venn diagrams were required using properties of different types of triangles and quadrilaterals. It has also been linked with dimensions and area of rectangle.Language: Simple English language was used but with a rich use of symbols and notations.(Contd…….)Language:Mostly simple English language was used with a mild use of Symbols and notations where parison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSCand GCE)Questions taken from the Textbooks(2013,Q2 from Ex 1.3,Q5); (2011,Q2 from Ex1.2,Q17)Questions taken from the Textbooks-------Questions taken from Previous Papers(2007,Q2a&b from 2004,Q2a&b);(2008,Q2b from 2000,Q2b); (2002,Q2b from 2000,Q2b); (1997,Q2b from 1995,Q2a)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Questions taken from Previous Papers-------(O-Level Classified Mathematics, Unit,10)Repetition of Similar Questions:In the following questions exactly same operation was repeated except some minor changes of numbers in the given sets.1.Cartesian Product(2013,Q2); (2009,Q2b); (2006,Q2b); (2003,Q2b); (2001,Q2b); (1999,Q2b); (1996,Q2b)2.Power Set(2008,Q2b); (2007,Q2a); (2004,Q2a); (2002,Q2b); (2000,Q2b); (1998,Q2b); (1997,Q2b); (1995,Q2b)(Contd…….)3.Proof of De Morgan’s Laws (2012,Q2); (2008,Q2a); (2007,Q2b); (2006,Q2a); (2005,Q2a); (2004,Q2b); (2003,Q2a); (2002,Q2a); (2001,Q2a); (2000,Q2a); (1999,Q2a); (1998,Q2a); (1997,Q2a)4.Symmetric Difference (A?B)(2011, Q2); (2010, Q2).(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Repetition of Similar QuestionsNo pattern of repetition of similar questions has been found.-------(O-Level Classified Mathematics, Unit,10)-------(O-Level Classified Mathematics, Unit,10)Questions in a Particular Section of PaperThe question on Sets is always given as the first question in Section A of the paper.Questions in a Particular Section of Paper-------Topics Never Assessed*Use of venn diagrams in Sets.*Graphical representation of Cartesian Product.*Function and its typesTopics Never Assessed-------Choice to Leave the Question in PaperAlwaysChoice to Leave the Question in PaperNeverQuestions on Application of Concepts in Real Life Problems-------(Contd…….)Questions on Application of Concepts in Real Life ProblemsA clear majority of questions entail a problem from practical life is given. Sample Questions from SSC and GCE PaperQ13295650423545U={x/x∈N, x≤ 10}A={2,4,6,8,10}B={3,6,9,10}Prove that (A ∪ B)? = A? ∩ B?(Annual,2012, Q2)Q2. If A = {1,2,3,4} and B = {2,4,6,8}, Show that( A ∪ B )?(A∩B) = A ? B(Annual,2011,Q.2)(Contd…….)*No question has been found in the previous 20 years of papers where a Venn diagram is required.Q1 B H3 15 16 5 2 p 9 S qIn a survey, 60 students are asked which of the subjects Biology (B),History (H ) and Spanish (S) they are studying.The Venn diagram shows the results.27 students study History.Find the values of p and q. Find n (H ?). Find n(B∪H ) ∩S’(N2012, p1,Q14) Q2.Mary has 50 counters. Some of the counters are square, the remainders are round.There are 11 square counters that are green. There are 15 square counters that are not green.Of the round counters, the numbers that are not green is double the numbers that are green.By drawing a Venn diagram, or otherwise, find the number of counters that are(i) round,(ii) round and green, (iii) not green(J2008,p2,Q5a)Table 193(b): System of Real Numbers, Indices and RadicalsSSCGCESystem of Real Numbers Exponents and RadicalsProperties of Rational NumbersDecimal Fractions as Rational and Irrational Numbers.Properties of Real NumbersExponents and Laws of ExponentsRational ExponentsThe nth Root of a Positive Real NumberSurds-------(Sindh Textbook Board Mathematics for IX-X, 2012, Ch., 2).(Contd…….)Rational Numbers, Integers, Indices and Standard FormRational Numbers.Terminating and Recurring Decimals Properties of Real NumbersIndices and Laws of IndicesFractional IndicesRadical and Index Form-------Standard Form (New Syllabus Oxford Mathematics Book1, Ch., 2, 3 & Book3, Ch., 2).Nature of the ContentsGeneral Objectives-Cognitive *Identification of the properties satisfied by Rational Numbers*Recognition of the property used in a given equation on Real Numbers.*Differentiate between Rational and Irrational Fractions.*Solve problems involving exponents using laws of Exponents.*Same*Use of the method of Rationalization in solving Surds.-------General Objectives-Cognitive*Use of the properties satisfied by Rational Numbers on Integers.*Use of the properties of Real Numbers on Integers.*Differentiate between Rational and Irrational Fractions and to covert fractions in recurring decimals.*Same*Enable students to solve sums having fractions as indices.-------*Solve simple equations involving indices.Ingredients of the Contents*Which property is used in the following example?i) 0.4+9=9+0.4 {Ans: (Commutative)}ii) x(y+z)=xy+xz {Ans: Distributive property of multiplication w.r.t addition}(Contd…….)iii) -5 < -4 0 < 1 {Ans: Additive property}*Contents to learn properties of Rational Numbers were given.*Contents on Laws of Exponents (similar)Ingredients of the Contents* Complete by appropriate operation symboli) (-5) □ (3) = (3) □ (-5) = -2 { Ans: +}* Replace each □ by an appropriate integerii) (-3)×(□+8) = (-3)×(-28) + (-3)×(8)= □{Ans:-28 & 60}*Fill in □ by < or >iii) 3-27□ -16*Contents on Arithmetical Operations on Rational Numbers & Problem Solving Involving Rational Numbers were given.For Example: James uses 13 of his land for growing durians, 14for bananas, 38 for guavas and the remaining 9 hectares for mangoes. What is the total area of his land?* Contents on Laws of Indices (similar)Presentation*Contents regarding properties of Real Numbers were presented in a way to name of property used.*Problems to practice the Laws of Exponents were presented.*Detailed sums on Rational Exponents were given.e.g.: Simplifyxlxml+m× xmxnm+n× xnxln+l(Ex,2.7,Q8)Presentation*Contents on properties of Real Numbers Reveals that use of properties was required instead the name of property.*Problems to practice the Laws of Indices were there with an addition of simple equations involving indices.e.g.: Solve 5x = 1*Simple sums on Fractional Indices were given.e.g.: Simplify3a5b6c4 (Book3,Ex,2e,Q2g)Sequencing: AppropriateSequencing: AppropriateLanguage:Simple (Contd…….)Language: SimpleComparison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSC and GCE)Questions taken from the Textbooks(2013,Q3 from Ex 2.7,Q7); (2012,Q3,Q4fromEx2.7,Q8 & Ex2.8,Q2); (2011,Q7 from Misc. II,Q8(i); (2010,Q3 from Ex2.7,Q8); (2008,Q3a from Misc.ExII,Q8(i); (2004,Q3a from Ex2.7,Q10); (2000,Q3a from Misc.ExII,Q8(ii); (1998,Q3a from Ex2.7,Q10); (1997,Q3a from Misc.ExII,Q8(iii)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Questions taken from the Textbooks-------(O-Level Classified Mathematics, Unit,1A-1D)Questions taken from Previous Papers(2009,Q3a, from 2006,Q3a);(2008,Q3a from 2007,Q8b; (2007,Q3a from 2003,Q3a); (2005,Q8a from 2004,Q3a)Questions taken from Previous Papers-------(O-Level Classified Mathematics, Unit,1A-1D)Repetition of Similar Questions:In these questions, exactly same operation was repeatedly required without any minor change in numbers. (Contd…….)1.Ex.2.7Q7: (2013; 2012; 2010)Q10 :(2005; 2004; 1998).2.Ex2.7(Old Syllabus)Q8: (2002),Q19: (2009; 2006; 1999)In the following10 years(1998,1999,2002,2004,2005.2006,2009,2010, 2012, 2013), question on this topic has been given from just 5 questions i.e. Q7, 8, 10, 8(Old Syllabus), 19(Old Syllabus).2.Misc.ExIIQ8(i): (2011; 2008; 2007)Q8 (ii): (2003; 2000), Q8 (iii): (1997).*Question on this topic has been given from overall 6 questions in last 17 years.(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Repetition of Similar QuestionsAddition, subtraction, multiplication and division of fractions have been found in pattern of repetition.(J1999,p1,Q1;J19997,p1,Q12; 1998,p1,Q2; J2001,p1,Q4; J2002,p1,Q2; J2006,p1,Q2; J2007,p2,Q4; J2008,p1,Q1; J2009,p1,Q2; J2010,p1,Q2; J2011,p1,Q3).*These questions carry just one mark and were presented in the beginning of paper1.*No other pattern of repetition has been found. A variety of ways have been found in which questions were given for the application of the learnt concepts.(O-Level Classified Mathematics, Unit 1A – 1D).Questions in a Particular Section of PaperThe question on this topic has always been found in Section B of the paper.Questions in a Particular Section of PaperQuestions on this topic have always been found in ics Never Assessed*Besides some fill in the blanks no other question except the above said 6 questions has been given in major section of the paper.(Contd…….)Topics Never Assessed-------Choice to Leave the Question in PaperAlwaysChoice to Leave the Question in PaperNeverQuestions on Application of Concepts in Real Life Problems-------Questions on Application of Concepts in Real Life Problems-------Sample QuestionsQ1.x2axa+bx2bxb+cx2cxc+a(Annual, 2011, Q7)Q2.Simplify 1252×864213 (June,2005,Q8a)(Contd…….)Q1.Evaluate14-2Evaluate 6423Simplify 4x2y9x4y12 (J2011,p1,Q21)Q2.It is given that N= 87 × 132Complete the statements.88×132=N+ -------87×131=N ? ------Hence evaluate this88×132 ? 87×131 (June,2005,p,1,Q15)Table 193(c) AlgebraSSCGCEAlgebraa)Algebraic Expressions-Variables and Constants, Coefficient, Algebraic expressions and their kinds.-Polynomials and their Classification. - Order of Algebraic Expressions- Value of Algebraic Expressions-Fundamental Operations on Algebraic Expressions.- Remainder Theorem.- Formulae and Their Applications.-------{Sindh Textbook Board Mathematics for IX-X, 2012, Ch., 4}b) Factorization, HCF, LCM, Simplification and Square Root- Factorization of the Form; a2-b2.- Factorization of the Form;x2+bx+c.- Factorization of the Form; a3+b3 and a3-b3 .- Factorization of the Form; a3+b3 +c3-3abc.- Factorization of the Form; a2b-c+b2c-a+c2a-b.(Contd…….)- Factorization using Remainder Theorem.- H.C.F. and L.C.M.- Simplification of Algebraic Fractions.- Square Root by Factor/Division Method.-------{Sindh Textbook Board Mathematics for IX-X, 2012, Ch., 5}c)Algebraic Sentences- Solution of Simple Linear Equations in One or Two Variables.- Graphical solution of two simultaneous Linear Equations.- Solution of Equation Involving Radicals in One Variable.- Solution of Equation Involving Absolute Value in One Variable.- Inequalities.- Solution of Quadratic Equations by Factorization, Completing Square Method or by Quadratic Formula.--------------(Contd…….){Sindh Textbook Board Mathematics for IX-X, 2012, Ch., 1, PartII}Algebraa)Fundamental AlgebraWriting an Algebraic Expression.Use of Brackets in Simplifications.-------SameSameSameSame--------------Construction of Formula.{New Syllabus Oxford Mathematics Book1, Ch., 5}b) Expansion and Factorization of Algebraic Expressions.Algebraic Manipulation and FormulaeSameSame----------------------------L.C.MSame-------Problem Solving involving Algebraic Fractions.{New Syllabus Oxford Mathematics Book2, Ch., 3,4}c)Algebraic Equations and Simple InequalitiesSolution to Quadratic Equations-Same-Same-Same--------Same-SameProblem Solving with AlgebraProblem Solving Involving Quadratic Equations.{New Syllabus Oxford Mathematics Book1, Ch., 7; Book 2, Ch., 5 & Book3, Ch., 1}Nature of the ContentsGeneral Objectives-Cognitive *Name different kinds of Algebraic Expressions and Classify Polynomials.--------------*Do fundamental operations (+, ?, × and ÷) on Algebraic Expressions.*Find remainder by means of Remainder Theorem.*Apply formulae on simplifying and factorizing Algebraic Expressions.-------*Factorize an Algebraic Expression by means of Remainder Theorem.*find L.C.M, H.C.F and Square Root of an Algebraic Expression. (Contd…….)*Solve a pair of simultaneous equations graphically.*Solve equations involving Radicals/Absolute Value.*Solve a quadratic equation using quadratic formula.-------General Objectives-Cognitive-------*writing of an Algebraic Expression*Translate a problem into a mathematical formula/equation choosing letters to represent quantities from given information.*Same-------*Same but application of only three formulae is required.*Solve word problems using Algebra.-------* L.C.M only*Same*Equations involving Radicals only*Solve a quadratic equation by factorization, completing square method or by applying quadratic formula.*Translate a given word problem into a quadratic equation and solve it.Ingredients of the Contenta)*Find the type (w.r.t.terms) and degree of the given polynomialx4y + y2 +y3*Write the given Algebraic Expression in ascending and descending order w.r.t ‘a’2a3y+ 4a y2 + 5a2y3*Find the value of 4a2?3ab +bc when a=0, b=4 and c=1*Addition, Subtraction, Product and Division of Polynomials.*Find the remainder by means of Remainder Theorem whenx3+x?1 is divided by x+1*Application of the Formulae:1. a(c+d)=ac+ad2. (x+a)(x+b)=x2+(a+b)x+ab3. (a+b)2=a2+2ab+b24. (a?b)2=a2?2ab+b25. (a+b)(a?b)=a2?b26. (a+b)2=(a?b)2+4ab7. (a?b)2=(a+b)2?4ab8. (a+b)2?(a?b)2=4ab9. (a+b)2+(a?b)2=2(a2+b2)10. (a+b+c)2=a2+b2+c2+2ab+2bc+2ca11. (a+b)3=a3+3a2b+3ab2+b312. (a?b)3=a3?3a2b+3ab2?b313. a3+b3=(a+b)(a2?ab+b2)14. a3?b3=(a?b)(a2+ab+b2)15. (a+b+c)( a2+b2+c2?ab?bc?ca) = a3+b3+c3?3abc(Contd…….)b)*Factorization of the Expressions of the types1. a2±2ab+b2=(a±b)22. a2?b2=(a+b)(a?b)3. a3±b34. a3+b3+c3?3abc5. a2b-c+b2c-a+c2a-b*Factorization by means of Remainder Theoremx3+x2?2*Find H.C.F & L.C.M by Factor/Division methodx3?y3 , x4?y4*Simplification of Algebraic FractionsSimplifya2+aba2-ab÷a2+ab+b2a3- b3 (Ex.5.11,Q11)*Find the Square Root by Factor/Division MethodFor what value of ‘p’, 4a4+4a3?3a2?pa+1 will be a perfect square? (Ex.5.14, Q 11).(Contd…….)c)*Solution of a pair of linear equations simultaneously by graphical method. (PartII, Ex, 1.2)*Solution of equations(i) 4x-5= 3x+7(ii) -6+5x-3=3*Solution of inequalities3(x+5) > 2(x+2)+8*Solution of quadratic equation by factorization, completing square method and by quadratic formula. (PartII, Ex, 1.6,1.7,1.8)(Contd…….)Ingredients of the Contenta)*Write an algebraic expression from the given information(i)Add 2x to twice 3y.(ii)Subtract 5x from half of y. (Book1, Ex, 5a)*Translate the given word expression into an algebraic expression(i)Eight more than half of a number.(ii)One quarter of a number which is 4 less than m? (Book1,Ex, 5a)*Addition, Subtraction and Product of algebraic expressions.*Simplify algebraic expressions with fractional coefficients.Simplify 2x 7 + x+15 (Book,Ex, 5f)(Contd…….)*Factorization(i)By taking common i.e. expressions of the type 4x + 12, 4m ?6my ?18mz(ii)By grouping first and then taking common.e.g.: 14cx + 10dy – 4cy – 35xd (Book1,Ex, 5g)*Solving simple equations(i) 5(7x-3) = 14(2x-2)(ii)5+4x9= -1*Evaluation of an Algebraic FormulaIf 1a = 1b + 1c +1d, find ‘c’ when a=2, b=3 and d=5. (Book1,Ex, 7d)*Construction of Formula(i)The vertical angle (xo) of an isosceles triangle whose base angle is yo(ii)A boy is b years old and his father is 6 times as old as him. Find the father’s age. Find also sum of their ages in y years’ time. (Book1,Ex, 7f,g)*Solution of Word Problems through Algebrae.g.: Tom, Dick and Harry share $256. Dick’s share is four times as much as Tom’s and Toms’ share is one-third of Harry’s. How much is each of their shares?(Book1,Ex, 7h)b)*Expansion and factorization using Formulae(i) a2±2ab+b2=(a±b)2(ii) a2?b2=(a+b)(a?b)*Factorization of quadratic expressions by breaking the middle term/trial and error method.*Simplification of Algebraic Fractions(i) m2-9m2-7m+12(ii) 12ba3 3ab2 ÷ 4abc3ad×14d2 7bc(iii)y2-4y+42-6y ×2y+43y2-12 (Book2,Ex,4b,c,d)*Addition and Subtraction of Algebraic Fractions by taking L.C.M.Simplify 12a-3 - 23-2a + 189-4a2*Changing the subject of a formulaMake (h) the subject of the given formula: pq=13nh+2k3h+k (Book2,Ex.4j)*Problem Solving Involving Algebraic Fractions.A piece of wood is 5cm longer than a second piece and 34 of the second piece is equal to 35 of the first, what is the length of the second piece? (Book2, Ex, 4h).c)*Same (Book2, Ex, 8d)*Changing the subject of a formula(i) Make ‘a’ the subject of the given formula 3a-2= ab(ii) Find the value of ‘c’ when b=9 and a=4 a=3b+cb-c (Book2, Ex, 4j,k)*Find the largest and smallest values of (i) x2+y2(ii) x2?y2 if ?10 ≤ x ≤ 10 and ?5 ≤ x ≤ 5* Show, unshaded, the region satisfied by the following inequalities.x ≥ 0 , y ≥ 0 , x+y < 7 , y > 2x(Book3, Ex,3d; Book4, Addendum,Ch,III)*Solution of word problems by forming an equation that reduces to quadratic and then solving it using any method.(Book2, Ex, 3h)Presentation*Contents have a number of operations on Algebraic Expressions. *A rich use of formulae in simplification/factorization has been found.*Content appeared to make the learners a good user of mathematical formulae.-------Presentation*Contents have only basic use of operations on Algebraic Expressions.*Minimum Use of formulae has been observed. *Content appeared to make the learners able to use algebra in problem solving.*Content presents a rich use of algebra in solving word problems.Sequencing*Content on Algebra has been presented in a logical sequence. *Content proceeds from simple to complex.Sequencing*Same*Content flow was very natural. First, the content relates word expressions to algebraic expressions, then it moves to arithmetical operations and in the end, its purpose was that the learner should be able to set up an equation from a given situation and use the learned algebraic operations to solve a daily life problem.Integration with other TopicsObservedIntegration with other TopicsObserved(relatively more)Language:Simple (Contd…….)Language: SimpleComparison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSC and GCE)Questions taken from the TextbooksThese questions are found either taken exactly from the textbook or in a few cases, with minor changes in signs or numbers.*Finding the value using formulaeEx,4.7, 4.8 and 4.9(2011,Q4 from Ex 4.9,Q2); (2010,Q5,from example4 of Ex4.7);(2009,Q3b from Ex, 4.7,Q1);(2008,Q5a from Ex4.8,Q2(vi); (2007,Q3b from Ex4.7,Q1); (2006,Q3b from Ex,4.9,Q2(v); (2005,Q3a from Ex4.7,Q1,2); (2004,Q3b from Ex,4.7,Q1); (2003,Q3a from Ex4.7,Q1); (2002,Q3b from Ex,4.9,Q2(v)(2000,Q7b from Ex,4.7,Q5);(1999,Q6b from Ex4.7,Q1);(1998,Q6b from Ex4.7,Q4);(1997,Q6b from Ex4.7,Q1);(1996,Q3b from Ex4.7,Q1);(1995,Q9a from Ex4.7,Q1);{Ex,4.7,Q1 has been taken 10 times in 20 years papers}*Factorization of the typea2b-c+b2c-a+c2a-bEx, 5.6(New exercise added in 2009)(2013,Q6 from Example1 of Ex,5.6);(2012,Q6 from Ex,5.6,Q2);(2011,Q5 from Ex,5.6,Q1);(2010,Q6 from Ex,5.6,Q1);*Factorization by means of Remainder TheoremEx,5.7 (New Syllabus) which was Ex,4.7(Old Syllabus)(2013,Q20b from Ex,5.7,Q6);(2012,Q20b from Ex,5.7,Q3);(2011,Q20b from Ex 5.7,Q2); (2010,Q20b from Ex,5.7,Q9);(2009,Q8a from Ex, 4.7,Q5);(2008,Q5b from Ex5.7,Q3); (2007,Q8a from Ex4.7,Q8); (2006,Q8a from Ex,4.7,Q11); (2005,Q6b from Ex4.7,Q13); (2004,Q7a from Ex,4.7,Q5); (2003,Q8a from Ex4.7,Q8); (2002,Q6b from Ex,4.7,Q12);(2001,Q6b from Ex,4.7,Q5);(2000,Q7a from Ex,4.7,Q3);(1999,Q7b from Ex4.7,Q7);(1998,Q7b from Ex4.7,Q5);(1997,Q3b from Ex4.7,Q3);(1996,Q9b from Ex4.7,Q3);(1995,Q3b from Ex4.7,Q8);{Q5(3 times), Q5(4 times), Q8(3 times)}*Square RootEx,5.14(New Syllabus) which was Ex,4.11(Old Syllabus)(2013,Q8 from Ex,5.14,Q9);(2012,Q8 from example,4 of Ex,5.14);(2011,Q8 from Ex 5.14,Q12); (2010,Q16 from example,4 of Ex,5.14);(2009,Q5b from Ex, 5.14,Q10);(2008,Q3b from Ex4.11,Q33;)(2007,Q5a from Ex4.11,Q31;)(2006,Q7a from Ex,4.11,Q33); (2005,Q9b from Ex4.11,Q31); (2004,Q5b from Ex,4.11Q31); (2003,Q5a from Ex4.11,Q31); (2002,Q7a from Ex,4.11,Q33)(2001,Q6a from Ex,4.11,Q30);(1999,Q3b from Ex4.11,Q35);(1998,Q3b from Ex4.11,Q14);(1997,Q7a from Ex4.11,Q13);(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)(Contd…….)FactorizationOne question having four expressions of the following types(i) a4 + b4(ii) ax2 + bx + c(iii) a3±b3(iv)a3+b3+c3?3abcTaken from Ex, 5.5, 5.3, 5.4 and 5.5 respectively.Graphical Solution of Simultaneous EquationsThe question has always been taken from the textbook.Solution of Quadratic Equation using Quadratic FormulaThe question has always been taken from the textbook.Solution of Equations involving Radical/Absolute ValueThe question has always been taken from the textbook except in 2013 and 2012. In these two years, the question on this topic has not been given in the main section of the paper.Instead, it has been given in Section A as an MCQ.(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)(Contd…….)Questions taken from the Textbooks---------------------(O-Level Classified Mathematics,Unit,2A-2D)(Contd…….)----------------------------(O-Level Classified Mathematics, Unit,2A-2D)(Contd…….)---------------------(O-Level Classified Mathematics, Unit,2A-2D)--------------(O-Level Classified Mathematics, Unit,2A-2D)Questions taken from Previous PapersThe above list shows the number of times a question has been taken from the textbook. It is clear from the list that the same question has been taken many times.Questions taken from Previous Papers------Repetition of Similar Questions:In these questions, the same operation is repeated without any minor change in numbers. Finding the value using formulae(Ex,4.7 new syllabus){Ex,4.7,Q1 has been taken 10 times in 20 years papers}Remainder Theorem (Ex,4.7 old syllabus){Repetition:Q5(3 times),Q5(4 times),Q8(3 times)}Square Root (Ex,4.11 old syllabus){Repetition:Q31(4 times),Q33(3 times)}(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Repetition of Similar Questions-------(O-Level Classified Mathematics, Unit 1A – 1D).Questions in a Particular Section of PaperThe question on this topic has always been always given in Section A of the paper.(Contd…….)Questions in a Particular Section of PaperQuestions on this topic have always been found in ics Never Assessed*No other question besides the 6 mentioned questions has been found in the major section of the ics Never Assessed-------Choice to Leave the Question in PaperAlwaysChoice to Leave the Question in PaperNeverQuestions on Application of Concepts in Real life Problems-------Questions on Application of Concepts in Real life ProblemsQuestions on application of algebra in real life problems have been observed in both paper 1 and paper 2.Sample QuestionsQ.1Factorize any four of the following:x2 – yz + xy – xz4x2 +5x – 21a4 + 41 +2ab – (a2 + b2)x3 – x – 2y + 8y3a3 – b3 – 27c3 – 9abc(Annual,2008,Q4)(Contd…….)Q.2Find the solution set of the following equations graphically;5x +7y =137x + 6y =3(Annual,2010,Q18)Q.3Find the factors of x3 – x2 ?14x + 24 with the help of remainder theorem.(Annual,2012,Q20b)Q.1(a) Factorize completely(i) 15x2 + 10x,(ii) t2 – 2t – 15.(b) Solve 4(x – 0.3) = 3(x – 0.2) (June,2008,paper1,Q19)Q.2Ahmed throws a ball to John. The ball travels 10 meters at an average speed of x meters per second.(a) Write an expression, in terms of x, for the time taken, in seconds, for the ball to travel from Ahmed to John. (b) John then throws the ball to Pierre.The ball travels 15 meters.The ball’s average speed is 0.5 meters per second greater than the ball’s average speed from Ahmed to John.Write an expression, in terms of x, for the time taken, in seconds, for the ball to travel from John to Pierre. (c) The time taken between John catching the ball and then throwing it to Pierre is 2 seconds.The total time taken for the ball to travel from Ahmed to Pierre is 7 seconds.Write down an equation in x, and show that it simplifies to 2x2 – 9x – 2 = 0. (d) Solve the equation 2x2 – 9x – 2 = 0, giving each answer correct to 2 decimal places. (e) (i) Find the average speed, in meters per second, of the ball as it travels from John to Pierre. (ii) How much longer does it take for the ball to travel from John to Pierre than fromAhmed to John?Give your answer in seconds.(June,2010,paper2,Q8)Give your answer in seconds.Table 193(d): MatricesSSCGCEMatrices*Introduction*Addition, subtraction and product of Matrices*Inverse of a Matrix*Solution of Simultaneous Linear Equations by Cramer’s Rule-------(Sindh Textbook Board Mathematics for IX-X, 2012, Unit, 6, Part-I).MatricesSameSameSame*Solution of simultaneous equations by Matrix method*Use of Matrices in Solving Everyday Life ProblemsNew Syllabus Oxford Mathematics Book3, Ch., 5).Sequencing: AppropriateSequencing: AppropriateIntegration with other Topics-------Integration with other TopicsThe contents are integrated with the solution of every day mathematics problems of sale, purchase, profit and loss.Language:Simple Language: SimpleComparison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSC and GCE)Questions taken from the TextbooksNew Edition Sindh Text Book Ex 6.4(Multiplicative Inverse of a Matrix) & Ex 6.5(Cramer’s Rule)(2013,Q9 from Ex 6.5,Q7); (2012, Q9 from Ex6.5, Q1); (2011, Q9 from Ex6.4, Q5a);(2010, Q7 from Ex6.5, Q3).(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Questions taken from the Textbooks-------(Contd…….)