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NATIONAL UNIVERSITY OF LESOTHO

FACULTY OF EDUCATION

|Course Outline |

|Course Title |CURRICULUM STUDIES IN MATHEMATICS |

|Course Code |SCE 423 |No. of Credits |7 |

|Department |Science Education |Faculty |Education |

|Pre-requisites |None, but exposure to SCE 335 and/or EDF 223|Co-requisites |none |

| |or equivalent courses will be helpful |course code | |

|Course Lecturer |Thabiso Nyabanyaba (PhD) and Nomusic Morobe (PhD) |

|E-mail: |Office: |Telephone: |

|t.nyabanyaba@nul.ls |BJO 215 |22-340601 |

|nomusicmorobe@ | |Ext: 3482 |

| | |Mobile phone: |

| | |58001702 |

| |

|Learning hours and venues |Mon: |Tues: |Wed: |Fri: |

| |10:10 |09:00 and 15:10 |15:10, 16:10 and 17:10 |14:10 |

| |BJO 302 |BJO 302 |BJO 302 |BJO 302 |

|Offer in academic year |1st and 2nd Semester |

|COURSE DESCRIPTION |

|This course is offered to final year science education students with the aim of equipping them with skills that are necessary for |

|teaching high school mathematics. It is a mixed mode offering which incorporates some face-to-face sessions with on-line |

|interactions. The course aims to deepen an understanding of the teaching of school mathematics based on the specific activity of |

|mathematics teaching. The course will also focus on the current key curricular development in Lesotho represented by a move from |

|the Cambridge Overseas School Certificate (COSC) Ordinary Level mathematics to the International General Certificate of Secondary |

|Education (IGCSE) and ultimately to Lesotho General Certificate of Secondary Education (LGCSE) and perhaps even to an Advanced |

|Level Certificate. |

| |

|The course is arranged in two parts with the first part intensively preparing students for the demands of teaching mathematics to |

|high school students. This part draws on the current literature in mathematics education to develop innovative teaching strategies |

|focusing on critical high school mathematics topics. It also prepares students for an independent project which is the main |

|component of the second part of the course. The second part is linked to and consolidates students teaching practice by requiring |

|them to reflect on students’ conceptual challenges, critical topics and assessment practices encountered during teaching practice. |

|This second part is mainly driven by an on-line interaction between students and the lecturer. |

|PREAMBLE |

|Probably there is no subject which offers such possibilities for misunderstanding between teacher and pupil as mathematics does. |

|The teacher stands at the blackboard. It is perfectly clear to him what the symbols mean, and what the conclusion can be drawn from|

|them. It is completely otherwise with many of the pupils. What the symbols are meant to represent, how the teacher knows what is |

|right and what is wrong, what is the object of the whole business anyway - all this is wrapped in mystery. The great majority of |

|students say to themselves, "We shall never learn this stuff, but we want to get through the exam. We'll have to learn it by |

|heart." |

|(Professor Warwick Sawyer’s address to the Indian Mathematical Association, approximately 65 years ago). |

|COURSE OBJECTIVES |

|Course Objective |

|This course is driven by questions rather than answers. It will therefore be important to reflect deeply upon our taken-for-granted|

|positions and challenge the regards and practices that have perpetuated a very restricted and inaccessible view of mathematics. |

|Most adults are proud to proclaim: ‘I was never any good at mathematics’. |

|What are the key characteristics of a good/bad mathematics teacher? |

|What practices currently pervade school mathematics teaching? |

|What practices and characteristics of mathematics teachers can improve the learning of the subject in Lesotho? |

|What are the different philosophical and epistemological underpinnings of (effective) mathematics teaching? |

|What common philosophical and epistemological orientations to mathematics permeate school and society? |

|How can a more nuanced orientation to mathematics drive a more inclusive and effective teaching of the subject? |

|What knowledge is essential for an effective teaching of mathematics? |

|What critical topics present the most challenges to teachers and students in high school? |

|How can we unravel these challenges to enable a deeper conceptual understanding of the subject based on the nature and historical |

|basis of such topics? |

|What curricular issues are embedded in the new IGCSE core and extended mathematics curriculum? |

|What curricular materials are available for a new mathematics teacher for the IGCSE? |

|What assessment practices can enhance the practice of IGCSE mathematics? |

|How can we use the teaching practice and the community of practice available to develop a reflective practice of mathematics |

|teaching? |

|How do we draw on on-line resources to support and improve our mathematics teaching? |

|How do we make better linkages between theories of mathematics education and the mathematics practices by documenting and sharing |

|experiences? |

|COURSE CONTENT |

| |Topic |Description |

|1 |Introduction |Course outline and survey |

|2 |Lesson plan |Expressing clear lesson objectives and selecting content and |

| | |material for an effective high school mathematics lesson |

|3 |Defining mathematics education |Conceptions of mathematics and mathematics education focusing on|

| | |philosophical and epistemic[1] underpinning of the current |

| | |problem-solving emphasis |

|4 |Characteristics of an effective mathematics |Largely using interactive electronic media, the topic builds on |

| |teacher |experiences of student-teachers regarding an |

| | |effective/ineffective mathematics teacher considering |

| | |professional and personal characteristics |

|5 |Theories of learning |The unit focuses on specific aspects of theories of learning |

| | |that relate to mathematics learning, particularly Piaget’s |

| | |notion of disequilibrium and Vygotsky’s concept of zone of |

| | |proximal development. |

|6 |Van Hiele |Building on theories of learning, particularly van Hiele’s |

| | |levels of geometric thinking to focus on specific mathematics |

| | |topics such as similarity and congruence and angle properties of|

| | |a cycle |

|7 |Community of practice |Building on the characteristics of an effective mathematics |

| | |teacher, particularly a reflective practitioner, and the concept|

| | |of a community of practice, the unit discusses the values of |

| | |reflections, collaboration and collegial exchange in an |

| | |effective mathematics teaching and learning context |

|8 |Test 1 |

|9 |Relevance of school mathematics |Exploring the mathematical idea, motifs and patterns of the |

| | |African culture and the relevance of mathematics to other fields|

| | |such as architecture |

|10 |Algebraic reasoning and thinking |With a view that algebra has its grounding in both early number |

| | |sense and in confident algebraic manipulation, the unit seeks to|

| | |raise the importance of making connections with prior knowledge |

| | |of learners and other mathematics topics as well as developing |

| | |algebra as a tool patterns and generalisation |

|11 |Probability and statistics |Evolving out of the notion of numeracy as the ability to make |

| | |sense of everyday data from a mathematical point of view, this |

| | |