-------(O-Level Classified Mathematics, Unit,12)Questions taken from Previous Papers(2009,Q5a, from 2008,Q8a);(2007,Q5b from 2003,Q5b);( 2007,Q3a from 2006,Q6a);( 2002,Q6a from 1999,Q7a)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Questions taken from Previous Papers-------(O-Level Classified Mathematics, Unit,12)Repetition of Similar Questions:Solution of simultaneous equations by Cramer’s Rule2013,2012,2010 (new exercise added in 2009)(3 times)Multiplicative Inverse2011,2009,2008,2007,2006,2003,2002,2001,19991,1998,1997)(11 times)(Contd……..)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Repetition of Similar QuestionsAddition, subtraction, multiplication and division of fractions have been found in pattern of repetition.(J1999,p1,Q1); (J19997,p1,Q12); (1998,p1,Q2); (J2001,p1,Q4); (J2002,p1,Q2); (J2006,p1,Q2); (J2007,p2,Q4); (J2008,p1,Q1); (J2009,p1,Q2); (J2010,p1,Q2); (J2011,p1,Q3).*These questions are just 1 mark questions that are presented in the beginning of paper1.*No other pattern of repetition has been found. A variety of ways have been found in which questions are given for the application of the learned concepts.(O-Level Classified Mathematics, Unit, 12).Questions in a Particular Section of PaperThe question on this topic has been seen in Section B of the new pattern of paper; previously it has been given in Section A.Questions in a Particular Section of PaperQuestions on this topic have always been found in ics Never Assessed-------Topics Never Assessed-------Choice to Leave the Question in PaperAlwaysChoice to Leave the Question in PaperNeverQuestions on Application of Concepts in Real Life Problems-------Questions on Application of Concepts in real Life ProblemsQuestions on practical application of Matrices in real life problems were included.Table 193(e): StatisticsSSCGCEInformation Handling*Introduction, Key Terms, Types of Variables, Types of Data*Collection and Presentation of Data*Frequency Distribution, Graphs (Histogram and Frequency Polygon)-*Bar Graphs, Pie Diagrams--------*Measures of Central Tendency (Mean, Median and Mode)(Contd…….)*Dispersion and its Measures (Variance and Standard Deviation), Their Merits & Demerits--------(Sindh Textbook Board Mathematics for IX-X, 2012, Unit, 4, Part-II).StatisticsSameSameSame Same*Stem and Leaf Diagram, Dot DiagramSame--------*Cumulative Frequency DistributionNew Syllabus Oxford Mathematics Book1, Ch13; Book2, Ch11& Book4, Ch5).Sequencing: AppropriateSequencing: AppropriateIntegration with other Topics-------Integration with other TopicsThe contentswere integrated mostly with problems related to probability.Language:Simple Language: SimpleComparison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSC and GCE)Questions taken from the Textbooks(2013,Q20a from Ex4.4,Q4); (2012,Q20a from Misc. Ex,Q3); (2011,Q20a from Ex4.3,Q7);( 2010 from Ex4.3,Q7)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)(Contd…….)Questions taken from the Textbooks-------(O-Level Classified Mathematics, Unit,9)Questions taken from Previous Papers(2011,Q20a from 2010,Q20a); (2009,Q16b, from 2000,Q16b); (2009,Q15a from 2002,Q15b from 1998,Q15b);(2008, Q15b from 1998, Q16b); (2004, Q16a from 1999, Q16b); (2003, Q15b from 2001, Q15b).Questions taken from Previous Papers-------Repetition of Similar Questions:Variance/S.D(2013,Q20a); (2009,Q15a); (2008,Q15b); (2007,Q16b); (2006,Q16b); (2005,Q15b); (2004,Q15b);(2003,Q16b); (2002,Q15b); (2001,Q16b); (200015a); (1999, Q15b); (1998, Q15b).Median (Grouped Data)(2012,Q20a);(2010,Q20a); (2008,Q16b);(2002,Q16a); (1998, Q16b).Mean (Grouped Data)(2011,Q20a); (2006,Q15b); (2003,Q15b); (2001,Q15b);(2000Q16b)Mode (Grouped Data) (2007,Q15b;2004,Q16a; 1999,Q16b)(Contd…….)Median (Ungrouped Data) (2007,Q16b);(2005,Q16b);( 2002,Q16a); (1998,Q16b)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Repetition of Similar Questions*No pattern of repetition has been found. A variety of ways have been found in which questions were given for the application of the learned concepts.-------(O-Level Classified Mathematics, 2012, Unit 1A – 1D).-------Questions in a particular section of paperThe question on this topic has Always been seen in Section C of the paper.Questions in a particular section of paperQuestions on this topic have been found in both paper1 and paper ics Never Assessed--------Topics Never Assessed--------Choice to Leave the Question in PaperAlwaysChoice to Leave the Question in PaperNeverQuestions on Application of Concepts in Real Life Problems-------Questions on Application of Concepts in Real Life SituationsA significant number of questions have been observed on the application of statistical concepts in real life problems.Table 193(f): GeometrySSCGCEGeometryThe geometry section has been found divided into three parts(i) Fundamental Concepts of geometry(ii) Demonstrative Geometry(iii) Practical Geometry(Sindh Textbook Board Mathematics for IX-X, 2012, Unit,7,8,9, Part-I & Unit, 5, 6, 7, Part II).GeometryThis section was found subdivided into the following parts(i) Properties of Angles, Angle Properties of Polygons(ii) Similarity, Congruency and Symmetry(iii) Circle Theorems(iv) Loci and Simple Constructions{New Syllabus Oxford Mathematics Book1, Ch14 & 15; Book2, Ch1; Book3, Ch. 8 & 9 & Book4, Addendum, Ch. IV)}Contents:(i) Fundamental Concepts of Geometry - Inductive and Deductive Reasoning- Characteristics of Deductive Reasoning- Basic Concepts Definitions and Postulates- Basic Concepts of Circle (Circumference, Chord, Secant, Tangent)- Circumscribed circle, Inscribed Circle and Escribed Circle of a Triangle- Theorems on Circles(ii) Demonstrative Geometry-Deductive Method of proving a Geometrical Theorem along with related steps-Theorems on Parallel Lines, Triangles, Parallelograms and Quadrilaterals(Contd…….)(iii) Practical Geometry- Construction of Triangles,- Constructions of Right Bisectors of Sides of a Triangle-Construction of Angle Bisectors, Median and Altitudes in a Triangle- Constructions (Circum-circle, Inscribed circle and Escribed Circle) of a triangle- Tangent to a Given Circle from a Point outside the Circle- Direct Common Tangents to Two Given Circles and Transverse Common Tangents to Two Given CirclesContents:(i) Properties of Angles, Angle Properties of Polygons- Complementary & Supplementary Angles- Alternate, Vertically Opposite, Interior & Corresponding Angles- Angle Properties of triangles, Quadrilaterals and Polygons- Sum of Interior and Exterior Angles of Polygons(ii) Similarity, Congruency and Symmetry- Similar Figures and Objects- Similarity and Enlargement- Similarity and Scale Drawings- Area and Volume of Similar Figures- Area and Volume of Similar Solids(iii) Circle Theorems- Geometrical Properties of Circles- Angle Properties of Circles- Angles in Opposite Segments of Circles- Problems on Angle Properties of Circles- Problems on Tangents from an External Point on a Circle(iv) Loci and Simple Constructions- Construction of triangle, Square, Rectangle, Parallelogram, Rhombus and any other Quadrilateral- Bisection of a line segment and an angle- Loci in two dimensions- Intersection of Loci- Loci in three dimensionsPresentation & Objectives of the Contents(i) Fundamental Concepts of Geometry The fundamental concepts of geometry were explained through figures. In the exercises, students were expected to define and draw figures of particular terms of geometry or differentiate between two terms (Ex7.1,PartI; Ex5.1,PartII)(ii) Demonstrations of the Proofs of Geometrical TheoremsThe methods with all its steps of proving a geometrical theorem were explained. Students were expected to prove a theorem deductively showing all the instructed steps. After each theorem an exercise was given in which statements are given to be proved by applying the same method as explained in the proof of theorem.Prove that* If two lines intersect, the vertically opposite angles so formed are congruent.* If a transversal intersect two parallel lines, the alternate angles so formed are congruent.* The sum of the measure of the angles of a triangle is 180o.* If a perpendicular is drawn from the center to a chord of a circle, it bisects the chord.* The measure of central angle of a minor arc of a circle is double that of the inscribed angle of the corresponding major arc.(Contd…….)* If a line is drawn perpendicular to the radial segment of a circle at its outer end, it is tangent to the circle at that point.* The two tangents, drawn to a circle from a point outside it, are equal in length.* Theorems on Locus are required to be proved by deductive method as well.- The locus of a point equidistant from two fixed points is the right bisector of the line joining the fixed points.- The locus of a point equidistant from the arms of an angle is the bisector of the angle.Presentation & Objectives of the Contents(i) Basic Geometrical ConceptsThe basic concepts of geometry about types of angles and triangles, properties of angles formed when a transversal cuts two parallel lines, angle properties of polygons and finding the sum of interior angles of polygons were explained through worked examples. Students were expected to apply their learned properties about angles to find the unknown angles in the figures given as sums in the exercises. Neither the definition of a term was required nor was the drawing of figure expected.(Book 3,Ch14 & 15)(ii) Use of Geometrical Theorems in the given FiguresThe proofs of theorems were not required; instead the use of theorems has been focused to solve a geometrical problem. Exercises provide a numbers of geometrical figures in which the missing angles are required to be found using theorems and all the reasons are rquired.Find the unknown angles* * * (i)Calculate angle BOC. (ii) Calculate angle OCA.* A and C are points on the circumference of a circle center B. AD and CD are tangents. Angle ADB = 40°.Explain why angle ABC is 100°. * Locus theorems are required to be demonstrated by accurate scale drawings.- Construct triangle ABC in which AB = 8cm , BC = 7.5 cm & AC = 6 cmOn the diagram Construct(i) Locus of a point P on the same side of AB as the point C and such that area of ?APB = area of ?ACP(ii) (a) Locus of a point equidistant from A and B (b) Locus of a point equidistant from A and C (c) The circle through A, B and C(Book4, Ex IVc,Q3) Language:More mathematical language has been used. (Contd…….)Language: Less mathematical language has been parison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSC and GCE)Questions taken from the TextbooksDemonstrative GeometryThe proofs of theoremsrequired in the papers have always been taken from the textbooks.Practical GeometryOne of the following type of questions has been observed each year(i) To draw the circumscribed circle after drawing a triangleThis question has been found 8 times(2013; 2008; 2007; 2003; 2001; 1999; 1997; 1995)(ii) To draw the direct common tangent after drawing two circles This question has been found 8 times(2011; 2010; 2009; 2005; 2004; 2000; 1998; 1994)(iii) To draw the transverse common tangent to two circlesThis question has been found 4 times(2012; 2006; 2002; 1996)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)(Contd…….)Questions taken from the Textbooks---------------------(O-Level Classified Mathematics, Unit,7A-7D)Repetition of Similar Questions:A pattern of repetition of similar questions has been observed. There were some theorems that have been found repeatedly in the subsequent papers.For instance:* If a perpendicular is drawn from the center to the chord of a circle, prove that it bisects the chord.The above question has been found 15 times in the last 20 year’s papers.(2013; 2011; 2009; 2007; 2006; 2005; 2004; 2003; 2002; 2001; 2000; 1999; 1997; 1999; 1995)* If two angles of a triangle are congruent, prove that the sides opposite to them are also congruent.The above question has been repeated 8 times.(2013; 2011; 2009; 2008; 2007; 2005; 2004; 1995)* If a transversal intersect two parallel lines, the alternate angles thus formed are congruent.The above question has been repeated 8 times.(2012; 2007; 2006; 2005; 2003; 2001; 1997; 1995)(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)Repetition of Similar QuestionsNo definite pattern of repeated questions from successive years has been observed.--------------(O-Level Classified Mathematics, 2012, Unit 7A – 7D).(Contd…….)Questions in a Particular Section of PaperThe questions on Demonstrative and Practical Geometry have always been found in section B till 2009. In the new pattern of the paper (2010 onwards), 2 or 3 questions on theorems were found in section B and 1 question,Q.19 (compulsory) was found in Section C. Question on Practical Geometry is coming in Section C in the new pattern of paper.Questions in a Particular Section of PaperQuestions on this topic have been found in both paper1 and paper ics Never Assessed* In demonstrative geometry, after every theorem, an exercise was given. Not even a single question has been found from these exercises in any of the past 20 years papers. Only the theorems were given in the papers.* In practical geometry, questions on the construction of triangles (the ambiguous case), drawing medians of triangles, drawing altitudes of a triangles and drawing inscribed circle of triangles have never been found.(Contd…….)Topics Never Assessed-------Choice to Leave the Question in PaperIn the old pattern of paper (till 2009), section B was reserved for both demonstrative and practical geometry. Three out of five questions were required.In these 5 questions, 4 were always given on theorems and 1 on practical geometry. Therefore, this section always had a choice of leaving the question on practical geometry but there was a compulsion to select a minimum of two questions on theorems.In the new pattern (2010 onwards), 2 or 3 short answer questions on theorems are given in section B, where 10 questions out of 15 are required to be attempted. Therefore, there is a complete choice to leave all the questions on theorems in this section. In section C, 3 out of 5, questions were required to be selected including Q.19 which was on theorems and was compulsory in this section. Therefore, in this section there is a choice of leaving two of the following topics completly: factorization, information handling and practical geometry.Choice to Leave the Question in Paper----------------------------Summary, Discussion and ConclusionsThe comparative analysis of the contents of the textbooks and question papers of the past twenty years of both systems reveal that although there are other differences in the contents of textbooks of two systems, a significant difference is in the approach of teaching the contents. This difference of approach in the two systems is due to the difference in the approaches and methods of assessment.The key issuesrevealed during the record analysis may be summarized and concluded as:Contents of SSC textbooks were leaned towards the provision of mathematical knowledge of procedures and operations while in GCE, there was a clear inclination found towards the application of mathematical procedures and operations in everyday problems. GCE textbooks and question papers were consisted of a majority of word problems while SSC textbooks and question papers constituted a very small number of word problems. SSC textbooks were found with a black and white illustrations and a discernible use of mathematical language while GCE textbooks had colourful presentation of pictures and diagrams with an indiscernible use of mathematical language embedded in common language.Objectives of SSC and GCE contentswere not very different except, less material on problem solving and application of concepts in word problems was found on SSC side.The use of contents of textbooks on SSC side was not aligned with the objectives mentioned in the books. This was due to the pattern of assessment where exact same questions from the textbooks were given. As a result, both teachers and students do not try to go beyond factual and procedural knowledge. Rather, students try to memorize certain areas of the content so that they can reproduce it with precision and get good marks in the examination.SSC question papers contained exactly the questions as the textbook questions but in GCE, no such evidence was found.SSC papers contained a number of repeated questions from the successive years while on GCE side, no clear pattern of repetition was observed.SSC papers have been found with a fixed pattern. Questions from certain chapters are always given in specific sections. An ample amount of choice is always given to select questions from different sections. As a result of this fixed pattern and ample choice, there is a high trend of selected study and leaving some areas of the syllabus untaught, in SSC system. GCE on the other hand neither has such a pattern nor such plenteous choice in the paper. Therefore, students in this system have to study all the topics in the syllabus.SSC papers were predictable due to a fixed pattern and repetition of questions. Therefore, a trend of guessing questions for the upcoming paper by analyzing the pattern of questions in the previous papers is present in this system. GCE papers were not predictable.SSC paper did not have any content on everyday mathematics (percentage, rate/sale/purchase/interest /money etc.) while on the GCE side, there are a substantial proportion of these topics in the paper.GCE textbooks were found relatively more internally coherent within different content areas than the SSC textbook.GCE textbooks contained contents for further exploration and discovery of a concept beyond the requirements of syllabus which was not present in the SSC textbook.GCE textbooks contained material for mental exercise (discipline of mind) that is not a requirement of the syllabus, but no such material was found in SSC textbooks.CHAPTER FIVESUMMARY, FINDINGS, CONCLUSIONS AND RECOMMENDATIONS5.1 SUMMARYThe focus of this study was on the comparative effectiveness of the SSC and the GCE (Ordinary Level)mathematics curriculum. The purpose was to trace out the factors involved in the problems and shortcomings of the curriculum objectives, contents, approaches and methods of teaching and examination system in the SSC system. The study’s specific focus was: (1) to compare and analyze the aims and objectives of teaching mathematics at SSC and GCE (O- Level); (2) to compare the contents of textbooks and exam papers of SSC and GCE mathematics courses; (3) to critically compare the effectiveness of approaches and teaching methods applied in both systems; (4) to compare and analyze the assessment patterns in both systems.The population of study comprised teachers, students, prescribed text books of mathematics taught at SSC and GCE (O- Level) and the question papers of the Examination Boardsof the two systems. The sample included the mathematics teachers teaching grade X (SSC) and O-Level final year (GCE). The students studying in 10th class (SSC) and O-Level final year (GCE). Textbook of mathematics for IX and X , published by Sindh Textbook Board and a set of four textbooks used in GCE (O-level) system, published by Oxford University Press; question papers of the past 20 years of Board of Secondary Education Karachi (BSEK) and Cambridge International Examinations (CIE) were also a part of the sample.As many as 10 subject experts, 180 teachers and 120 students were selected from the SSC system. From the GCE system, 10 subject experts, 120 teachers and 80 students were selected. Questionnaires designed with a five-point rating scale were administered to the sample. A semi-structured interview was conducted to the subject experts.A content analysis was done to compare the contents of textbooks and question papers of both SSC and O-Level mathematics course. The quantitative data collected were tabulated and analyzed using t-test.5.2 SECTION WISE RESULTS OF DATA ANALYSISThe results of data analysis for each section have been summarized in the following four tables.Table 194(a): (Significance of Mathematics / Aims / Objectives)KEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% ? (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)Sr.NoH0Aims / ObjectivesA/Rt-ValueA(Percentage)DA(Percentage)TeachersSSCGCESSCGCE1There will be no significant difference between SSC and GCE teachers on the statement that mathematics is one of the most important subjects in the school curriculum.A0.34596.7%95%2.2%3.2%2There will be no significant difference between SSC and GCE teachers on the statement that the aim of mathematics education is to train or discipline the mind.A1.54687.8%80%4.4%6.7%3There will be no significant difference between SSC and GCE teachers to take the practical value of mathematics as an aim of its education.A0.54992.3%93.4%5.5%3.3%4There will be no significant difference between SSC and GCE teachers regarding the development of problem solving skills as an aim of its education.R1.97592.8%95%6.1%5%5There will be no significant difference between SSC and GCE teachers on the statement that the aims of mathematics education are convincing.(Contd…….)R5.98255.6%80%25%3.3%6There will be no significant difference between SSC and GCE teachers on the statement that aims of mathematics education are achievable.A0.28385.6%81.6%9.4%6.7%7There will be no significant difference between SSC and GCE teachers that the aims of mathematics education can be translated into small educational objectives.A0.61865.5%70.9%8.9%8.3%8There will be no significant difference between SSC and GCE teachers on the statement that the objectives of current teaching are derived from actual aims.R2.20262.2%71.7%16%8.3%9There will be no significant difference between SSC and GCE teachers on the statement that objectives of mathematics teaching are well defined.A1.42875.6%76.7%15%10%10There will be no significant difference between SSC and GCE teachers on the statement that objectives of mathematics education are clearly transmitted to teachers.R2.26157.8%76.7%29%15%H0Aims / ObjectivesA/Rt-ValueA(Percentage)DA(Percentage)StudentsSSCGCESSCGCE11There will be no significant difference between SSC and GCE students on the statement that I do mathematics because teachers emphasize its importance.A1.72841.6%58.8%37%29%12There will be no significant difference between SSC and GCE students on the statement that I do mathematics because it is compulsory to take this subject at school level.(Contd…….)R4.68984.2%36.3%4.2%56%13There will be no significant difference between SSC and GCE students on the statement that school places a special emphasis on mathematics than the other subjects.A0.68267%65%25%8.8%14There is no significant difference between SSC and GCE students on the statement that mathematics is important because it trains the mind.A0.72990.8%96.3%0.8%2.5515There is no significant difference between SSC and GCE students on the statement that mathematics is important because it is a compulsory subject in school curriculum.A1.20879.2%75%10%18%16There is no significant difference between SSC and O-Level students on the statement that mathematics is important because it is largely applied at the higher education level.A1.21967.5%67.5%21%15%17There is a significant difference between SSC and O-Level students on the statement that mathematics is important because it is applied in many other subjects.R2.04185.8%93.8%5%1.6%18There is no significant difference between SSC and O-Level students on the statement that mathematics is a scoring subject.A1.17693.3%96.3%1.6%2.5%Responses of Experts on Aims / Objectives of MathematicsQ1Is teaching of mathematics according to some clear objectives? If yes, then according to your observation, what is the major objective?SSCAgreed70%Disagreed20%Undecided10%Responses*Percentage of each Response*To meet the needs of further education of this subject.30%*To enable students to do basic operations of mathematics.10%*To enable students to solve different types of problems by applying mathematical rules and procedures.20%*Aims and objectives are not clear to teachers; the only objective is to make students pass the examination with good marks.(Contd…….)10%GCEAgreed100%Disagreed0%Undecided0%Responses*Percentage of each Response*Enhancement of thinking skills.20%*Preparation of students for GCE Exam.40%*Prepare students for future education.20%*Enable students to think within horizon before thinking beyond horizon.10%*Making students good problem solvers.10%*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%Table 194(b): Contents / TextbooksKEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% ? (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)Sr.NoH0Contents / TextbooksA/Rt-ValueA(Percentage)DA(Percentage)TeachersSSCGCESSCGCE1There will be no significant difference between SSC and GCE teachers that contents of the textbooks are properly sequenced.A1.25074.6%84.1%21%8.9%2There will be no significant difference between SSC and GCE teachers on the statement that contents develop interest in students.A0.60862.7%65.3%23%17%3There will be no significant difference between SSC and GCE teachers that contents incits the sense of enquiry.R3.09058.9%70.3%28%12%4There will be no significant difference between SSC and GCE teachers that language of the textbooks is simple.A1.72084.5%90%13%1.7%5There will be no significant difference between SSC and GCE teachers that the contents cover application of abstract principles in real life problems.R3.27554.4%73.3%29%12%6There will be no significant difference between SSC and GCE teachers on the statement that worked examples in the text books provide sufficient guidance.(Contd…….)R3.84667.9%80%24%12%7There will be no significant difference between SSC and GCE teachers on the statement that the contents are in accordance with intellectual level of students.R3.91363.4%78.4%24%13%8There will be no significant difference between SSC and GCE teachers that contents covers problems whose solutions can be found by personal investigation.R6.31151.1%80%32%6.7%9There will be no significant difference between SSC and GCE teachers that contents covers a proper proportion of mathematical representations.A1.75881.2%91.7%11%3.3%10There will be no significant difference between SSC and GCE teachers that the contents include an appropriate proportion of activities to develop the habit of thinking.R5.23142.2%71.7%49%15%11There will be no significant difference between SSC and GCE teachers that the contents are balanced in terms of key areas.R4.75273.4%91.6%19%6.7%12There will be no significant difference between SSC and GCE teachers that the pictures and colorful presentations help in conceptual understanding.R4.07166.7%85%21%8.3%H0Contents / TextbooksA/Rt-ValueA(Percentage)DA(Percentage)StudentsSSCGCESSCGCE13There will be no significant difference between SSC and GCE students on the statement that mathematics textbooks have an attractive look.A0.35531.6%27.5%44%60%14There will be no significant difference between SSC and GCE students on the statement that language used in the textbooks is clear.(Contd…….)A1.11171.6%75%18%15%15There will be no significant difference between SSC and GCE students on the statement that language of mathematics textbooks is difficult to understand.R4.77943.3%18.8%40%70%16There will be no significant difference between SSC and GCE students on the statement that all the topics in the textbooks are taught completely for the preparation of final examination.R5.23859.2%83.8%29%7.5%17There will be no significant difference between SSC and GCE students on the statement that methods to solve different types of problems are explained through worked examples in the textbooks.R2.73470.8%88.8%14%7.5%18There will be no significant difference between SSC and GCE students on the statement that textbooks are illustrated with concept-related pictures from real life.R3.83233.3%55%53%28%19There will be no significant difference between SSC and GCE students on the statement that the pictures facilitate in comprehending the concepts.A0.39264.2%65%17%23%20There will be no significant difference between SSC and GCE students on the statement that diagrams are the frightening element of the textbooks.R2.82129.2%12.5%57%80%21There will be no significant difference between SSC and GCE students on the statement that I can study a new topic through worked examples provided in the textbook.R5.77464.2%27.5%26%63%22There will be no significant difference between SSC and GCE students on the statement that the contents explained by teacher only should be studied.(Contd…….)R5.11441.6%15%44%75%23There will be no significant difference between SSC and GCE students on the statement that the contents of textbooks is in accordance with the intellectual level of studentsA0.20353.8%55.8%14%18%24There will be no significant difference between SSC and GCE students on the statement that the language of textbooks is in accordance with the language proficiency of studentsA1.01660%60%13%11%Responses of Experts on Contents / Textbooks of MathematicsQ1Are you satisfied with the contents of textbooks of mathematics used at secondary level?SSCAgreed40%Disagreed40%Undecided00%Responses*Percentage of each Response* Problem is not with the contents; it is with the methods of teaching and assessment10%* Some topics like number sequence, probability etc. should be included.10%GCEAgreed50%Disagreed30%Undecided0%Responses*Percentage of each Response*Books are not written locally, they serve the needs in terms of contents but book of local authors will be better.20%Q2What changes would you like to suggest improving these textbooks?SSC*Percentage of each ResponseSuggestions* New topics should be added.30%*World problems should be increased.40%*Contents should be updated.30%*Worked examples should be improved.10%*Textbooks should be activity based.20%* In lower grades, schools frequently change books. It affects the logical sequence of contents and vertical integration of concepts.(Contd…….)20%GCE*Percentage of each ResponseSuggestions*Books should be written by local authors.30%*Reference books should be used instead of textbooks.40%*Contents on problem solving should be increased.20%* A teachers’ manual should be published with each book for their guidance.20%* Answers of graph and loci questions should be given in the form of constructed graphs and geometrical figures respectively.10%Q3Are you satisfied with the current methods of selection and sequencing of contents? If not, please give your opinion.SSCAgreed20%Disagreed70%Undecided10%Responses*Percentage of each Response*Sequence is not appropriate between the contents taught at lower secondary and secondary level.20%*Selection of contents should be made accordingly with the sequence of the textbooks.30%*Selection is made to incorporate (arithmetic, algebra, geometry) but the prime concern of this selection is to ensure a balanced exam paper.40%*Selection, elimination and sequence of contents are made according to the choice of concerned teachers and feasibility of completing it within the available time30%GCEAgreed70%Disagreed30%Undecided0%Responses*Percentage of each Response*It should be done on logical grounds40%*The selection of contents should be done on the basis of educational needs of students50%*In the process of selection and its sequencing, no special consideration is made on the prerequisites, interests and needs of students.30%*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%Table 194 (c): Approaches / Methodology KEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% ? (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)Sr.NoH0Approaches / MethodologyA/Rt-ValueA(Percentage)DA(Percentage)TeachersSSCGCESSCGCE1There will be no significant difference between SSC and GCE teachers on the statement that students should solve problems by teachers’ explained method only.R2.32861.1%26.7%61%27%2There will be no significant difference between SSC and GCE teachers on the statement that additional material is usually used for rigorous drill of learned material.A0.08873.4%68.4%16%15%3There will be no significant difference between SSC and GCE teachers on the statement that additional material used is mostly previous exam papers.A1.25954.5%66.7%32%28%4There will be no significant difference between SSC and GCE teachers on the statement that previous papers are solved as a rehearsal for the actual exam paper.A1.63083.5%86.7%8.8%3.3%5There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions of previous papers are considered important.A0.80354.5%65%34%28%6There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions from previous papers often repeat in the new papers.R2.31367.2%41.4%25%48%7There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved to understand the pattern of questions coming in the recent papers.(Contd…….)A0.10891%90.1%5.5%3.3%8There will be no significant difference between SSC and GCE teachers on the statement that teacher-constructed problems are presented in the class.A0.95781.2%81.7%11%13%9There will be no significant difference between SSC and GCE teachers on the statement that students are allowed to construct and present their own problems in the class.R2.60581%66.4%11%18%10There will be no significant difference between SSC and GCE teachers on the statement that procedures of solving a problem are explained but not the reason for the selection of that procedure.R7.50051.4%46.8%32%41%11There will be no significant difference between SSC and GCE teachers on the statement that there are some topics in the textbooks that are always left as no question comes in the paper from these topics.R3.12554.6%30.7%36%65%12There will be no significant difference between SSC and GCE teachers on the statement that homework is given in order to complete the syllabus as it cannot be completed by solving all sums in the class.A0.91470%66.7%26%28%13There will be no significant difference between SSC and GCE teachers on the statement that emphasis is given on neat and tidy written work.R4.79694.5%66.7%3.3%16%14There will be no significant difference between SSC and GCE teachers on the statement that homework is assigned and checked regularly.R3.22088%68%7.7%25%15There will be no significant difference between SSC and GCE teachers on the statement that topics are not explored in depth; only the procedure of solving a sum is explained. (Contd…….)R4.00054.2%33%37%57%16There will be no significant difference between SSC and GCE teachers on the statement that unexplained short-cuts are told to solve certain problems.A1.26854%54%37%38%17There will be no significant difference between SSC and GCE teachers on the statement that derivation of the formula is not clarified; only the method of its application is explained.A0.21433%30%57%60%18There will be no significant difference between SSC and GCE teachers on the statement that teachers do not emphasize students to check answers.R2.77452.2%31.6%40%58%19There will be no significant difference between SSC and GCE teachers on the statement that teachers true role is to generate a question in the mind of a child before it is answered.R3.75083.3%94.4%6.6%3.3%20There will be no significant difference between SSC and GCE teachers on the statement that both posing and answering questions by teachers produce shallow understanding.A0.09172.2%70%11%12%21There will be no significant difference between SSC and GCE teachers on the statement that retention of learned material in the memory becomes stronger with repetition.A0.10988.8%86.6%3.3%6.6%22There will be no significant difference between SSC and GCE teachers on the statement that repetition of a learned material may attach meaningful relationships among the fragments of knowledge.(Contd…….)A0.47690%88.3%4.4%1.6%H0Approaches / MethodologyA/Rt-ValueA(Percentage)DA(Percentage)StudentsSSCGCESSCGCE23There will be no significant difference between SSC and GCE students on the statement that doing important topics is better than doing all the topics to get good marks.R5.67362.5%27.5%31%64%24There will be no significant difference between SSC and GCE students on the statement that generally the last questions (star questions) of the exercises are usually left unsolved.A0.58159.2%67.5%29%28%25There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize students to solve the sums using only their explained methods.A1.38671.3%65.8%19%28%26There will be no significant difference between SSC and GCE students on the statement that there is more than one method to solve a problem.A1.48586.6%95%3.3%1.3%27There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize neat and tidy work.R4.71284.2%63.8%12%35%28There will be no significant difference between SSC and GCE students on the statement that additional material is used to get further practice of the sums.A1.06969.2%73.8%24%15%29There will be no significant difference between SSC and GCE students on the statement that teacher-constructed problems are presented in the class.R4.71767.5%38.8%20%53%30There will be no significant difference between SSC and GCE students on the statement that separate activities are done for low achievers in the class.(Contd…….)R5.66851.6%16.3%37%78%31There will be no significant difference between SSC and GCE students on the statement that teachers arrange activities to engage high achiever students to help their low achiever class fellows.R2.05452.5%42.5%36%51%32There will be no significant difference between SSC and GCE student on the statement that in mathematics class of 40 minutes students normally ask less than 5 questions.R2.89246.6525%23%63%33There will be no significant difference between SSC and GCE students on the statement that in mathematics class of 40 minutes teachers normally explain for less than 15 minutes.A0.40222.5%35%57%56%34There will be no significant difference between SSC and GCE students on the statement that students mostly ask ‘HOW’ type questions in the class.A0.09190.8%93.8%7.5%3.8%35There will be no significant difference between SSC and GCE student on the statement that teachers do not encourage ‘WHY’ type questions in the class.R2.11250%66.3%33%19%36There will be no significant difference between SSC and GCE students on the statement that procedure of solving a problem is explained but not the reason for the selection of that procedure.A1.25857.5%68.8%24%23%37There will be no significant difference between SSC and GCE student on the statement that some topics of the textbooks are never taught.R6.22173.3%30%15%53%38There will be no significant difference between SSC and GCE students on the statement that homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in class. (Contd……..)A1.16880%78.8%11%14%39There will be no significant difference between SSC and GCE student on the statement that homework is assigned and checked regularly by the teachers.R9.43868.3%18.8%24%75%40There will be no significant difference between SSC and GCE students on the statement that topics are not explored in depth; only the procedure of solving a sum is explained.A0.22349.2%42.5%38%44%41There will be no significant difference between SSC and GCE students on the statement that the activities of mathematics class are largely a repetition of similar sums.A0.27969.2%72.5%21%19%42There will be no significant difference between SSC and GCE students on the statement that reference books are taken from the library to explore the topics in depth.A0.16025.8%31.3%65%64%Responses of Experts on Approaches / Methodology Q1In your opinion what changes should be made in approaches and methods of teaching mathematics?SSCAgreed70%Disagreed20%Undecided10%Responses*Percentage of each Response*Activity based teaching. 40%*Project based teaching. 20%*Taking the aid of technology (audio-video aides, internet etc.). 40%*Mathematics should be taught just like a language. 10%*Mostly emphasis is given on product but the process is also as important as the product. 10%*Teachers should have to address all the cognitive levels in their teaching (knowledge, comprehension, application, analysis, synthesis and evaluation). 10%*Step by step instructions should be given instead of giving the key to open the lock (a method to solve the problem). (Contd…….)20%GCEAgreed100%Disagreed0%Undecided0%Responses*Percentage of each Response*Activity based teaching. 20%*Use maximum time on basic concepts. 40%*Preference should be given to mental calculations and calculators should be avoided as much as possible. 30%*Instead of teaching a large number of chapters, teach a chapter in depth. 20%*Computer Assisted Instruction (CAI) should be increased. 10%*Make the students confident by rigorous practice. 60%*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%Table 194 (d): Assessment / EvaluationKEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% ? (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)Sr.NoH0Assessment / EvaluationA / Rt-ValueA(Percentage)DA(Percentage)TeachersSSCGCESSCGCE1There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to assess the level of achievement of the instructional objectives.R2.532100%91.6%0%6.6%2There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to categorize students into successful and unsuccessful groups.R4.03572.2%56.6%23%32%3There will be no significant difference between SSC and GCE teachers on the statement that the verbal/written remark of teacher on the basis of assessment is evaluation.(Contd…….)A0.65476.6%81.6%13%12%4There will be no significant difference between SSC and GCE teachers on the statement that assessment helps both teacher and learner in the process of teaching and learning.A1.07195.5%90%2.2%1.6%5There will be no significant difference between SSC and GCE teachers on the statement that the fear of assessment motivates students for hard work.R4.31893.3%80%3.3%6.6%6There will be no significant difference between SSC and GCE teachers on the statement that a teacher is always engaged in the process of assessing his/her students during the class.A0.58381.1%85%12%6.6%7There will be no significant difference between SSC and GCE teachers on the statement that the encouraging remarks of a teacher after assessment produce positive effect on the performance of students.A0.00094.4%90%3.3%1.6%8There will be no significant difference between SSC and GCE teachers on the statement that methods of assessment should enable students to reveal what they know, rather than what they do not know.R2.11578.8%85%13%8.3%9There will be no significant difference between SSC and GCE teachers on the statement that the main purpose of assessment is to improve teaching and learning of mathematics.A1.60990%91.6%2.2%5%10There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the objectives of teaching mathematics.(Contd……)A1.36480%81.6%8.8%5%11There will be no significant difference between SSC and GCE teachers on the statement that the exam papers are balanced in terms of content areas.A0.12787.7%90%7.7%1.6%12There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the actual educational objectives of teaching mathematics.A0.23080%80%15%3.3%13There will be no significant difference between SSC and GCE teachers on the statement that the system of checking papers is fair.R5.25966.6%88.3%25%1.6%14There will be no significant difference between SSC and GCE teachers on the statement that examinations are conducted under strict vigilance.R6.75271.1%93.3%24%1.6%15There will be no significant difference between SSC and GCE teachers on the statement that use of unfair means in the paper of mathematics is common.R6.71242.2%30%40%62%16There will be no significant difference between SSC and GCE teachers on the statement that grading system of (SSC/ GCE) is appropriate.R4.73768.8%81.6%20%6.6%17There will be no significant difference between SSC and GCE teachers on the statement that teachers’ assessment during class is as important as the final examination.A1.86087.7%91.6%7.7%1.6%18There will be no significant difference between SSC and GCE teachers on the statement that students’ weekly/monthly/terminal test scores are added in the marks of their final exam paper in junior grades.(Contd…….)R2.35987.7%70%8.8%3.3%19There will be no significant difference between SSC and GCE teachers on the statement that final examinations assess the factual and procedural knowledge only.R4.23782.2%56.6%11%32%20There will be no significant difference between SSC and GCE teachers on the statement that questions in the exam papers are given according to a set pattern.R2.07775.5571.6%18%20%21There will be no significant difference between SSC and GCE teachers on the statement that questions are taken from the textbooks in (SSC/GCE) papers.R7.25960%23.3%34%65%22There will be no significant difference between SSC and GCE teachers on the statement that questions are taken from past papers in (SSC/GCE) papers.R5.44843.3%40%46%45%23There will be no significant difference between SSC and GCE teachers on the statement that some topics from the syllabus may be dropped due to ample choice of in the paper.R3.81368.8%53.3%26%38%24There will be no significant difference between SSC and GCE teachers on the statement that on the basis of previous papers, some questions can be predicted for the upcoming paper.R5.54780%53.3%17%35%25There will be no significant difference between SSC and GCE teachers on the statement that sections of exam paper are made in such a way that questions from some particular chapters always come in a specific section.R4.87283.3%65%7.7%23%26There will be no significant difference between SSC and GCE teachers on the statement that all the teaching and learning process in the class is designed and implemented to pass the final examinations.(Contd…….)A1.26177.7%73.3%20%18%H0Assessment / EvaluationA /Rt-ValueA(Percentage)DA(Percentage)StudentsSSCGCESSCGCE27There will be no significant difference between SSC and GCE students on the statement that assessments help in confidence building.R1.98487.5%85%5%8.8%28There will be no significant difference between SSC and GCE students on the statement that assessments help in identifying and reducing mistakes.A0.31693.3%95%3.3%1.3%29There will be no significant difference between SSC and GCE students on the statement that assessments help in the preparation of final examinations.A0.21786.6%97.5%3.3%1.3%30There will be no significant difference between SSC and GCE student on the statement that quizzes (short tests based on calculations without using calculators) are conducted regularly in the class.R2.13539.2%55%53%40%31There will be no significant difference between SSC and GCE students on the statement that speed tests are conducted regularly.A1.74624.2%35%68%59%32There will be no significant difference between SSC and GCE students on the statement that positive remarks of the teacher on student’s assessment produce better result.sA0.34981.6%82.5%7.5%8.8%33There will be no significant difference between SSC and GCE student on the statement that I am well aware of the pattern of (GCE/SSC) paper.R2.10587.5%82.5%5%14%34There will be no significant difference between SSC and GCE students on the statement that students study seriously under the pressure of tests/examinations.(Contd…….)A0.93977.5%87.5%15%11%35There will be no significant difference between SSC and GCE student on the statement that teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paper.R4.97469.2%37.5%21%54%36There will be no significant difference between SSC and GCE student on the statement that questions in SSC/GCE papers are given according to a fixed pattern.R7.68886.6%40%8.3%49%37There will be no significant difference between SSC and GCE student on the statement that questions are taken from the textbooks in SSC/GCE paper.R11.50378.3%16.3%13%71%38There will be no significant difference between SSC and GCE student on the statement that questions are taken from past papers in SSC/GCE paper.R8.28276.6%30%14%60%39There will be no significant difference between SSC and GCE student on the statement that some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper.R8.07073.3%22.5%21%60%40There will be no significant difference between SSC and GCE student on the statement that on the basis of previous papers, some questions can be predicted for the upcoming paper.R7.53290%50%4.2%43%41There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the whole syllabus.R5.56944.2%80%49%13%42There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the topics covered in the final term only. (Contd……)R7.35661.6%15%32%71%43There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term.R5.97648.3%12.5%44%73%Responses of Experts on Assessment / Evaluation of MathematicsQ1Are you satisfied with current system of assessment in mathematics at school level? If not, please suggest some changes.SSCAgreed40%Disagreed60%Undecided10%Suggestions*Percentage of each Response* Formative assessments should be increased.20%* Rote memorization of contents should be discouraged by giving application based problems as much as possible.30%* Understanding of students is to be checked rather than checking that the student can solve a sum or not.20%* Sums should not be given directly from the textbook or previous exam papers.40%GCEAgreed70%Disagreed30%Undecided0%Suggestions*Percentage of each Response* Tests should be held more frequently30%* More quizzes and mental math’s tests should be administered20%* Teachers should construct their own sums instead of taking them from past papers30%Q2Are you satisfied with the current pattern of mathematics paper (GCE/SSC)? What improvement should be made in it according to your opinion?SSCAgreed20%Disagreed80%Undecided0%Opinions*Percentage of each Response* Questions should not be taken from textbooks / previous papers.40%* Pattern of paper should be such that it discourages guess work and selected study habits.(Contd……)30%* Pattern of questions should be such that students can use their skills to solve them.20%* Vigilance system during examination should be improved.40%Workshops/Refresher-Courses for papers setters and checkers should be organized.30%System of assessing the papers should be improved.20%GCEAgreed70%Disagreed20%Undecided10%Opinions*Percentage of each Response* Selective learning should be discouraged.30%* More application based questions should be included.20%* It should test deep understanding instead of basic knowledge.10%*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%FINDINGS5.3.1 SECTION I: (Significance / Aims / Objectives)5.3.1.1 Significance of MathematicsTeachersNo significant difference has been found between SSC and GCE teachers on the importance of mathematics in the school curriculum, an extremely high trend for agreement; SSC (97%) and GCE (95%) have been found for it (Table 194a. no.1).No significant difference between SSC and GCE teachers has been found regarding the statement that mathematics course is important atthe school level due to its application in practical life. An extremely high trend for agreement in both groups; SSC (92%) and GCE (93%), have been found for the statement (Table 194a, no.3).A decreasing trend of agreement for the following statements (given in an order from highest to least) has been found in both groups of teachers for the importance to mathematics (Table 13b, graph 1).It is largely applied in practical life (Agreed: SSC 96%; GCE 95%).It is largely applied in other subjects (Agreed: SSC 90%; GCE 98%).It develops the power of intellect (Agreed: SSC 95%; GCE 93%).It develops desirable habits (Agreed: SSC 58%; GCE 67%).It develops desirable attitudes (Agreed: SSC 57%; GCE 56%).Students No significant difference has been found between SSC and GCE students regarding the following statements.Mathematics is important because it trains the mind(Agreed: SSC 91%; GCE 96%).Mathematics is important because it is compulsory to pass this subject in order to succeed (Agreed: SSC 79%; GCE 75%).Mathematics is important because it is largely applied at the higher education level (Agreed: SSC 68%; GCE 67%). (Table 194a, no.14, 15, 16)A decreasing trend of agreement for the following statements (given in an order from highest to least) has been found in both groups of students for the importance to mathematics (Table 126b, graph 6).It trains the mind (Agreed: SSC 91%; GCE 96%).It is applied in many other subjects (Agreed: SSC 88%; GCE 94%).It is compulsory to pass this subject to get promoted to the next grade at school level (Agreed: SSC 79%; GCE 75%).It is largely applied in admission tests at higher education level (Agreed: SSC 68%; GCE 67%).There is a significant difference between SSC and GCE students on the statement,“I do mathematics to get good marks as it is a scoring subject”. A high trend for agreement (84%) on SSC side while a low trend for agreement (36%) on GCE side have been found for this statement (Table 194a, no. 12).5.3.1.2 Aims TeachersNo significant difference has been found between SSC and GCE teachers on the following aims of mathematics (Table.194a, no. 2, 3).Disciplinary aim (training of mind) (Agreed: SSC 88%; GCE 80%).Utilitarian aim (practical value in real life) (Agreed: SSC 92%; GCE 93%).Moreover, there is no significant difference between the two groups regarding the following statements.Aims of mathematics education are achievable (Agreed: SSC 86%; GCE 82%).Aims of mathematics education can be translated into small educational objectives(Agreed: SSC 66%; GCE 71%). (Table 194a, no. 6, 7)There is a significant difference between the teachers of two groups on the following statements.Development of problem solving skills is an aim of education (Agreed: SSC 93%; GCE 95%).Aims of education are convincing (Agreed: SSC 56%; GCE 80%). (Table194a, no. 4, 5)Students There is no significant difference between SSC and GCE students on the disciplinary aim of mathematics education with an agreement of 91% on SSC side and 96% on GCE side (Table.199a, no. 14).Objectives TeachersThere is no significant difference between SSC and GCE teachers on the statement that objectives of mathematics teaching are well defined (Agreed: SSC 92%; GCE 93%). (Table.194a, no. 9)There is a significant difference between SSC and GCE teachers on the following statements.Objectives of current teaching are derived from real aims (Agreed: SSC 62%; GCE 72%).Objectives are transmitted clearly to teachers(Agreed: SSC 58%; GCE 77%) (Table.194a, no. 8, 10).Students There is no significant difference of opinion between SSC and GCE students on the following statements.I have to do mathematics because of teachers’ emphasis on its importance (Agreed: SSC 42%; GCE 59%).School gives a special emphasis on mathematics over the other subjects (Agreed: SSC 67%; GCE 65%) (Table.194a, no. 11, 13).Curriculum A significance difference has been found between the teachers of SSC and GCE system on the following statements about curriculum.The curriculum prepares the students to apply mathematical knowledge in their daily lives (Agreed: SSC 73%; GCE 85%).The curriculum prepares the students for future vocations (Agreed: SSC 72%; GCE 83%).The focus of curriculum is on the needs of future education (Agreed: SSC 68%; GCE 87%).The curriculum is comparable with other countries of the region (Agreed: SSC 44%; GCE 72%).The curriculum is correlated with topics of other subjects (Agreed: SSC 73%; GCE 83%).The curriculum is flexible (Agreed: SSC 63%; GCE 77%).The curriculum reflects state-of-the-art (Agreed: SSC 54%; GCE 83%).The curriculum leads the students to achieve the set aims of mathematics education (Agreed: SSC 59%; GCE 85%). (Table 23, 24, 25, 26, 27, 28, 29 30)SECTION II: (Contents / Textbooks)Teachers No significant difference of opinion has been found between SSC and GCE teachers on the following statements about contents.The language of contents is simple (Agreed: SSC 85%; GCE 90%).Contents cover a proper proportion of mathematical representations (Agreed: SSC 81%; GCE 92%).It is properly sequenced (Agreed: SSC 75%; GCE 84%).It develops interest among students (Agreed: SSC 63%; GCE 65%). (Table 194b, no. 1, 2, 4, 9)A significant difference has been found on the opinions of teachers in the two groups on the following statements about contents.The pictures and colorful presentations in the textbooks help in conceptual understanding (Agreed: SSC 67%; GCE 85%).The content is balanced in terms of key areas of mathematics (Agreed: SSC 73%; GCE 92%).It contains worked examples that provide sufficient guidance to solve given problems on a topic easily (Agreed: SSC 68%; GCE 80%).It is according to the intellectual level of students (Agreed: SSC 63%; GCE 78%).It constitutes a proper proportion of activities to develop the habit of thinking (Agreed: SSC 42%; GCE 72%). It constitutes an appropriate proportion of problems on application of abstract principles of mathematics in real life situations (Agreed: SSC 54%; GCE 73%).It incites the sense of enquiry (Agreed: SSC 59%; GCE 70%).(Table 194b, no 3, 5, 6, 7, 8, 10, 11, 12)A significant difference has been found between SSC and GCE teachers on the following statements about the contents of text books (Table 37b, Graph 2)It develops logical reasoning (Agreed: SSC 69%; GCE 93%).It develops analytical and critical thinking (Agreed: SSC 60%; GCE 85%).It develops problem-solving skills (Agreed: SSC 67%; GCE 88%).It develops a spirit of exploration and discovery (Agreed: SSC 50%; GCE 63%).It develops the power of concentration (Agreed: SSC 54%; GCE 78%).Students There is no significance difference between the students of SSC and GCE system regarding the following statements.Textbooks have an attractive look (Agreed: SSC 32%; GCE 28%).Language of textbooks is clear and according to the proficiency of students (Agreed: SSC 72%; GCE 75%).The difficulty level of problems in the content is in accordance with the intellectual level of students (Agreed: SSC 54%; GCE 56%).Pictures facilitate in comprehending the concepts (Agreed: SSC 64%; GCE 65%). (Table 194b, no.13, 14, 19, 23)A significant difference has been found between the two groups of students on the following statements.Language of textbooks is difficult (Agreed: SSC 43%; GCE 19%).Content is illustrated with concept-related pictures from daily life (Agreed: SSC 33%; GCE 55%).Methods to solve different types of problems are explained through worked examples in the textbooks (Agreed: SSC 71%; GCE 89%).Diagrams are the frightening element of the textbooks (Agreed: SSC 29%; GCE 13%).I can study a new topic through worked examples provided in the textbook (Agreed: SSC 64%; GCE 28%).Only the contents explained by teacher should be studied (Agreed: SSC 42%; GCE 15%).All the topics in the textbooks are taught completely for the preparation of final exam (Agreed: SSC 59%; GCE 84%). (Table 194b, no.15, 16, 17, 18, 20, 21, 22)No significant difference between SSC and GCE students has been found for the statement (i) & (ii) while a significant difference has been found for the statement (iii) & (iv) about the components of the contents that are to be memorized (Table 143b, Graph7)Formulae should be memorized (Agreed: SSC 83%; GCE 80%).Steps of long procedures should be memorized (Agreed: SSC 70%; GCE 70%).Definitions should be memorized (Agreed: SSC 67%; GCE 23%).Proofs of geometrical theorems should be memorized (Agreed: SSC 82%; GCE 26%).A significant difference has been found between SSC and GCE students on the following remark about questions involving graphs (Table 150b, no. 1, Graph 9).Graphs are difficult (Agreed: SSC 49%; GCE 23%).SECTION III: (Approaches / Methods)TeachersApproaches No significant difference has been found between the teachers of SSC and GCE system on approach (i) and (iii) while a significant difference has been found on approach (ii) and (iv) (Table 47b, Graph 3).The selection, sequence and focus of entire instructional activities remain on the needs and interests of the learner (Agreed: SSC 95%; GCE 87%).The focus remains on the contents but with an emphasis placed on the development of understanding of concepts among the learners (Agreed: SSC 87%; GCE 93%).The focus remains on contents but with an emphasis on solving problems from textbooks and becoming expert in them (Agreed: SSC 80%; GCE 78%).The focus remains on the maintenance and continuous flow of planned activities in the class with an emphasis of class discipline (Agreed: SSC 85%; GCE 68%).The highest trend of agreement (95%) for approach (i) but a relatively low trend of agreement (80%) for approach (iii) has been observed in SSC group of teachers. On the other hand, the highest trend of agreement (93%) was for approach (ii) and a relatively low trend of agreement (68%) for approach (iv) has been observed in GCE group of teachers. MethodsNo significant difference has been found between the teachers of SSC and GCE system on method (ii), (iii) and (iv) while a significant difference has been found on method (i) and (v).All the sums from an exercise should be solved on the black/white board (Agreed: SSC 39%; GCE 25%).Some questions should be solved on the board and students should have to do the remaining sums in class (Agreed: SSC 93%; GCE 80%).Only important points should be explained on the board and students should be encouraged to solve problems with teacher’s help (Agreed: SSC 69%; GCE 77%).Problems should be given to solve and teacher should help students only when they ask for it (Agreed: SSC 66%; GCE 65%).Problems should be given to students in groups to find their solutions with the cooperation of teacher and other members of the group (Agreed: SSC 77%; GCE 72%).The highest trend of agreement (93%) for method (ii) while the least trend of agreement (39%) for approach (i), has been found in SSC group of teachers. On the other hand, the highest trend of agreement (80%) was for approach (ii) and the least trend of agreement (25%) for approach (i) has been found in GCE group of teachers. It shows that there is no difference of opinions on the role of a teacher in both groups. No significant difference has been found between SSC and GCE teachers on the following statements.Repetition of a learned material may attach meaningful relationships among the fragments of knowledge(Agreed: SSC 90%; GCE 88%).Retention of learned material in the memory becomes stronger with repetition (Agreed: SSC 89%; GCE 87%).For rigorous drill, additional material is used (Agreed: SSC 73%; GCE 68%).Additional material used for drill is mostly previous exam papers (Agreed: SSC 55%; GCE 67%).Previous exam papers are solved to understand the pattern of paper (Agreed: SSC 91%; GCE 90%). (Table 194c, no. 2, 3, 7, 21, 22)A significant difference has been found between SSC and GCE teachers on the following statements.Sums should be solved by the teacher’s explained method only (Agreed: SSC 61%; GCE 27%).Questions of previous papers often repeat (Agreed: SSC 67%; GCE 42%).Some topics are always left untaught (Agreed: SSC 55%; GCE 31%).Homework is assigned and checked regularly (Agreed: SSC 88%; GCE 68%).Emphasis is placed on neat and tidy written work (Agreed: SSC 95%; GCE 67%).Emphasis is not placed on checking answers (Agreed: SSC 52%; GCE 32%).Topics are not explored in depth; only the procedures of solving the sums are explained (Agreed: SSC 54%; GCE 33%). (Table 194c, no. 1, 6, 11, 13, 14, 15, 18)StudentsLearning ExperiencesNo significant difference has been found between SSC and GCE students on the following statementsUsually, the last questions (star questions) of the exercises are left unsolved (Agreed: SSC 59%; GCE 68%).There is more than one method to solve a problem (Agreed: SSC 87%; GCE 95%).Emphasis is given by teachers to solve problems by their explained methods only (Agreed: SSC 71%; GCE 66%).Additional material (worksheets/workbooks etc.) is used to get further practice of the sums (Agreed: SSC 62%; GCE 74%).Teachers normally explain for less than 15 minutes in a class (Agreed: SSC 23%; GCE 35%).Homework is assigned in order to complete the syllabus (Agreed: SSC 80%; GCE 79%).Topics are not explored in depth; only the procedure of doing a sum is explained (Agreed: SSC 49%; GCE 43%).The activities of mathematics class are largely a repetition of similar sums (Agreed: SSC 62%; GCE 73%).Students mostly ask ‘HOW’ type questions in the class (Agreed: SSC 91%; GCE 94%). (Table 194c, no. 24, 25, 26, 28, 33, 38, 40, 40, 42) A significant difference has been found between SSC and GCE students on the following statements.Doing important topics is better than doing all the topics for getting good marks (Agreed: SSC 63%; GCE 28%).Most of the teachers emphasize neat and tidy work (Agreed: SSC 84%; GCE 64%).Teacher-constructed problems are presented in the class (Agreed: SSC 68%; GCE 39%).Separate activities are done for low achievers in the class (Agreed: SSC 52%; GCE 16%).Teachers arrange activities to engage high achiever students to help their low achiever class fellows (Agreed: SSC 53%; GCE 43%).Students normally ask less than 5 questions in a period (Agreed: SSC 47%; GCE 25%).‘WHY’ type questions are not encouraged by teachers in the class (Agreed: SSC 50%; GCE 66%).Some topics of the textbooks are never taught (Agreed: SSC 73%; GCE 30%).Homework is assigned and checked regularly by the teachers (Agreed: SSC 68%; GCE 19%). (Table 194c, no. 23, 27, 29, 30, 31, 32, 33, 37, 39)No significant difference has been found between the students of SSC and GCE system on method (i) and (iv) while a significant difference has been found on method (ii) and (iii). (Table 171b, Graph 10)Teachers explain some problems from an exercise in the textbook on the board (Agreed: SSC 91%; GCE 94%).Teachers explain all the problems from an exercise in the textbook on the board (Agreed: SSC 37%; GCE 24%).Teachers explain the important procedures and points on the board and helping us in solving sums individually (Agreed: SSC 72%; GCE 86%).Teachers give us problems and facilitate us in finding their solutions (Agreed: SSC 30%; GCE 34%).The highest trend of agreement (91%) for method (i) while the least trend of agreement (30%) for approach (iv), has been found in SSC group of students. On the other hand, the highest trend of agreement (94%) was for approach (i) and the least trend of agreement (24%) for approach (ii) has been found in GCE group of teachers. It shows that there is no difference of opinion on the methods experienced by them. In both groups of students the commonly experienced methods are found (i) & (iii) i.e. teachers solve some questions on the board by explaining important procedures and help students to solve the other. No significant difference of opinion between SSC and GCE students has been found on attribute (iii). Moreover, a high trend of agreement, SSC 93%&GCE 98% has been found in both groups for it. It means that students of both groups like those teachers who present difficult things in an easy manner. (Table 172b, Graph 11)SECTION IV: (Assessment / Evaluation)TeachersNo significant difference has been found between SSC and GCE teachers on the following statements.The verbal/written remark of teacher on the basis of assessment is evaluation (Agreed: SSC 77%; GCE 82%).Assessment helps both teacher and learner in the process of teaching and learning (Agreed: SSC 96%; GCE 90%).A teacher is always engaged in the process of assessing his/her students during the class (Agreed: SSC 81%; GCE 85%).The encouraging remarks of a teacher after assessment produce positive effect on the performance of students (Agreed: SSC 94%; GCE 90%).The main purpose of assessment is to improve teaching and learning of mathematics (Agreed: SSC 90%; GCE 92%).The exam papers are balanced in terms of content areas (Agreed: SSC 88%; GCE 90%).Teachers’ assessment during class is as important as the final examination (Agreed: SSC 88%; GCE 92%).All the teaching and learning process in the class is designed and implemented to pass the final examinations (Agreed: SSC 78%; GCE 73%) (Table 194d, no. 3, 4, 6, 7, 9, 11, 17, 26). A significant difference has been found between SSC and GCE teachers on the following statements.Tests/Exams are conducted to assess the level of achievement of the instructional objectives (Agreed: SSC 100%; GCE 92%).Tests/exams are conducted to categorize students into successful and unsuccessful groups (Agreed: SSC 72%; GCE 57%).The fear of assessment motivates students to work hard work (Agreed: SSC 93%; GCE 80%).Assessment should enable students to reveal what they know rather than what they do not know (Agreed: SSC 79%; GCE 85%).The system of checking papers is fair (Agreed: SSC 67%; GCE 88%).Examinations are conducted under strict vigilance (Agreed: SSC 71%; GCE 93%).Use of unfair means in the paper of mathematics is common (Agreed: SSC 42%; GCE 30%).Grading system of (GCE/SSC) is appropriate (Agreed: SSC 69%; GCE 82%).Students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior grades (Agreed: SSC 88%; GCE 70%).Final examinations assess the factual and procedural knowledge of mathematics only (Agreed: SSC 82%; GCE 57%).Questions in the exam papers are given according to a set pattern (Agreed: SSC 76%; GCE 72%).Questions are taken from the textbooks in (GCE/SSC) papers (Agreed: SSC 60%; GCE 23%).Questions are taken from past papers in (GCE/SSC) papers (Agreed: SSC 43%; GCE 40%).Some topics from the syllabus may be dropped on the basis of ample choice of question in the exam paper (Agreed: SSC 69%; GCE 53%).On the basis of previous papers some questions can be predicted for the upcoming paper (Agreed: SSC 80%; GCE 53%).Sections of exam papers are made in such a way that questions from some particular chapters always appear in a specific section (Agreed: SSC 83%; GCE 65%).(Table 194d, no. 1,2,5,8,13,14,15,16,18,19,20,21,22,23,24,25)StudentsNo significant difference has been found between SSC and GCE students on the following statements.Assessments help in identifying and reducing mistakes (Agreed: SSC 93%; GCE 95%).Assessments help in the preparation of final examinations (Agreed: SSC 87%; GCE 98%).Speed tests are conducted regularly in the class (Agreed: SSC 24%; GCE 35%).Positive remarks of the teacher on student’s assessment produce better results (Agreed: SSC 82%; GCE 83%).Students study seriously under the pressure of tests/examinations (Agreed: SSC 78%; GCE 88%). (Table 194d, no. 28, 29, 31, 32, 34) A significant difference has been found between SSC and GCE students on the following statements.Assessments help in confidence building (Agreed: SSC 88%; GCE 85%).Quizzes (short tests based on calculations without using calculators) are conducted regularly in the class (Agreed: SSC 39%; GCE 55%).I am well aware of the pattern of (GCE/SSC) paper (Agreed: SSC 88%; GCE 83%).Teachers leave some topics completely on the basis of their insignificance in the (GCE/SSC) paper (Agreed: SSC 69%; GCE 38%).Questions in (GCE/SSC) papers are given according to a fixed pattern (Agreed: SSC 87%; GCE 40%).Questions come from the textbooks in (GCE/SSC) papers (Agreed: SSC 78%; GCE 16%).Questions are taken from past papers in SSC/GCE paper (Agreed: SSC 77%; GCE 30%).Some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper (Agreed: SSC 73%; GCE 23%).On the basis of previous papers some questions can be predicted for the upcoming paper (Agreed: SSC 90%; GCE 50%).In junior grades (VI – VIII); the final paper is set from the whole syllabus (Agreed: SSC 44%; GCE 80%).In junior grades (VI – VIII); the final paper is set from the topics covered in the final term only (Agreed: SSC 62%; GCE 15%).In junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term (Agreed: SSC 48%; GCE 13%).A significant difference has been found between SSC and GCE students on the methods of revision (i), (ii), (iv) and (v). Only method (iii) is one on which no significant difference has been found (Table 188b, Graph 12).An extremely high trend for agreement SSC 88% & GCE 94% has been found in both groups of students for method (iii).It means that there is no significant difference between the two groups of students on solving sums from past papers (five years) as a method of revision. CUMULATIVE FINDINGS GeneralSSC and GCE systems were in a complete agreement on the significance of mathematics in the school curriculum but in GCE system, a higher satisfaction level has been found in the current practice of teaching.The clarity of aims and objectives of teaching mathematics, as expected in their corresponding curricula, was much higher among teachers of the GCE system than the teachers of the SSCsystem.Teachers and students of both systems gave importance to mathematics due to its practical and disciplinary value. There was a ‘one year’s suspension’ of mathematics during grade IX on the SSC side but no such discontinuity of mathematics educationwas found in GCE system at school level.GCE students were found completing their course in five years while SSC students complete their course in one year. GCE system was using a series of four textbooks, Book1 – Book 4. From grade VII - XI; they study selected contents of these four books. On the other hand, schools in SSC system were found using different series of textbooks till grade VIII, after which they all use the same textbook published by Sindh Textbook Board (in grade X).GCE system has been found with a focus on ‘depth versus breadth’, while SSC system has a focus on ‘breadth versus depth’. It means that teachers of GCE system emphasize more on proficiency in knowledge and skills while on the other hand there is a focus on furthering subject’s knowledge in SSC system.There was a relatively higher chance of drill (practice) of learned material found on GCE side than on the SSC side. This is because GCE system gives more time to complete the syllabus and has a policy of revisiting the topics in the exams successively at different grade levels to refresh the learning.CurriculumThe mathematics curriculum ofthe GCE system was found state-of-the-art and comparable with the curricula of other countries of the region while the SSC curriculum was not found such.The curriculum of GCE system was foundto be based on the principles of ‘utility’ and ‘preparation’. It prepares students for practical life and further studies. On the other hand, SSC curriculum’s prime focus has been on the principle of preparation for further studies.GCE curriculum has been found relatively more inclusive in terms of key content areas than the SSC curriculum.The focus of GCE curriculum was on coherence within different areas of the contents but SSC curriculum was relatively less coherent.The focus of GCE curriculum on coherence was on both, linear and upward integration and on the integrated application of learned concepts of one topic into other topics. The coherence within different areas of content was found only on the basic operational level in the SSC curriculum.The focus on articulation in GCE curriculum was also more than the SSC curriculum.ContentsThe logical sequence of the contents of GCE curriculum was more than the SSC curriculum.The contents for the development of problem solving skills in the students were found quite large in number in GCE course as compared to SSC course.SSC textbook did not have any content on everyday mathematics (percentage, rate/sale/purchase/interest /money etc.) while on the GCE side, there were a substantial proportion of these topics in the textbooks.The worked examples found in the textbooks of GCE system were more self-explanatory than the examples found in SSC textbooks. There was a wide gap of standards in terms of different areas of contents of SSC and HSC, while the difference between the course contents of O-Level and A-Level was not as much.Contents of SSC textbooks were found leaning towards the provision of mathematical knowledge of procedures and operations while on the GCE side there was a clear inclination towards the application of mathematical procedures and operations in everyday problems. GCE textbooks and question papers comprised of word problems in excess while SSC textbooks and question papers constituted a very small number of word problems. Textbooks of SSC system were not colourful, and had a discernible use of mathematical language while GCE textbooks were found having colourful presentation of pictures and diagrams with an indiscernible use of mathematical language embedded in common language.GCE textbooks were found containing contents for further exploration and discovery of a concept beyond the requirements of syllabus which were not present on SSC side.Textbooks of GCE system were found containing material for mental exercise (discipline of mind) beyond the requirement of syllabus but no such material was found in the SSC textbook.ApproachesThe approach of SSC teachers in selecting the contents for teaching was found significantly different from GCE teachers. SSC teachers select contents on the basis of three content areas i.e. arithmetic, algebra and geometry. It was found that this is done in order to set a paper for internal assessments with three sections, each containing questions from the above stated three areas. GCE teachers were found selecting contents in a logical sequence; mostly sequence of textbooks was used without a consideration to incorporate different areas of content.The approach of GCE system in organizing the contents for instruction was found to some extent spiral (concentric), while SSC system was applying a topical approach.The approach of teaching mathematics of GCE teachers was found ‘Content-Focused’ with an emphasis on understanding and performance. The approach of SSC teachers, on the other side was also ‘Content-Focused’ but emphasis was simply on performance. Students of SSC system were observed with an approach of selective study and prediction of questions for the upcoming paper. Students of GCE system on the other hand were found usingan approach of comprehensive study to have an experience of various ways of setting a problem on a topic in different situations. SSC students were found with an approach towards rote memorization especially in the geometrical theorems. GCE students did not show the approach of memorizing the mathematical contents except learning the formulae and procedures for solving the sums.GCE students were found to solve maximum of problems with an approach having the following steps: comprehending the problem, analyzing and evaluating the given situation, selecting a method of its solution, retrieving the procedure and/or formula from memory same or similar to given situation, applying it and finding its solution. On the other hand, SSC students were usually recognizing the problem by linking it with the textbook where they had previously solved it, retrieving from memory the method and/or formula, and using it to find the solution.MethodsThere was no significant difference found in the methods of teaching in both systems. Teachers of both systems were found to solve some problems of different types on the blackboards/whiteboards by explaining important points, procedures and formulae. Some problems were given to be solved in the class and some as homework.SSC teachers ensure that students keep proper notes of the solution of textbook problems. Regular checking of these notes has been observed on this side. GCE teachers were not found following this procedure.Homework is regularly and more properly checked on the SSC side than on the GCE side.SSC system emphasizes on neatness and tidiness of work which has been observed relatively less on GCE side.Teachers on SSC side mostly assert students to use the method explained by them, but on GCE side, relatively less teachers stress on it.GCE and SSC systems prepare their students for examination in the same manner. Both systems emphasize the solving of previous papers of CIE and BSEK respectively.There was no significant difference in the construction of tests in both systems. Teachers of both systems did not have a trend of constructing their own problems. SSC teachers were found usually taking these problems from textbooks and previous papers. GCE teachers were found taking them from workbooks, internet and previous papers.There was a significant difference in the method of assessment in both systems. Formative assessment was found more systematic on GCE side than SSCsystem. Formative assessments are done systematically on regular intervals and students’ performance is accumulated in their final exam’s performance. As a result, students use to take these assessments seriously. SSC system was found relying only on summative assessments. Moreover, in most of the SSC schools, there is a terminal system (semester system). They move forward on topical bases. Once a topic has been taught and assessed in a termdoes not come in the next term or even in the final examination.AssessmentQuestion papers of SSC system contain textbook questions but O-Level papers contain problems entirely different from those in textbooks. There is a pattern of repetition of the same questions in successive years in SSC papers while on GCE side, no clear pattern of repetition has been observed.There is a fixed outline of SSC papers in the sense that questions from certain chapters are always given in specific sections. An ample and consistent choice is always given to select questions from different sections. As a result of this fixed design and ample choice, a high trend of selected study and deletion of topics from the syllabus has been observed to be prevailing in this system. GCE papers on the other hand neither have a fixed design nor plenteous choice in the paper. Students of this system have to study all the topics from their syllabus.SSC papers were found predictable to a large extent, due to a fixed design and repetition of questions. Therefore, a trend of guessing questions for the upcoming papers by analyzing the pattern of questions in the previous year’s papers has been found in this system. GCE papers were neither easily predictable nor did they follow a pattern.GCE examinations were found to be held under strict vigilance while there was a common observation of the use of unfair means in the SSC examinations.There is more flexibility of taking examinations on GCE side. Students can appear for the examination twice in a year either in May or in November. On the SSC side, there is only one annual examination to appear in. However, a supplementary examination is held for those candidates who have not passed their annual examination.5.5 CONCLUSIONSOn the basis of analysis of data and findings of the study, the following conclusions were drawn.The GCE (O-Level) mathematics curriculum has been found being more effectively implementedas compared to the SSC curriculum.The first major factor found accountable for the effectiveness of GCE curriculum was the clarity of aims and objectives of this curriculum among GCE teachers which was not found, to that extent, among SSC teachers. Two important reasons are found of irrelevance of SSC system from the expected aims and objectives of their curriculum. The first reason is that the aims and objectives are neither easily approachable to teachers nor is there a movement in school managements to make them available. The second and most important reason is the worthlessness of these objectives for teachers as the method of examination was found to be fulfilling only shallow expectations of the curriculum.The second key factor found responsible for the effectiveness of GCE curriculum was the contents of their textbooks. These contents provide support in attaining the expected aims and objectives of their curriculum. These contents were found well balanced according to different domains of knowledge and they were found to promote problem solving, critical thinking and reasoning skills among students which is the requirement of the curriculum. Moreover, additional material such as workbooks and previous papers also found supportive to their textbooks in serving this cause. Textbooks on SSC side were not incorporated with additional resources including teacher’s manual, workbook and electronic resources according to the recommendations and guidelines of the national curriculum. Also, the contents of the textbooks were not found to be according to the standards and benchmarks by the National Curriculum of Mathematics (Government of Pakistan, 2006).The third prime factor found for the effectiveness of GCE curriculum was the difference in their approaches regarding: concentric organization of the contents for teaching; focus on depth versus breadth; systematics formative assessment and focus on investigation and application of knowledge versus dispensation of knowledge. SSC system has a topical approach of sequencing the contents for instruction. With this approach, a topic once taught does not appear in the next term or in the final internal school examinations at VI – VIII levels. SSC system focuses on breadth versus depth (expansion of content knowledge), dispensing information versus investigation and assessment of learning (summative) versus assessment for learning (formative). The aforementioned approaches were found to be the key reasons of relatively lower effectiveness of the SSC curriculum in achieving its aims.Methods of teaching were not that different but methods of assessment were found to be entirely different in the two systems, which is the fourth major factor of difference in the effectiveness of theses curricula. Method of assessment of GCE was based on its curriculum expectations. GCE papers have been observed neither with a fixed pattern of repetition of questions nor with a plenteous choice. Moreover, examinations of this system were found to be held under strict vigilance. The fifth and most damaging factor found in the assessment system of SSC was that in this system, questions from textbooks are given in both internal school examinations and in the papers of BSEK. As a result, students who feel some difficulty in grasping the concept start drifting towards memorizing the contents. Besides this, a fixed pattern of papers, with an ample choice in different sections and repetition of same questions successively was found. Moreover, a deviation towards selective study i.e. leaving some topics completely and guessing the contents of the upcoming papers has been observed. Also, the exams are not found to be conducted under such strict vigilance as was found in the GCE system.The sixth dominant factor found for the difference in the effectiveness was the suspension of mathematics education in grade IX in the SSC system. This suspension has been found to be another negative contributor because after such a long interruption, students who fail to recall their previous knowledge, a prerequisite for furthering on that topic, suffer problems in concept building because they cannot attach the new information with their previously learned knowledge. No such discontinuation of mathematics at school level has been found in the GCE system, which is another contributor in making curriculum more effective. RECOMMENDATIONSIn the light of drawn conclusions, the following recommendations are made.It is recommended that the expected aims and objectives of teaching mathematics at SSC level are transmitted to teachers. This document should be made public on the internet and should also be provided in schools. There is an urgent need to divert the focus of our schools towards enhancing thinking skills among students, especially higher order thinking skills (analysis, synthesis and evaluation). These thinking skills can be produced through proper teaching and assessment of mathematics in our schools. For this, two steps are suggested. The first step is motivation and counseling of school heads. To achieve this, it is recommended that a ‘Focus Program’ with a possible motto, “work for learning via work on thinking”, should be started for the school heads. Ministry of Education can conduct this program in collaboration with Board of Secondary Education Karachi (BSEK), to ensure the participation of heads of all registered schools in BSEK. In this program, school heads can be guided and counseled to focus on students’ thinking skills in their schools. They may be directed to ensure the teaching of mathematics according to the expected aims and objectives of SSC curriculum, in their institutions. It is recommended that the contents of the SSC textbook be revised. Contents on everyday application of mathematics (profit / loss / sale / purchase / hire-purchase / percentage / interest / money etc.) may be incorporated. Topics involving geometrical figures such as mensuration (area and volume of 2D / 3D figures) and trigonometry should be included. Topics that enhance logical reasoning such as number sequence and geometrical patterns should also be included. It is also recommended to increase the coherence within different areas of content by integrating them through word problems. Student’s monotonous outlook towards textbook should be changed by including material on the solution of real life problems through mathematical concepts; reducing excessive use of mathematical language with simple language and including colorful pictures and illustrations related to topic may be used to enhance conceptual understanding.It is strongly recommended that approaches of mathematics teachers should be changed. For this, the earlier recommended“Focus Program” may also be helpful. There is a dire need of proper training for mathematics teachers, at least basic training of teaching mathematics with proper approaches should be provided to all teachers. This may be done by organizing short training sessions under the supervision of school heads within the umbrella of “Focus Program”. Moreover, it is also recommended that separate professional degree programs from Bachelor to Ph.D. level for mathematics education should be started.There is an urgent need to change the method of assessment in the SSC system, both in internal school examinations and in BSEK examinations. There is an urgent need of changing the routine of giving textbook questions in the papers. To solve the problem of rote memorization in mathematics, it is recommended not to include any material in the paper in the same framework as is given in the textbooks. To discourage the approaches of selective study and prediction of papers, it is recommended that the pattern of sectioning papers on the basis of topics be changed and the choice of selection among questions should be minimized.It is strongly recommended that nature of questions in the SSC papers should be changed. Items of the question papers should assess application of knowledge rather than assessing theprecision in replication of content knowledge (facts, principles and algorithms). Word problems that assess higher order thinking skills should be included and increased gradually. The quality of questions can be improved by constructing those items in which figures, diagrams and graphs are involved.Moreover, problems that require insight solutions (problem-solving strategies) may also be included gradually.There is a dire need of continuation of mathematics as a subject at all levels in school curriculum. It is therefore recommended that the suspension of mathematics for a whole year during grade IX should be stopped. The textbook of mathematics consists of two merged parts: part I & part II. The part wise examination of each subject i.e. part I in grade IX and part II in grade X may be adopted, to ensure continuation of mathematics and naturally other subjects in addition.5.7 FUTURE RESEARCHAreas for further research may parison of Assessment and Evaluation System of SSC and GCEComparative Analysis of the Contents of Textbooks of SSC and GCEREFERENCESAmirali, M., & Halai, A. (2010). Teachers’ knowledge about the nature of mathematics: A survey of secondary school teachers in Karachi, Pakistan. Bulletin of Education and Research, 32 (2), 45-61.Anderson, L.W., & Krathwohl (Eds.). (2001). A taxonomy for learning, teaching and assessing: A revision of Bloom's taxonomy of educational objectives. New York: Longman.Arif , M. (2011). 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How Chinese learn mathematics: Perspectives from insides (pp. 189-207).Singapore: World Scientific Press.Hamdard Institute of Education and Social SciencesHAMDARD UNIVERSITY KARACHIA Comparative Analysis of the Effectiveness of Mathematics Curriculum Taught at GCE (O-Level) and SSC System of Schools in KarachiQUESTIONNAIRE FOR TEACHERSSECTION I: PARTICULARS ABOUT THE RESPONDENT.DIRECTIONS: Please fill in the given spaces or tick (√) mark as appropriate from the followingName (Optional):-------------------------------------------------------------------------------------------Gender: a) Male:----------- b) Female:-----------Marital Status: a) Married:--------- b) Unmarried:--------- Age: i) Less than 30 years: ------------ ii) 30 to 34 years: -----------iii) 35 to 39 years: -------- iv) 40 to 44 years: ---------- v) 45 to 49 years: ---------- vi) 50 years and above: -------Area of Residence:-----------------------------------------------------------------------------------------6. Qualification:a) Academic: -----------------------------------------------------------------------b) Professional: --------------------------------------------------------------------7. Teaching Experience: a) SSC (Matric): i) Less than 5 years----------- ii) 5 to 9 years-------- iii) 10 to 14 years---------iv) 15 to 19 years------------ v) 20 years and above----b) GCE (O-Level): i) Less than 5 years----------- ii) 5 to 9 years-------- iii) 10 to 14 years---------iv) 15 to 19 years------------ v) 20 years and above----8. Please specify the system (GCE/SSC), for which you are responding: ------------------------------9. Name & Address of Institution: ---------------------------------------------------------------------------10. Control of Institution: a) Public: --------------------------- b) Private: -----------------------------11. System of Education in the Institution (GCE/SSC/Both):--------------------------------------------12. Location of Institution: a) Town--------------------------------- b) District: --------------------------13. Monthly Income: i) Less than 40 thousands: -------------- ii) 40 to 60 thousands: --------------- iii) 60 to 80 thousands: ---------- iv) 80 to 100 thousands: --------- v) 100 thousands plus: ---------SECTION II: CURRICULUM-EFFECTIVENESS SCALEDIRECTIONS: Please tick (√) mark as appropriate from the following columns:SA=Strongly Agree, A=Agree, UD=Undecided, DA=Disagree, SD=Strongly Disagree.S.#ItemsAims/Objectives1Mathematics is one of themost important subjects in the school curriculum.SAAUDDSD2Mathematics is an important subject because:-it is used largely in practical lifeSAAUDDSDit is largely applied in other subjectsSAAUDDSDit develops powers of intellectSAAUDDSDit develops desirable habitsSAAUDDSDit develops desirable attitudesSAAUDDSD3The aim of mathematics education is to train or discipline the mind.SAAUDDSD4The aim of mathematics education is to transfer mathematical knowledge in order to apply it in real life.SAAUDDSD5The aim of mathematics education is to develop problem solving skills.SAAUDDSD6The aims of mathematics education are convincing.SAAUDDSD7The aims of mathematics education are achievable.SAAUDDSD8The aims of mathematics education can be translated into small educational objectives.SAAUDDSD9The educational objectives of the current curriculum of mathematics are derived from the real aims of mathematics education.SAAUDDSD10The objectives of mathematics education are well defined.SAAUDDSD11The objectives of mathematics education are clearly transmitted to teachers.SAAUDDSDCurriculum12The curriculum prepares the students to apply mathematical knowledge in their daily lives.SAAUDDSD13The curriculum prepares the students for future vocations.SAAUDDSD14The focus of curriculum is on the needs of future education.SAAUDDSD15The curriculum is comparable with the curricula of other countries of the region.SAAUDDSD16The curriculum is correlated with topics of other subjects.SAAUDDSD17The curriculum is flexible.SAAUDDSD18The curriculum reflects state-of-the-art.SAAUDDSD19The curriculum leads the students to achieve the set aims of mathematics education.SAAUDDSDContents20Contents of the textbooks are properly sequenced.SAAUDDSD21Contents of the textbooks develop interest in students.SAAUDDSD22Contents incite the sense of enquiry in students.SAAUDDSD23Language of the textbooks is simple.SAAUDDSD24Contents have a proper proportion of sums on application of abstract principles of mathematics in real life situations.SAAUDDSD25Worked examples in the textbooks provide sufficient guidance to solve all the sums given for exercise on that topic. SAAUDDSD26Contents of the textbooks develops:-logical reasoningSAAUDDSDanalytical and critical thinkingSAAUDDSDproblem-solving skillsSAAUDDSDspirit of exploration and discoverySAAUDDSDpower of concentration SAAUDDSD27Contents are in accordance with intellectual level of students.SAAUDDSD28Contents cover problems that can be solved by personal investigation without having any method to solve them.SAAUDDSD29The contents include a proper proportion of mathematical representations (graphs, figures, diagrams, tables).SAAUDDSD30The contents include an appropriate proportion of activities for mental exercise (puzzles/riddles etc.).SAAUDDSD31The contents are balanced in terms of key areas (number operation, geometry, algebra, measurement, data analysis and probability).SAAUDDSD32Pictures and colorful presentations in the textbooks put a positive effect on students’ conceptual understandings.SAAUDDSD33The number of problems on a certain topic given in the textbook affects conceptual understanding positively.SAAUDDSD34Chaining (bit by bit addition of new material in the sums) on a certain topic in the text booksput a positive effect on conceptual understanding.SAAUDDSD35Contents of the textbooks are properly chained.SAAUDDSDApproaches/Methods 36The approach of a mathematics teacher should be:-The selection, sequence and focus of entire instructional activities remain on the needs and interests of learner.SAAUDDSDThe focus remains on content but with an emphasis on the development of understanding of concepts among the learners.SAAUDDSDThe focus remains on content but with an emphasis on solving problems from textbooks and becoming expert in them.SAAUDDSDThe focus remains on the maintenance and continuous flow of planned activities in the class with an emphasis of class discipline.SAAUDDSD37I as a mathematics teacher like to: solve all the sums from an exercise on the board SAAUDDSDsolve some questions on the board and let the students do remaining sums in the classSAAUDDSDexplain only important points on the board and encourage students to solve problems with my helpSAAUDDSDgive them problems to solve by their own and help them only when they ask for itSAAUDDSDgive problems to groups of students in the class to discussand find solutionsSAAUDDSD38Sums should be solved usingthe method explained by the teacher only.SAAUDDSD39Additional material is usually used for deeper understanding of concepts.SAAUDDSD40Additional material is usually used for rigorous drill of learned material.SAAUDDSD41Mostly previous exam papers are used as an additional materialSAAUDDSD42Past papers are solved as a rehearsal for the actual exam papers.SAAUDDSD43Past papers are solved because questions of previous papers are considered important.SAAUDDSD44Past papers are solved because questions from previous papers often repeat in the new papers.SAAUDDSD45Past papers are solved to understand the pattern of questions coming in the recent papers.SAAUDDSD46Teacher-constructed problems are presented in the class.SAAUDDSD47Students are allowed to construct and present their own problems in the class.SAAUDDSD48Procedures of doing a problem are explained but not the reason for the selection of that procedure.SAAUDDSD49There are some topics in the textbooks that are always left untaught as no question comes in the paper from these topics.SAAUDDSD50Homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in class.SAAUDDSD51Completion of a topic means that teacher has explained the topic and students have done the sums in their copies.SAAUDDSD52Emphasis is placed on neat and tidy written work.SAAUDDSD53Homework is assigned and checked regularly.SAAUDDSD54Topics are not explored in depth; only the procedure of doing a sum is explained.SAAUDDSD55Unexplained short-cuts are told to solve certain problems.SAAUDDSD56Derivation of the formula is not clarified, only the method of its application is explained.SAAUDDSD57Usually students avoid checking answers.SAAUDDSD58Usually students try to skip graph questions.SAAUDDSD59Teachers do not emphasize checking of answers by students.SAAUDDSD60Teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of classSAAUDDSD61Mathematics has a significant application in other subjectsSAAUDDSD62Teachers’ true role is to generate a question in the mind of a child before it is answered.SAAUDDSD63Both posing questions and giving their answers by teacher himself/herself produce shallow understanding.SAAUDDSD64Students can communicate mathematical ideas, reasoning and results.SAAUDDSD65Students take teaching of mathematics as a pleasant activity.SAAUDDSD66Students exhibit courage in facing unfamiliar problems.SAAUDDSD67Students express tolerance in solving difficult problems.SAAUDDSD68Retention of learned material in the memory becomes stronger with repetition.SAAUDDSD69Repetition of learned material may attach meaningful relationships among the fragments of knowledge.SAAUDDSDAssessment/Evaluation70Tests/Exams are conducted to assess the level of achievement of the instructional objectives.SAAUDDSD71Tests/exams are conducted to categorize students into successful and unsuccessful groups.SAAUDDSD72The verbal/written remark of a teacher on the basis of assessment is evaluation.SAAUDDSD73Assessment helps both teacher and learner in the process of teaching and learning.SAAUDDSD74The fear of assessment motivates students to work hard.SAAUDDSD75The fear of final examinations is actually the fear of being insulted on its results.SAAUDDSD76A teacher is always engaged in the process of assessing his/her students during the class.SAAUDDSD77The encouraging remarks of a teacher after assessment produce a positive effect on the performance of students.SAAUDDSD78The discouraging remark of a teacher produces a negative effect on the performance of students.SAAUDDSD79Methods of assessment should enable students to reveal what they know, rather than what they do not know.SAAUDDSD80Students take mathematics assessments confidently.SAAUDDSD81The main purpose of assessment is to improve teaching and learning of mathematics.SAAUDDSD82The exam papers assess the objectives of teaching mathematics.SAAUDDSD83The exam papers are balanced in terms of content areas.SAAUDDSD84The exam papers assess the actual educational objectives of teaching mathematics.SAAUDDSD85The system of checking papers is fair.SAAUDDSD86Examinations are conducted under strict vigilance.SAAUDDSD87Use of unfair means in the paper of mathematics is common.SAAUDDSD88Grading system of SSC/GCE is appropriate.SAAUDDSD89Teachers’ assessment during class is as important as the final examination.SAAUDDSD90Students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior grades.SAAUDDSD91Final examinations assess the factual and procedural knowledge of mathematics only.SAAUDDSD92Questions in the exam papers are given according to a set pattern.SAAUDDSD93Questions are given from the textbooks in SSC/GCE papers.SAAUDDSD94Questions are given from past papers in SSC/GCE papers.SAAUDDSD95Some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paper.SAAUDDSD96On the basis of previous papers some questions can be predicted for the upcoming paper.SAAUDDSD97Assessment is done to distinguish students for the improvement of learning.SAAUDDSD98Test items of SSC/GCE papers cover all objectives of the curriculum.SAAUDDSD99Sections of exam paper are designed in such a way that questions from particular chapters always come in a specific section.SAAUDDSD100The entire teaching and learning process in the class is designed and implemented to pass the final examinations.SAAUDDSDHamdard Institute of Education and Social SciencesHAMDARD UNIVERSITY KARACHIA Comparative Analysis of the Effectiveness of Mathematics Curriculum Taught at GCE (O-Level) and SSC System of Schools in KarachiQUESTIONNAIRE FOR STUDENTSSECTION I: PARTICULARS ABOUT THE RESPONDENT.DIRECTIONS: Please fill in the given spaces or tick (√) mark as appropriate from the following:Name(Optional):-----------------------------------------------------------------------------------2. Class: -----------------------GCE (O-Level): -------------------- SSC (Matric) -------3. Name of Institution: -------------------------------------------------------------------------------4. Location of Institution: ----------------------------------------------------------------------------5. System of Education in the Institution (GCE/SSC/Both):------------------Age: ---------------------years.7. Gender: a) Male: ---------- b) Female: ----------8. Qualification of Parents:a) Father: i) Graduate: ------------- ii) Undergraduate: --------b) Mother: i) Graduate: ------------- ii) Undergraduate: --------9. Area of Residence: -----------------------------------------------------------------------------------------10. District: -----------------------------SECTION II: CURRICULUM-EFFECTIVENESSSCALEDIRECTIONS: Please tick (√) mark as appropriate from the following columns:SA=Strongly Agree, A=Agree, UD=Undecided, DA=Disagree, SD=Strongly Disagree.Sr.#ItemsGeneral1Mathematics is an interesting subject.SAAUDDSD2I feel pleasure in doing mathematics.SAAUDDSD3I do mathematics because teachers emphasize its importance.SAAUDDSD4I do mathematics because it is a compulsory subject at school level.SAAUDDSD5Mathematics demands rigorous practice.SAAUDDSD6Mathematics requires concentration.SAAUDDSD7High achievers in mathematics argue strongly.SAAUDDSD8High achievers in mathematics are good analysts. SAAUDDSD9High achievers in mathematics raise more questions.SAAUDDSD10School gives a special emphasis on mathematics over the other subjects.SAAUDDSD11What is your view about mathematics as a subjectits contents are useless in daily lifeSAAUDDSDit is difficult to memorize the formulaeSAAUDDSDthere is useless repetition of similar sumsSAAUDDSDit requires a lot of time for practiceSAAUDDSD12High achievers in mathematics also achieve high grades in other science subjects.SAAUDDSD13Doing mathematics means doing mental exercise.SAAUDDSD14Correct solution of a problem gives a feeling of achievement.SAAUDDSD15Mathematics is very important subject becauseit trains the mindSAAUDDSDit is compulsory to pass this subject for getting promotion in next grade at school levelSAAUDDSDit is largely applied in admission tests at higher education levelSAAUDDSDit is applied in many other subjectsSAAUDDSD16Mathematics is a scoring subject.SAAUDDSDTextbooks/Contents17Textbooks of mathematics have an attractive look.SAAUDDSD18Language used in the textbooks is clear.SAAUDDSD19Language of mathematics textbooks is difficult because excessive mathematical terminologies are used. SAAUDDSD20All the topics in the textbooks are taught completely for the preparation of final examination.SAAUDDSD21Methods to solve different types of problems are explained through worked examples in the textbooks.SAAUDDSD22Textbooks are illustrated with concept-related pictures from real life.SAAUDDSD23The pictures facilitate in comprehending the concepts.SAAUDDSD24Diagrams are the frightening element of the textbooks.SAAUDDSD25I can study a new topic through worked examples provided in the textbook.SAAUDDSD26I study the topic from the textbook first before it is explained by the teacher in class.SAAUDDSD27I have questions in mind before starting a new lesson.SAAUDDSD28Only the contents explained by teacher should be studied.SAAUDDSD29It is to memorize in mathematicsformulaeSAAUDDSDsteps of long proceduresSAAUDDSDdefinitionsSAAUDDSDproofs of geometrical theoremsSAAUDDSD30Contents of the textbooks are in accordance with intellectual level of students.SAAUDDSD31Language of the textbooks is in accordance with language proficiency of students SAAUDDSDLearning Experiences32Getting afraid of a problem in the first look makes it very difficult to solve.SAAUDDSD33Doing important topics is better than doing all the topics in order to get good marks.SAAUDDSD34The last questions (star questions) of the exercises are generally left unsolved.SAAUDDSD35To solve a mathematics problem we think to retrieve formula and method from memorySAAUDDSDto develop our own strategy to solve the problemSAAUDDSDto get an insight(idea/clue) for solutionSAAUDDSDto recall from which chapter and exercise number the problem belongsSAAUDDSD36Most of the teachers emphasize solving the sums using their explained methods only.SAAUDDSD37There is more than one method to solve a problem.SAAUDDSD38Most of the teachers emphasize neat and tidy work.SAAUDDSD39Drawing graphs isdifficultSAAUDDSDboringSAAUDDSDtime consumingSAAUDDSDannoyingSAAUDDSD40Additional material (worksheets/workbooks etc.) is used to get further practice of the sums.SAAUDDSD41Teacher-constructed problems are presented in the class.SAAUDDSD42Separate activities are done for low achievers in the class. SAAUDDSD43Teachers arrange activities to engage high achiever students to help their low achiever class fellows.SAAUDDSD44In a mathematics class of 40 minutes, students normally ask less than 5 questions.SAAUDDSD45In a mathematics class of 40 minutes, teachers normally explain for less than 15 minutes.SAAUDDSD46Students mostly ask ‘HOW’ type questions (How to solve it? / How to use it?) in the class.SAAUDDSD47‘WHY’ type questions (Why this method is used?) are rarely posed by students.SAAUDDSD48Teachers do not encourage ‘WHY’ type questions in the class.SAAUDDSD49Procedure of doing a problem is explained but not the reason for the selection of that procedure.SAAUDDSD50Some topics of the textbooks are never taught.SAAUDDSD51Homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in class.SAAUDDSD52Completion of a topic means that teacher has explained the topic and students have done the sums in their notebooks.SAAUDDSD53Homework is assigned and checked regularly by the teachers.SAAUDDSD54Classwork of students is checked regularly by the teachers.SAAUDDSD55Topics are not explored in depth; only the procedure of doing a sum is explained.SAAUDDSD56Short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explained.SAAUDDSD57Derivation of formula is not explained only the method of its application is told.SAAUDDSD58The activities of mathematics class are largely doing repetition of similar sums.SAAUDDSD59Reference books are taken from the library to explore the topics in depth.SAAUDDSD60Teachers teach mathematicsby explaining some problems from an exercise in the textbook on the boardSAAUDDSDby explaining all the problems from an exercise in the textbook on the boardSAAUDDSDby explaining the important procedures and points on the board and helping students in solving sums individuallySAAUDDSDby giving students well-structured problems and facilitating them in finding their solutions by their own methodsSAAUDDSD61A good teacher of mathematics is that who:Starts a lesson with the revision of previous workSAAUDDSDPresents an uninteresting thing in an interesting waySAAUDDSDMakes difficult things easySAAUDDSDExplains a lengthy topic very concisely SAAUDDSDKeeps the students alert and attentive by creating humor or by interesting stories SAAUDDSDGives encouraging feedback to studentsSAAUDDSDEngages all the class in workSAAUDDSDEnds a lesson with summarizationSAAUDDSDTests/ Examinations62Assessments help in confidence building.SAAUDDSD63Assessments help in identifying and reducing mistakes.SAAUDDSD64Assessments help in the preparation of final examinations.SAAUDDSD65Quizzes (short tests based on calculations without using calculators) are conducted regularly in the class. SAAUDDSD66Speed tests are conducted regularly in the class.SAAUDDSD67Positive remarks of the teacher on student’s assessment produce better results.SAAUDDSD68Negative remarks by a teacher on student’s assessment produce demoralization. SAAUDDSD69I am well aware of the pattern of SSC/GCE paper.SAAUDDSD70Students study seriously under the pressure of tests/examinations.SAAUDDSD71Teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paper.SAAUDDSD72Questions in SSC/GCE papers are given according to a fixed pattern.SAAUDDSD73Questions are taken from the textbooks in SSC/GCE papers.SAAUDDSD74Questions are taken from past papers in SSC/GCE papers.SAAUDDSD75Some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper.SAAUDDSD76Some questions can be predicted for the upcoming paper on the basis of previous.SAAUDDSD77Revision for mathematics test/ examination is done bysolving all sums on the topic from the textbookSAAUDDSDsolving different types of sums from the exercises in the textbooksSAAUDDSDsolving sums from the past papers (five years)SAAUDDSDreading solved sums from the notebooks (notes maintained in the form of solution of sums)SAAUDDSDreading worked examples from the textbooksSAAUDDSD78In junior grades (VI – VIII); the final paper is set from the whole syllabus.SAAUDDSD79In junior grades (VI – VIII); the final paper is set from the topics covered in the final term only.SAAUDDSD80In junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term.SAAUDDSDINTERVIEW PROTOCOLFOR EXPERTS OF THE SUBJECTName (optional):-----------------------------------------------------------------------------------2. Qualifications: a) Academic: ---------------------------------b) Professional: ------------------------------3. Designation: --------------------------------------------4. Name of Institution: -------------------------------------------------------------------------------5. Control of Institution:a) Government: ------------------------b) Private: -------------------------------6. Experience (in years):a) Teaching: --------------------------------------------------------b) Other (Please mention): ---------------------------------------7. Please specify the system (GCE/SSC) for which you are responding: -------------------Q.1 Are you satisfied with the current routine of teaching mathematics at school level? If not, what are your reservations?---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.2 Is teaching of mathematics according to some clear objectives? If yes, then according to your observation, what is themajor objective?------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.3 Do you agree that these objectives can fulfill the true aims of mathematics education?-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.4 Do you agree that mathematics education in Pakistan is competitive with the other countries of Asia?--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.5 Do you agree that mathematics should be the prime focus of school curriculum as it develops cognitive, affective and psychomotor faculties of an individual ?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.6 Are you satisfied with the contents of textbooks of mathematics used at secondary level?--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.7 What changes would you like to suggest to improve these textbooks?------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Q.8 Are you satisfied with the current methods of selection and sequencing of contents? If not, please give your opinion.---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.9 In your opinion, what changes should be made in the approaches and methods of teaching mathematics?--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.10 Are you satisfied with current system of assessment in mathematics at school level? If not, please suggest some changes.----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.11 Are you satisfied with the current pattern of mathematics paper (GCE/SSC)? In your opinion, what improvements should be made in it?----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.12 What are the major strengths of the current system of teaching and learning mathematics in your opinion?------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.13 What are the major weaknesses in your opinion in the current system of mathematics education?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.14 What changes would you like to suggest for the overall improvement of mathematics education?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 1System: SSCInstitution: PrivateDesignation: HMQualification: B.Sc. M.EdTeaching Experience: 45 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Unsatisfied because objectives of teaching are not coherent with the needs of students and society.Agreed, objective is to provide basic knowledge to study this subject in higher classes.Disagreed.Disagreed.Agreed.Unsatisfied.New topics should be added on everyday mathematics. Word problems sould be increased and examples in the textbooks should be improved. Sequence of contents is not proper at lower secondary and secondary level. Teaching should be activity-based Unsatisfied. We mostly rely on final examinations. It will be better to use forrmative assessment system.Pattern of paper should be such that it discourages guess work and selected-content study habit.It provides strong factual and procedural knowledge of different operations in mathematics.Syllabus is too lengthy for a 9-month session.Curriculum should be revised and its expected learning outcomes should be transmitted to teachers. Moreover, pattern of SSC paper should be changed to assess the level of attainment of true objectives of the curriculum. Refresher courses should be conducted for teachers. INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 2System: SSCInstitution: PrivateDesignation: HMQualification: B.Sc. MEdTeaching Experience: 35 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Unsatisfied because mostly untrained teachers are teaching mathematics in most of the schools Agreed.Disagreed.Disagreed.Agreed.Satisfied.Word problems on everyday mathematics should be included and increased.Sequence of contents needs improvement.Activity-based teaching willbe more productive than the routine teaching.Discourage rote memorization of contents by giving application based problems as much as possible. Vigilance system during SSC examinations should be improved.The system develops among students, a skill of presenting their learned material in a well-organized and orderly manner.There is a discontinuation of one complete year for the study of mathematics in the system. Students after class VIII study mathematics in class X. The suspension of mathematics in grade IX is the biggest weakness of the current system.Teaching of mathematics should be made uninterrupted by eliminating the one year suspension of mathematics during class IX. Refresher courses should be organized.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 3System: SSCInstitution: PrivateDesignation: HMQualification: M.ScM.EdTeaching Experience: 21 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Unsatisfied because there is a discontinuation of one year in its teaching. This subject is not taught in grade IX which creates problems in the conceptual understanding of students. Agreed, objective is to continue this subject in higher grades.Disagreed.Disagreed.Agreed.Unsatisfied.Textbooks should be updated regularly. Worked examples in the textbooks should be improved. Improvement in the sequence of contents of the textbook is required.Teaching with the aid of technology (audio-video aides, internet etc.) is required.Understanding of students should be checked rather than checking that the student can solve a sum or not. System of assessing papers should be improved. Examinations should be conducted under strict care to control the increasing trend of cheating.It provides strong content knowledge for further studies.Discontinuation of mathematics in grade IX is the major weakness.Textbooks should be revised. Mathematics should be taught without a break during school education. It should be taught in Karachi Board during grade IX like Federal Board and all the Boards of the province Punjab.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 4System: SSCInstitution: PrivateDesignation: HODQualification: M.ScTeaching Experience: 15 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.SatisfiedUndecidedAgreedAgreedOther subjects should also be given equal importance.Satisfied.New topic should be included in the textbook.Textbooks should be activity-based that can develop interest among students. Selection and sequencing of content should be made according to educational needs of the students.Mathematics should be taught just like a language.Textbooks sums should not be given in the papers.Satisfied, but exams should be conducted under proper supervision and use of unfair means should be controlled.It provides basic knowledge of mathematical procedures and formulae.Use of unfair means in the examination is the biggest problem of this system.Curriculum and textbooks should be revised.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 5System: SSCInstitution: PrivateDesignation: HODQualification: M.Sc M.EdTeaching Experience: 27 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Not satisfied, as there is a shortage of trained teachers who can teach mathematics in a professional manner. Disagreed, objective is to make students learn formulae and procedures to solve different kinds of problems.Disagreed.Disagreed.Agreed.Unsatisfied.Word problems designed to apply mathematical concepts in real life situations should be increased.Selection of contents should be made accordingly with the sequence of the textbooks. Emphasis is mostly given on the product but the process is also as important as the product. Rote memorization should be discouraged by increasing word problems in the textbooks.Workshops and refresher-courses should be organized for paper setters and checkers.It develops a habit of doing neat and tidy work in students. It develops a sense of responsibility by maintaining notes (solution of problems) and making them checked from their teachers regularly.System of current examination encourages cramming.Improving the assessment system and improving the contents of the textbook.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 6System: SSCInstitution: PrivateDesignation: HODQualification: M.Sc B.EdTeaching Experience: 23 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Schools lack in educational resources required to teach students properly.Agreed.Disagreed.Disagreed.Agreed.Satisfied.Word problems in the texbooks should be increased. Textbooks’ worked examples should be improved.Sequence of the textbook should be used.Teaching of mathematics should be activity based.Don’t give textbook sums in the asssessments. Assessment items should be made with a great care.Questions should neither be taken from textbooks nor from the previous year’s papers.It provides enough knowledge required to continue this subject in higher classes.Examinations are not conducted under proper vigilance. System of paper setting and its assessment also needs improvement. Taking textbook questions in the internal school papers as well as in SSC papers is the major weakness.Making neutral places as centers of examination to curb the problem of cheating.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 7System: SSCInstitution: PrivateDesignation: Sn. TeacherQualification: M.Sc B.EdTeaching Experience: 30 years Gender: FemaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Not satisfied, there is a need of computer assisted instruction (CAI) to teach mathematics effectively. Agreed, syllabus is designed to further this subject in higher grades.Undecided.Disagreed.Agreed.SatisfiedWord problems designed to apply mathematical concepts in real life situations should be increased.Not satisfied, textbook sequence is better to use.Project-based teaching should also be introduced in the current practice of teaching.Assessment should check the understanding of concepts rather than checking the memorization of contents.Pattern of the paper should be such that it promotes comprehensive study habit.Provides knowledge of basic operations and procedures.System encourages rote learning and promotes an approach of studying important topics rather than the entire syllabus.Improvement should be made in the textbooks and in the examination system.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 8System: SSCInstitution: PrivateDesignation: HODQualification: M.Sc B.EdTeaching Experience: 28 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.SatisfiedAgreed, enable students to do basic operations and calculations of mathematics.Agreed.Agreed.Agreed.Yes, but some topics like number sequence, probability, etc. should be included. In lower grades, too many books of different publishers are used and schools frequently change these books. If a series of textbooks is used in one year and next year is replaced by another series, it will affect the logical sequence of contents and vertical integration of conceptsSelection is made taking topics from the three key areas (arithmetic, algebra, geometry) but the prime concern of this selection is to ensure making a balanced question paper for terminal/half-yearly examination.Step by step instructions should be given instead of giving the key to open the lock (a method to solve the problem). Sums should not be taken from textbooks or previous papers. Teacher should construct their own problems to give in assessments.Pattern of paper should be such that students use their skills to solve problems rather than learning and reproducing them.It provides a rich knowledge of mathmatical language, terminologies, symbols, formulae and procedures. System encourages selected study of some topics, leaving some of the topics completely untouched.Assessment system should be improved.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 9System: SSCInstitution: Designation: Sn. TeacherQualification: M.Sc M.EdTeaching Experience: 16 years Gender: FemaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied Agreed.Agreed.Agreed.Agreed.Yes, but problem is not with the contents. It is with the methods of teaching and assessment. Textbooks should be revised.Teachers select contents from three areas arithmetic, algebra and geometry to make a balanced paper.Activity based and project based teaching should be started with the routine teaching methods.Satisfied, but the habit of using unfair means during examination sould be controlled.Vigilance during examinations should be made better.------------Massive use of unfair means is the major problem.Revision of curriculum, improvement in the textbooks and strict examination system.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 10System: SSCInstitution: PrivateDesignation: Sn. TeacherQualification: M.Sc M.EdTeaching Experience: 35 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Not fully satisfied because there is shortage of resources in schoolsDisagreed, objectives are not clear to teachers. The only objective in my opinion is to make students memorize the contents and procedures to get good marks in the SSC examination.Undecided.Undecided.Agreed but only if our teaching touches theses domains. The current focus is on contents only.Unsatisfied.Books of same publisher should be used. It is better to use the books of Sindh Textbook Board in lower grades also.Not fully satisfied, it is done in a sitting of teachers where the selection, elimination and sequence of contents are made according to their choice and feasibility of completing it within the available time.Teachers should have to address all the cognitive levels in their teaching (knowledge, comprehension, application, analysis, synthesis and evaluation). Formative assessment should be used. Application based sums should be increased. The present routine of taking problems from textbooks is increasing the trend of rolte learning.Teachers should be trained and their knowledge about test construction and assessment should be updated. Enables the students to do computation with knowledge of long procedures and formulae.There is a wide gap of standards between SSC and HSC.Without a fair and vigilant examination and consistent assessment system no improvement can be made in the standards of education.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 1System: GCEInstitution: PrivateDesignation: HODQualification: M.Sc Teaching Experience: 15 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.The syllabus is too lengthyAgreed, objective is to prepare students for CIE.Agreed.Not fully agreed.Agreed.Unsatisfied.To cover all the topics of O-Level mathematics syllabus the books have an addendum at the end of each book. It will be better if all the contents given in the addendum are incorporated into the main part of the books. It should be done on logical grounds. Spend maximum time of your teaching in building basic concepts. Emphasize mental calculations and practice of learned concepts.Agreed, but tests should be held more frequently.Agreed, but selective study habit should be discouraged.A standardized, fair and unbiased system of assessment.It is not for majority of students.This system should be made available to as many students students as possible.Coursework should be included because syllabus is too lengthy.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 2System: GCEInstitution: PrivateDesignation: HODQualification: M.Sc Teaching Experience: 17 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Unsatisfied because increasing trend of private tutions of this subject is reducing the interest of students in the class.Agreed, making students able to think and making them good problem solvers.Agreed.Mathematics education is much better in Singapure and other Asian countries like China, Japan etc.Agreed.Yes, books are not written locally. They serve the needs in terms of contents but it will be better if books are written by local authors.Reference books should be used instead of textbooks keeping in view the needs of students. In the process of selection and its sequencing, no special consideration is made on the prerequisites, interests and needs of students.Activities in the class should be increased and made more interesting. Practice is very important in mathematics.More quizzes and mental maths tests should be administered. It should test deeper understanding instead of basic knowledge.It is internationally recognized.Excessive use of private tuitions is the major problem in this system.Discouraging the increasing trend of selective studyand private tuitions.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 3System: GCEInstitution: PrivateDesignation: Sn. TeacherQualification: M.Sc B.Ed. Teaching Experience: 15 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, enable students to think within the horizon before thinking beyond the horizon.Agreed.Agreed.Agreed.Satisfied.Books of local authors should be used. Moreover, reference books should be used instead of textbooks keeping in view the needs of students. Selection and sequencing of contents should be based on interests and needs of students.Preference should be given to mental calculations and use of calculators be minimized. Basic operations and procedures should be taught properly.Satisfied.Satisfied.Paper is balanced in terms of calculations done mentally (Paper-I) and using calculators (Paper-II).It is very expensive and not for masses.Schools should play their role to discourage the trend of private tutions.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 4System: GCEInstitution: PrivateDesignation: HOD Qualification: M.ScTeaching Experience: 35 years Gender: FemaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, objective is to prepare students for GCE examUndecided.Agreed.Agreed.ic given in the addendum separately should be incorporated in the textbooks.The organization of contents should be coherent. Computer Assisted Instruction (CAI) should be introduced. Practice should be maximized.Teachers should construct their own problems rather than taking them from past papers. More application based questions should be included.It is internationally recognized.It is very expensive.Trend of crash-courses at different private tuition centers should be discouraged.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 5System: GCEInstitution: PrivateDesignation: Sn. TeacherQualification: M.Sc PGCCTeaching Experience: 17 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, provision of basic mathematical knowledge a prerequisite for higher studies.Agreed.Agreed.Agreed.Satisfied.Use of referencebooks is better than using textbooks according to the needs of students. The selection and arrangement of contents should be logical based on the needs of students.It is better to teach a small content in depth than teaching a large number of topics superficially.Satisfied. Satisfied.A strict and vigilant examination with a fair assessment system is its major strength.Very lengthy syllabus.A coursework should be incorporated in the curriculum.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 6System: GCEInstitution: PrivateDesignation: Sn. TeacherQualification: M.Sc B.EdTeaching Experience: 25 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, objective is to make students able to pass GCE exam with excellent grades.Agreed.Agreed.Agreed.Satisfied.Books should be written by local authors. Refernce books should be used according to the needs of students.It should be done sensibly with the need of the learners. Students should be made confident by rigorous practice of sums. Calculators should be used but not unnecessarily.Satisfied, but number of tests/assessmentsshould be increased.Satisfied, but application based problems should be increased.There is room to incorporate different methods of teaching in this system.Private tutions are taken excessively in this system and this trend is increasing day by day.Discouraging the trends of tuitions especially shortcuts (crash-courses) at different private tuition centers. Contents that produce thinking skills should be increased.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 7System: GCEInstitution: PrivateDesignation: Sn. TeacherQualification: B.Sc M.Ed. Teaching Experience: 15 years Gender: FemaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, objective is to develop thinking skills.Agreed.In my opinion, mathematics education in Pakistan needs improvement.Agreed.Unsatisfied.Content on number sequence and problem solving should be increased. Contents should be organized on the basis of interests and needs of students.Basic concepts should be taught and revised periodically. Practice and application of basic concepts repeatedly makes students confident.Small-scale asssessments should be organized regularly and periodically.Satisfied.Examinations are conducted under strict vigilance. There is no chance of using unfair means.It is based on (2+ 2.5) hour’s performance of students. Learning of students in previous 4 years should to be incorporated.Discouraging the trend of selectivestudy andincreasing the contents that enhance critical thinking skills.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 8System: GCEInstitution: PrivateDesignation: Sn. Teacher Qualification: M.Sc B.Ed Teaching Experience: 16 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, prepare students for higher learning giving them first-hand knowledge.Agreed.Agreed.Agreed.Satisfied.A teachers’ manual should be published with each book for their guidance. The selection of content should be done on the basis of needs of students.Activities in classes should be increased.Satisfied.Satisfied.A standaradrized system of assessing papers is the major strength of this system.Syllabus is too lengthy.This system should be within reach of common people.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 9System: GCEInstitution: PrivateDesignation: HODQualification: M.Sc B.Ed Teaching Experience: 16 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, objective is to prepare students for CIEAgreed.Agreed.Agreed.Unsatisfied.Answers of graph and loci questions should be given in the form of constructed graphs and geometrical figures respectively. It should focus the need of students.Practice of learned concepts should beincreased.Calculations should be done mentally avoiding calculators as much as possible. Satisfied.Satisfied.Flexibility of appearing for CIE paper is its strength. Students can appear in the examination either in May or November, twice in a year.The system is expensive.Increasing the contents that improve thinking skills.INTERVIEW PROTOCOLResponses of the Subject ExpertsInterview: 10System: GCEInstitution: PrivateDesignation: Sn. TeacherQualification: M.Sc PGCCTeaching Experience: 22 years Gender: MaleQ. Nos.Responses1.2.3.4.5.6.7.8.9.10.11.12.13.14.Satisfied.Agreed, objectives are to enhance thinking skills of students.Agreed.Agreed.Agreed.Yes but the names of persons and places are not familiar to our students. If these are familiar, students can mentally visualize the context of that problem and learning of the concept becomes more concrete. It is better if the books are written by local authors. The method of selection and sequencing of contents should be based on needs of students.Teach the students to use the (FFF) approach in solving a problem i.e. face it, fight it and finish it.Satisfied, but the number of quizzes and class tests should be increased.Satisfied, but selective learning should be discouraged.It requires a comprehensive study and does not allow leaving atopic from the entire prescribed syllabus.Syllabus is very lengthy.Coursework should be included along with the final paper.Contents that developreasoning skills should be increased.PILOT TESTINGCOMPUTATION OF PEARSON’S ‘r’Computation of Pearson’s ‘r’ for Teachers’ QuestionnaireX (SSC)Y (GCE)X2Y2XY417410173889168100149720380433144400173889136524500464250000215296156364507455257049207025156348519473269361223729155769429441184041194421165505471450221841202500180188?X=3223?Y=3126?X2=1500581?Y2=1398620?XY=1444821Formular = N?xy- (?x)(?y) N?x2- ?x2 N?y2- ?y2Calculations r = 7(1444821)- (3223)(3126) 7(1500581)- 32232 7(1398620)- 31262r = 10113747- 10075098 10504067- 10387729 9790340- 9771876r = 38649 116338 18464 r = 386492148064832r = 3864946347.220r = 0.834Computation of Pearson’s ‘r’ for Students’ QuestionnaireX (SSC)Y (GCE)X2Y2XY403388162409150544149720372367138384134689136524419395175561156025156364421428177241183184156348394380155236144400155769404387163216149769165505411379168921143641180188?X=2824?Y=2724?X2=1140968?Y2=1062252?XY=1100418Formular = N?xy- (?x)(?y) N?x2- ?x2 N?y2- ?y2Calculations r = 7(1100418)- (2824)(2724) 7(1140968)- 28242 7(10622520)- 27242r = 7702926- 7692576 7986776- 7974976 74357640- 7420176 r = 10350 11800 15588 r = 10350183938400r = 1035013562.389r = 0.763SYLLABUS (SSC)MATHEMATICSPart-ISets- Revision of the work done in the previous classes.- Notation of Sets, subset and its types, power set, Exercises.- Operations on Sets; their properties and Venn-Diagram, Exercises.- Cartesian product, Exercises.- Binary Relations; domain and range. - Functions, types of functions, Exercises.- Cartesian coordinate system for a plane, Exercises.- Graphical representation of Cartesian product, Exercises. System of Real Numbers, Exponents and Radicals- Properties of Rational Numbers, Decimal fractions as Rational and Irrational Numbers - Properties of Real Numbers- Properties of equality and inequality of Real Numbers, Exercises- Exponent, Laws of exponents, Exercises- Concept of Radicals and Square Root of a Positive Real Number, Exercises- The nth Root of a Positive Real Number, Exercises- Rational Exponents, Exercises- Surds, Exercises3. Logarithms- Scientific Notation, Exercises- Definition of Logarithm, Exercises- Laws of Logarithms, Exercises- Common Logarithms, Exercises- Anti Logarithms, Exercise- Application of Logarithms in Computations, Exercises4. Algebraic Expressions- Variables and Constants, Coefficient, Algebraic expressions and their kinds, Exercises- Polynomials, Classification of polynomials, Exercises- Order of Algebraic Expressions, Exercises- Value of Algebraic Expressions, Exercises- Fundamental Operations on Algebraic Expressions, Exercises- Remainder Theorem, Exercise- Formulae and Their Applications, ExerciseFactorization, H.C.F, L.C.M, Simplification and Square Roots- Revision of the work done in the previous classes, Exercises- Factorization of the Form; a2-b2, Exercises- Factorization of the Form;x2+bx+c, Exercises- Factorization of the Form; a3+b3 and a3-b3 ,Exercises- Factorization of the Form; a3+b3 +c3-3abc, Exercises- Factorization of the Form; a2b-c+b2c-a+c2a-b,Exercises- Factorization using Remainder Theorem, Exercises- H.C.F. and L.C.M., Exercises- Simplification of Algebraic Fractions, Exercises- Square Root by Division method, ExerciseMatrices- Introduction, Notation, Order of a Matrix, Exercises- Types of Matrices, Exercises- Transpose, Addition and Subtraction of Matrices, additive Inverse, Exercises- Multiplication of Matrices, Exercises- Determinant, Adjoint and Multiplicative Inverse of a Matrix, Exercises- Solution of two Simultaneous Linear Equations using Matrices, Exercises- Cramer’s rule, ExercisesFundamental Concepts of Geometry- Inductive and Deductive Reasoning- Characteristics of Deductive Reasoning- Basic Concepts Definitions and Postulates, ExerciseDemonstrative Geometry- Theorems on Lines and Polygons- Methods of proofs of Theorems-Theorems their Proofs and an Exercise after each theoremPractical Geometry- Revision of Construction of Triangles, Exercises-The Ambiguous Case of Construction of a Triangle, Exercise- Constructions of Right Bisectors of Sides of a Triangle, Exercises-Construction of Angle Bisectors, Median and Altitudes in a Triangle, ExercisesSYLLABUS (SSC)MATHEMATICSPart-II1. Algebraic Sentences- Solution of Simple Linear Equations in One or Two Variables, Exercises- Graphical solution of two simultaneous Linear Equations, Exercises- Solution of Equation Involving Radicals in One Variable, Exercises- Solution of Equation Involving Absolute Value in One Variable, Exercises- In equations, Exercises- Solution of Quadratic Equations by Factorization, Completing Square Method or by Quadratic Formula, Exercises2. Elimination- Concepts- Elimination of One Variable from Two Equations, Exercises3. Variations- Basic Concepts of Ratio, Proportion and Variation, Exercises- K-Method and Theorems on Proportion, Exercises- Properties of Proportions, Exercises- Word Problems, Exercises4. Information Handling- Introduction, Definitions of Key Terms, Types of Variables, Types of Data- Collection and Presentation of Data- Frequency Distribution, Graphs (Histogram and Frequency Polygon), Exercises- Bar Graphs, Pie Diagrams, Exercises- Measures of Central Tendency (Mean, Median and Mode), Their Merits &Demerits, Exercises- Dispersion and its Measures (Variance and Standard Deviation), Their Merits &Demerits, Exercises5. Fundamental Concepts of Geometry- Basic Concepts of Circle (Circumference, Chord, Secant, Tangent, Exercises- Circum-circle, Inscribed Circle and Escribed Circle of a Triangle, Exercises- Theorems on Circles, Exercises6. Demonstrative Geometry- Introduction- Theorems, Exercises after every Theorem7. Practical Geometry- Constructions (Circum-circle, Inscribed circle and Escribed Circle), Exercises- Tangent to a Given Circle from a Point outside the Circle, Direct Common Tangents to Two Given Circles and Transverse Common Tangents to Two Given Circles, Exercises8. Trigonometry- Introduction- Trigonometric Ratios of Acute Angles - Values of Trigonometric Ratios of Angles of (300, 450,600),Exercises- Trigonometric Identities, Exercises- Solution of a Right Triangle, Exercises- Finding Heights and Distances using Trigonometric Ratios, ExercisesSYLLABUS (GCE)O-LEVELMATHEMATICS(4024)1. Number ? use natural numbers, integers (positive, negative and zero), prime numbers, common factors and common multiples, rational and irrational numbers, real numbers;? continue given number sequences, recognize patterns within and across different sequences and generalize to simple algebraic statements (including expressions for the nth term) relating to such sequences.Set language and notation ? use set language and set notation, and Venn diagrams, to describe sets and represent relationships between sets as follows:Definition of sets, e.g. A = {x : x is a natural number}B = {(x, y): y = mx + c}C = {x : a ≤ x ≤ b}D = {a, b, c... }b) Notation:Union of A and B A ∪BIntersection of A and B A ∩ BNumber of elements in set A n(A)“ . . . is an element of . . . ” ∈“ . . . is not an element of . . . ”? of set A A’The empty set ?Universal setεA is a subset of B A ?BA is a proper subset of B A ?BA is not a subset of B A ?BA is not a proper subset of B A ?BFunction notation use function notation, e.g. f(x) = 3x ? 5, f: x →3x ? 5 to describe simple functions, and the notationf-1(x) = x+53 and f-1(x) = x+53to describe their inverses.4. Squares, square roots, cubes and cube roots? calculate squares, square roots, cubes and cube roots of numbers.4. llabus content5. Directed numbers ? use directed numbers in practical situations (e.g. temperature change, tide levels).6. Vulgar and decimal fractions and percentages? use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts; ? recognise equivalence and convert between these forms.Ordering ? order quantities by magnitude and demonstrate familiarity with theSymbols =, ≠, >, <, ≤, ≥8. Standard form ? use the standard form A × 10nwhere n is a positive or negative integer,and 1 ≤ A < 10.9. The four operations ? use the four operations for calculations with whole numbers, decimal fractions and vulgar (and mixed) fractions, including correct ordering of operations and use of brackets.10. Estimation? make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.11. Limits of accuracy ? give appropriate upper and lower bounds for data given to aspecified accuracy (e.g. measured lengths); ? obtain appropriate upper and lower bounds to solutions of simple problems (e.g. the calculation of the perimeter or the area of a rectangle) given data to a specified accuracy.12. Ratio, proportion, rate ? demonstrate an understanding of the elementary ideas and notation of ratio, direct and inverse proportion and common measures of rate;? divide a quantity in a given ratio;? use scales in practical situations, calculate average speed;? express direct and inverse variation in algebraic terms and use this form of expression to find unknown quantities.13. Percentages ? calculate a given percentage of a quantity;? express one quantity as a percentage of another, calculate percentage increase or decrease;? carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage profit.4. Syllabus content14. Use of an electronic calculator? use an electronic calculator efficiently;? apply appropriate checks of accuracy.15. Measures ? use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.16. Time? calculate times in terms of the 12-hour and 24-hour clock;? read clocks, dials and timetables.17. Money ? solve problems involving money and convert from one currency toanother.18. Personal and household finance? use given data to solve problems on personal and household finance involving earnings, simple interest, discount, profit and loss;? extract data from tables and charts.19. Graphs in practical situations? demonstrate familiarity with Cartesian coordinates in two dimensions;? interpret and use graphs in practical situations including travel graphs and conversion graphs;? draw graphs from given data;? apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and retardation;? calculate distance travelled as area under a linear speed-time graph.20. Graphs of functions ? construct tables of values and draw graphs for functions of the form y = axnwhere n = –2, –1, 0, 1, 2, 3, and simple sums of not more than three of these and for functions of the form y = kaxwhere a is a positive integer;? interpret graphs of linear, quadratic, reciprocal and exponential functions;? find the gradient of a straight line graph;? solve equations approximately by graphical methods;? estimate gradients of curves by drawing tangents.21. Straight line graphs ? calculate the gradient of a straight line from the coordinates of two points on it;? interpret and obtain the equation of a straight line graph in the form y = mx + c;? calculate the length and the coordinates of the midpoint of a line segment from the coordinates of its end points.4. Syllabus content22. Algebraic representation and formulae? use letters to express generalized numbers and express basic arithmetic processes algebraically, substitute numbers for words and letters in formulae;? transform simple and more complicated formulae;? construct equations from given situations.23. Algebraic manipulation ? manipulate directed numbers;? use brackets and extract common factors;? expand products of algebraic expressions;? factorise expressions of the form:ax + ayax + bx + kay + kbya2x2– b2y2a2+ 2ab + b2ax2+ bx + c? manipulate simple algebraic fractions.24. Indices ? use and interpret positive, negative, zero and fractional indices.25. Solutions of equations and inequalities? solve simple linear equations in one unknown;? solve fractional equations with numerical and linear algebraic denominators;? solve simultaneous linear equations in two unknowns;? solve quadratic equations by factorization and either by use of the formula or by completing the square;? solve simple linear inequalities.26. Graphical representation of inequalities? represent linear inequalities in one or two variables graphically.(Linear Programming problems are not included.)4. Syllabus content27. Geometrical terms and relationships? use and interpret the geometrical terms: point, line, plane, parallel, perpendicular, right angle, acute, obtuse and reflex angles, interior and exterior angles, regular and irregularpolygons, pentagons, hexagons, octagons, decagons;? use and interpret vocabulary of triangles, circles, special quadrilaterals;? solve problems and give simple explanations involving similarity and congruence;? use and interpret vocabulary of simple solid figures: cube, cuboid, prism, cylinder, pyramid, cone, sphere;? use the relationships between areas of similar triangles, with corresponding results for similar figures, and extension to volumes of similar solids.28. Geometrical constructions ? measure lines and angles;? construct simple geometrical figures from given data, angle bisectors and perpendicular bisectors using protractors or set squares as necessary;? read and make scale drawings.(Where it is necessary to construct a triangle given the three sides, ruler and compasses only must be used.)29. Bearings ? interpret and use three-figure bearings measured clockwise from the north (i.e. 000°–360°).30. Symmetry ? recognize line and rotational symmetry (including order of rotational symmetry) in two dimensions, and properties of triangles, quadrilaterals and circles directly related to theirsymmetries;? recognize symmetry properties of the prism (including cylinder) and the pyramid (including cone);? use the following symmetry properties of circles:(a) equal chords are equidistant from the center;(b) the perpendicular bisector of a chord passes through the center;(c) tangents from an external point are equal in length.31. Angle ? calculate unknown angles and give simple explanations using the following geometrical properties:(a) angles on a straight line;(b) angles at a point;(c) vertically opposite angles;(d) angles formed by parallel lines;(e) angle properties of triangles and quadrilaterals;(f) angle properties of polygons including angle sum;(g) angle in a semi-circle;(h) angle between tangent and radius of a circle;(i) angle at the center of a circle is twice the angle at the circumference;(j) angles in the same segment are equal;(k) angles in opposite segments are supplementary.32. Locus ? use the following loci and the method of intersecting loci:(a) sets of points in two or three dimensions(i) which are at a given distance from a given point?(ii) which are at a given distance from a given straight line?(iii) which are equidistant from two given points?(b) sets of points in two dimensions which are equidistant fromtwo given intersecting straight lines.33. Mensuration? solve problems involving(i) the perimeter and area of a rectangle and triangle,(ii) the circumference and area of a circle,(iii) the area of a parallelogram and a trapezium,(iv) the surface area and volume of a cuboid, cylinder, prism, sphere, pyramid and cone (formulae will be given for the sphere, pyramid and cone),(v) arc length and sector area as fractions of the circumference and area of a circle.34. Trigonometry ? apply Pythagoras Theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle (angles will be quoted in, and answers required in, degrees and decimals of a degree to one decimal place);? solve trigonometrical problems in two dimensions including those involving angles of elevation and depression and bearings;? extend sine and cosine functions to angles between 90° and 180°; solve problems using the sine and cosine rules for any triangle and the formula 12ab sin C for the area of a triangle;? solve simple trigonometrical problems in three dimensions.(Calculations of the angle between two planes or of the angle between a straight line and plane will not be required.)35. Statistics ? collect, classify and tabulate statistical data; read, interpret and draw simple inferences from tables and statistical diagrams;? construct and use bar charts, pie charts, pictograms, simple frequency distributions and frequency polygons;? use frequency density to construct and read histograms with equal and unequal intervals;? calculate the mean, median and mode for individual data and distinguish between the purposes for which they are used;? construct and use cumulative frequency diagrams; estimate the median, percentiles, quartiles and interquartile range;? calculate the mean for grouped data; identify the modal class from a grouped frequency distribution.36. Probability ? calculate the probability of a single event as either a fraction or a decimal (not a ratio);? calculate the probability of simple combined events using possibility diagrams and tree diagrams where appropriate. (In possibility diagrams outcomes will be represented by points on a grid and in tree diagrams outcomes will be written at the end of branches and probabilities by the side of the branches.)Syllabus content37. Matrices ? display information in the form of a matrix of any order;? solve problems involving the calculation of the sum and product (where appropriate) of two matrices, and interpret the results;? calculate the product of a scalar quantity and a matrix;? use the algebra of 2 × 2 matrices including the zero and identity 2 × 2 matrices;? calculate the determinant and inverse of a non-singular matrix.(A–1 denotes the inverse of A.)38. Transformations ? use the following transformations of the plane: reflection (M), rotation (R), translation (T), enlargement (E), shear (H), stretching (S) and their combinations (If M(a) = b and R(b) = c the notation RM(a) = c will be used; invariants under these transformations may be assumed.); ? identify and give precise descriptions of transformations connecting given figures; describe transformations using coordinates and matrices. (Singular matrices are excluded.)39. Vectors in two dimensions ? describe a translation using a vector represented byxy, ABor a;? add vectors and multiply a vector by a scalar;? calculate the magnitude of a vector xy as x2+ y2? represent vectors by directed line segments; use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors; use position vectors.OUTLINE OF MATHEMATICS PAPERBOARD OF SECONDARY EDUCATION KARACHISECONDARY SCHOOL CERTIFICATE (SSC) (CLASS X - SCIENCE GROUP)Time: 3 Hours(Compulsory) Max. Marks: 100Time: 30 Min. Section “A” Multiple Choice Questions (MCQ’S) (20 Marks)Note: Choose the correction answers for each from the given options:Q.1 MCQ’S (carrying 1 mark each) =20Time: 2 ? Hours SECTION “B” & “C” Max. Marks: 80Section “B” (Short-Answers Questions)(50 Marks)Note: Answer any 10 questions from this Section Q.2 - Q.16 (15 single item questions each carrying 5 marks)Section “C” (Detailed-Answers Questions)(30 Marks)Note: Attempt any 3 questions from this Section including Q.No.19 which is compulsoryQ.17 Factorize the following:Given four algebraic expressions each carrying 2.5 marks(i) (iii)(iii)(iv)Q.18 Find the solution set of the following equations graphically. (10 marks)(Find four ordered pairs of each equation).Given a pair of linear equations in two variables Q.19 Proof of a geometrical theorem carrying 10 marksQ.20 (a) Question on information handling carrying 5 marks(b) Question on factorization with the help of remainder theorem carrying 5 marksQ.21 Question on practical geometry carrying 10 marksOUTLINE OF MATHEMATICS PAPERUNIVERSITY OF CAMBRIGE INTERNATIONAL EXAMINATIONSGENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL (O-LEVEL)SYLLABUS D (4024/12)MATHEMATICS (SYLLABUS D)4024/12Paper 1May/June (YEAR)2 hoursCandidates answer on the Question Paper.Additional Materials:Geometrical instrumentsREAD THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.Answer all questions.If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks.ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.This paper contains on average 25 questions (every question is discrete in carrying marks)MATHEMATICS (SYLLABUS D)4024/22Paper 2May/June (YEAR)2 hours 30 minutesCandidates answer on the Question Paper.Additional Materials:Geometrical instrumentsElectronic calculatorREAD THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.Section AAnswer all questions.Section BAnswer any four questions.If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks.You are expected to use an electronic calculator to evaluate explicit numerical expressions.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 100.Section A [52 marks]Answer all questions in this section.Q.1 – Q. 7 (each question contains multiple parts and every part is distinct in carrying marks)Section B [48 marks]Answer four questions in this section.Each question in this section carries 12 marks.Q8 – Q.12 (each question contains multiple parts and every part is distinct in carrying marks)LIST OF SCHOOLS SSCDISTRICT (SOUTH)Sr. No.Names of Schools1Aisha Bawani Academy, Shahrah-e-Faisal2Al Habib Grammar School, PECHS, Block 23Al Hamd Kids Heaven Secondary School, Mehmoodabad4Al-Farooq Secondary School, Manzoor Colony5Al-Murtaza School, P.E.C.H.S6Al-Sehar Secondary School, Manzoor Colony7Ameer Bahadur Children Academy, Upper Gizri8Brooks Grammar School, Chanesar Halt9Central Model High School, P.E.C.H.S10Customs Public School, P.E.C.H.S11Defence Foundation School, P.E.C.H.S12Defence Institute and Computer Centre, Defence View13Ebrahim Ali Bhai Govt. Boys High School K.A.E.C.H.S14Excellence Model School, Kharadar15Faran Public School, Azam town16Fatimiyah Boys School, Britto Road Karachi17Fatimiyah Girls School, Britto Road Karachi18Govt Girls Higher Secondary School, Green Belt, Mehmoodabad19Govt. Girls Higher Secondary School, Chanesar Goth (Urdu Medium)20Govt. Girls Secondary School, Akhtar Colony21Govt. Noor-e-Islam High School, Green Belt Mehmoodabad22Govt. Norwegian High School Azam Basti23Green Flag Boys Secondary, K.A.E.C.H.S24Green Flag Girls Secondary School, K.A.E.C.H.S25Greenwich Public School, .P.E.C.H.S26Gulistan (SAL) Boys Secondary School, S.M.C.H.S27Gulistan (SAL) Girls Secondary School, S.M.C.H.S28Habib Girls School, Garden29Habib Public School, Sultanabad30Happy Home School, Clifton31Haq Foundation School, Muslimabad32Heaven Foundation Secondary School, Manzoor Colony33High Rise Academy School, Akthar Colony34Hyderi Public School, Sarwar Shaheed Road, Saddar35Imran Public School, Mehmoodabad Gate36Iqra Huffaz Boys Secondary School, Razi Road, P.E.C.H.S37Karachi Cambridge School, Shahrah-e-Quaideen38Karachi Cambridge School, Tariq Road39Karachi Public School, K.A.E.C.H.S40M.E Foundation Secondary School, Mehmoodabad No.641Mama Baby Care School, Saddar42Meezan School System, Mehmoodabad No.543Meritorious Schools Network, P.E.C.H.S44Muslim Public School, Manzoor Colony45Nasra Secondary School, Soldier Bazar, Saddar46New Generation's School, P.E.C.H.S47New St. Andrews School, Defence Phase I48Oxford English High School, Sultanabad49Pak Grammar School, Garden East50PECHS Girls School ,51Progressive Public School Dhoraji Colony52Radiant English School, Mehmoodabad No.553Rainbow Public School, Azam town54Rose Petal Primary & Secondary School, Soldier Bazaar 155Saifiyah Boys High School, Saddar56St Paul's English High School, Saddar57St. Anthony's School, Karachi Cantt.58St. Joseph’s Convent School, Saddar59St. Matthew's Model High School, PECHS, Block 660The Islamic Public School, P.E.C.H.SDISTRICT (EAST)Sr. No.Names of Schools1Al-Abbas Secondary School, Qayyumabad2Alpha Secondary School, Shah Faisal Colony3Army Public School (COD), Rashid Minhas Road, Gulshan-e-Iqbal 4Ataturk School, Gulistan-e-Johar, Block 135Banglore Town School, Banglore town6Bright Career Public Secondary Schools, Gulistan-e-Johar7C.F. English Grammar Secondary School, Korangi8C.P Berar High School for Girls, Dhoraji9Chiniot Islamia School and College, Opp. Safari Park Gulshan-e-Iqbal10Dehli Mercantile School, D.M.C.H.S11Fareedi Memorial Girls Secondary School, Gulistan-e-Johar12Ghaus-ul-Azam High School, Gulshan-e-Iqbal13Golden Model School, Goldentown, Shah Faisal Colony14Government Boys Secondary School, Airport15Government Boys Secondary School, Jail Road16Green Channel Grammar School, Nasir Colony, Korangi17Happy Home School, Modern Housing Society18Hayat-ul-Islam Public School, Gulshan-e-Iqbal19Ideal English Secondary School, Korangi No. 220Jinnah Academy, Gulzar-e-Hijri21Kingston English Grammar School, Korangi No.222Little Folk’s Secondary School, Kashmir Road23Morning Glory Grammar School Shah Faisal Colony24Muhammadi Public School, Gulistan-e-Johar, Block 1325Mukkaram Ali Memorial School Shah Faisal Colony26Nasir English Secondary School, SKC Landhi No. 227National High School, Gulshan-e-Iqbal28National Public School, Lukhnow Society, Korangi29New Model High School, Dar-us-Salam Society, Korangi30New Roomi Boys & Girls Secondary School, Korangi No 231Noor Academy Primary and Secondary School, Korangi 2 ?32Orchard Grammar School, Gulistan-e-Johar, Block 1333Practical Schooling System, Gulshan-e-Iqbal34Primrose Public School, Shah Faisal Colony35Programmer Girls School, Gulshan Iqbal36Radient Grammar School, Gulshan Iqbal Block 1337S.M Public Academy, Gulistan-e-Johar, Block 1338Sadequain Academy , NIPA, Gulshan-e-Iqbal39Scosit Secondary School, Korangi40Shaheen Public School, Gulshan-e-Iqbal41Sohail Academy Secondary School, Landhi No.142St. Peter’s School, near Kashmir Road43Stratford School Gulshan-e-Iqbal44The American Foundation Cambridge School, Gulistan-e-Johar45The Crescent Academy, Gulshan-e-Iqbal, Block 346The NR School, Korangi, No.647The RAS School, Korangi, No.448Usman Grammar School, Shah Faisal Colony49Warraich Public Secondary School, Qayyumabad50White House Grammar School, Gulshan-e-Iqbal DISTRICT (CENTRAL)Sr. No.Names of Schools1Albatross Grammar School, Hyderi2Albatross Grammar School, North Nazimabad3Al-Eman Education System, Block 10, F.B.Area4Asra Public School, U.P More North Karachi5Bahria Foundation School, Liaqatabad 6Bright Career Public Secondary School - F.B Area 7Crescent Grammar School, Surjani Town, Sector 18Dawn Public School, North Karachi9Education World, North Nazimabad10Falcon House Grammar School, North Nazimabad11Gallant Public Secondary School, Nazimabad No.512Glamour Children Secondary School, Liaquatbad No. 413Happy Palace Grammar School, F.B. Area14Harvard Public Grammar School, North Nazimabad15Iqra Roza-tul-Atfal, School Nazimabad No. 216Karachi Generation School, 11-B, near Saleem Centre, North Karachi17Karachi Honors School, Block 17, F.B.Area18Kazmi Grammar Primary School, Allama Iqbal Town,North Nazimabad19Lycos Grammar School, 11/C/1, North Karachi20MA Tutor Academy, Shadman Town, North Karachi21Manhattan Grammar School, near Nagan Chowrangi22Metropolitan Academy, Incholi23Mount View Secondary School, North Nazimabad, Block I24National Grammar Higher Secondary School, North Nazimabad 25New Preston Grammar School, Nazimabad No.226Oxford Cambridge School, Rizvia Society27Pak Horizon Grammar School, Sector 11-F North Karachi28Preston Grammar School, Rizvia Society29Progressive Children's Academy, Nazimabad No. 430Rangers Public School and College, North Nazimabad31R.G Public School, North Nazimabad32Royal Grammar Secondary School, Nazimabad No.233Rasheeda Memorial Secondary School, Sector 11, North karachi34Saeeda Academy, 11/C/1, North Karachi35Sesame Cambridge School, North Nazimabad36Shaheen Cambridge School Nazimabad, No.137Shaheen Mama Montessori Nazimabad No.138Shahwilayat Public School, F.B. Area39Shining Star English Secondary School, North Nazimabad 40Sir Syed Children's Academy, Nazimabad41SK Grammar School, Muslim Town, North Karachi42S.M.B. Academy School Boys & Girls, North Karachi43St. George's School, North Nazimabad 44St. Jude's High School, North Nazimabad45St. John's High School, North Nazimabad46Sultan Muhammad Shah School, Karimabad 47Trueman Education System, North Nazimabad48Western Grammar Secondary School, Nazimabad No. 349Wonderland Grammar School, 11/C/1, North Karachi50Yasir Academy, North Nazimabad DISTRICT (WEST)Sr. No.Names of Schools1Al Hera Secondary School, Sector 11 ?, Orangi Town2Danish Children School, Tauheed Colony, Sector 11, Orangi Town3Government Boys Secondary School, Lasipara, Baldia Town4Islamia Public School, Zia Colony No. 2, Orangi Town5Premier Grammar School, Rasheedabad, Baldia Town6Shoeby Grammar Secondary School, Sector 5, Orangi7S.M. Hafiz-ur-Rahman High School, Sector 11 ?, Orangi Town8Sir Gee Schooling System, Sector10, Orangi Town9Syed Sulaiman Nadvi Secondary School, Sector 11 ?, Orangi Town10Unique Grammar Secondary School, Tauheed Colony, Sector 11, Orangi DISTRICT (MALIR)Sr. No.Names of Schools1City Public School, Model Colony, Primary, Secondary, Malir2Government Boys Secondary School, Malir Colony (for boys)3Info-Line English Grammar School, Murad Memon Goth, Malir4Model Day Care Secondary School, Model Colony, Malir5Sana English Grammar School, Malir6Sun Rise Progressive School, 23/13 Model Colony, Malir7Superior Grammar School, R-66 Pak Kausar Town, Malir Town8Sweet Home School, Model Colony, Malir9The Harvards House Of Education, B-97, Kehkashan Society, Malir Halt10White House Grammar School, Airport Branch, Model ColonyLIST OF SCHOOLSGCEDISTRICT (SOUTH)Sr. No.Names of Schools1Aisha Bawany Academy, O-Level, 185, Shahrah-e-Faisal2Al-Aira Group Of Schools, 13-E, Muhammad Ali Society, Dhoraji3Army Public School, O-Level, 158, Iqbal Shaheed Road, Saddar4Bay View Academy, SL - 3, 12th Street, Phase 8, D.H.A5Bay View High School, College Campus, 8-Flench Street, Civil Lines6Beaconhouse School System , P. E. C. H. S, Opp. Greet Belt Mehmoodabad7Beaconhouse School System Defence Campus, Saba Avenue, Phase 8, DHA8Convent of Jesus and Mary,101-Clifton9Foundation Public School, O-Level, Defence Campus10Foundation Public Scool, College Campus, P. N. Shifa , Phase 2, DHA 11Habib Public School, M.T. Khan Road12Haque Academy, 208 - A, 32nd Street ,Phase 8, DHA13Head Start School System, 41-C, P.E.C.H.S, Block 614Inspire School of Advanced Studies, C-S-C, 2nd Floor, Phase 7, Ext. D.H.A15Jaffar Public School, 245 / 1 / H, P.E.C.H.S, Block 616Karachi Cadet School, 241 / B / 4, P.E.C.H.S, Block 217Karachi Grammar School, 19 ,Street , Block 5, Khayaban-e-Saadi, Clifton18Kingsley American School, 28 - B / 1, P.E.C.H.S, Block 6 19River Oaks Academy, 43 / 15 / F, Block 6, P.E.C.H.S20Springfield School, ST - 5, K.D.A. Scheme No. 121St. Joseph’s Convent School, Shahrah-e-Iraq, Saddar22St. Michael's Convent School, St - 5, Kehkashan, Block 7, Clifton23St. Patrick's High School, Saddar24St. Paul's English High School, Opp. P.N.S Dilawar, Saddar25St. Peter's High School, 81-Muslimabad 26Suffah Saviors School, 13 - C, P.E.C.H.S, Block 627The Anchorage School,145 C, Hali Road, P.E.C.H.S, Block 228The Aureole School, C - 54, Block 2, Kehkashan Clifton29The C.A.S. School, Saba Avenue, Phase 8, D.H.A30The City School, Darakshan Campus, Phase 6, D.H.A31The City School, PAF Chapter, O-Levels, Shaheed-e-Millat Road 32The City School, Senior Boys Branch, 42 - Q, Block 6, P.E.C.H.S33The City School, Senior Girls Branch, 42 - T, Block 6, P.E.C.H.S34The Indus Academy, 62-Old Clifton35The OASYS School, C 53, Block 2, Clifton36Toronto School of Academic Excellence, 10 / D, Muhammad Ali Society37Usman Public School, D - 196, Block 2, P.E.C.H.S38Washington International School, 32nd Street, Phase 8, D.H.A39Westminster School & College, D - 120, Block 4,Clifton 40World Academy, 14 CF, Old Clifton, Near Mohatta Palace DISTRICT (EAST)Sr. No.Names of Schools1Bahria Foundation College, Block 7,Abul Hasan Isphani Road, Gulshan-e-Iqbal2Beaconhouse, Jubilee Campus, Darulsalam Housing Society, Korangi3Beaconhouse School System, Cambridge Branch, E-23, Block 7, Gulshan-e-Iqbal4Chiniot Islamia School & College, Block 7, Gulshan-e-Iqbal, Opp. Safari Park5Dawood Public School, Bahadurabad, Dawood Co-Operative Housing Society6Delsol, The School, Muhammad Ali Housing Society, Tipu Sultan Road7Montessori Complex Cambridge School, C - 83, Block 14, Gulistan-e-Jauhar8National High School, Block 13-A, Hasan Square, Gulshan-e-Iqbal9Practical Schooling System,C-2, Block 13-D, Gulshan-e-Iqbal10Progressive Public School, 130-Faran Society, Dhoraji Colony11Shaheen Public School, 14th Street, Block 2, Gulistan-e-Jauhar12ST. Gregory's High School,C - 5, Block 3, Moti Mahal,Gulshan-e-Iqbal13Summit Educational System, B - 61, Block 3, Gulshan-e-Iqbal14The American Foundation Cambridge School, C-65,Block 13, Gulistan-e-Jauhar15The City School Gulshan Boys Campus, PB - 6, N.C.E.C.H.S, Gulshan-e-Iqbal16The Educational Centre, 214 C, Block 6, Gulshan-e-Iqbal17The Fahims School System,B - 13, Block 13 D / 2, Gulshan-e-Iqbal18The Froebel's School, E - 26, Block 7, Gulshan-e-Iqbal19The Metropolitan Academy,18 Street, Block 15,Gulistan-e-Jauhar20White House Grammar School, 9th Street, Block 4, Gulshan-e-IqbalDISTRICT (CENTRAL)Sr. No.Names of Schools1Bahria Foundation College, IV E - 11 / 8, Nazimabad, No. 42Beaconhouse School System, (Cambridge), F-118 / 119,Block 7,North Nazimabad3Falconhouse Grammar School, F - 71, Block B, North Nazimabad4Generation's School, F - 100, Block B, North Nazimabad5Happy Home School, 12 / A, Hussainabad, F.B Area, Block 26Karachi Public High School, D-32, Block-L, North Nazimabad7Ladybird Grammar School,F - 124, Block F, North Nazimabad8Little Folks Paradise Cambridge School, Block F, North Nazimabad9Raunaq-e-Islam Sara Bai School, L - 6, Block M, North Nazimabad 10The City School Senior Boys, 102, F, Block F, North NazimabadLIST OF SUBJECT EXPERTSSSCMr. Ameenullah Farooqi (Senior Examiner BSEK and AKU-EB),Head of Mathematics Department, Nasra Public SchoolMr. Amjad Roshan (Head of Mathematics DepartmentArmy Public School and College, Malir Cantt.Mr. Habib Ur Rehman, (Gold Medalist), Head Examiner, Paper Setter (BSEK) and Master Trainer of Science Teachers,Principal, Orchard Grammar School Mr. Husnain Javaid, Vice Principal and Coordinator of Mathematics,Fatimiyah Education Network (Boys Section)Mrs. Kausar Tahir, Senior Mathematics Teacher,Happy Home Secondary SchoolMr. Muhammad Shahid ,Head of Mathematics Department, Sheikh Khalifa Bin Zaid (SKBZ) College, DHAMr. Nadeem Ahmad Kirmani,Professional Development Facilitator, Senior Mathematics Teacher, Al-Murtaza School (Professional Development Center)Mrs. Naeema Akhter, Senior Subject Specialist (Mathematics),Government Girls Higher Secondary School, Chanesar Goth (U.M)Mr. Rais Uddin Siddiqui, Principal,Customs Public School Mr. Zahid Ahmed Latif, Teacher Educator (Mathematics)Administrator and Principal, Alpha Public School Shah Faisal ColonyLIST OF SUBJECT EXPERTS GCEMr. Abdul Wasiq, Senior Mathematics Teacher Habib Public SchoolMrs. Aileen Soares, HOD and Senior Mathematics Teacher,St. Joseph’s Convent SchoolMr. Iftikhar Ahmad Khan, Senior Mathematics Teacher,Beaconhouse School SystemMr. Muhammad Adnan Jamil, HOD and Senior Mathematics Teacher,Washington International School and Jaffar Public SchoolMr. Muhammad Asim, HOD and Senior Mathematics Teacher,Toronto School of Academic Excellence,Senior Mathematics Teacher, The City SchoolMr. Muhammad Faizan Hashmani, Senior Mathematics Teacher,Foundation Public SchoolMr. Muneer Ahmad Naveed, Senior Mathematics Teacher,Beacon Askari Secondary and Cambridge SchoolMr. Nadeem Ahmad, Senior Mathematics Teacher,Bay View High SchoolMr. Syed Muhammad Hussain, Head of Mathematics Department,Karachi Grammar SchoolMrs. Zareen Jawaid, Senior Mathematics Teacher,Aisha Bawany Academy (Cambridge Section) ................
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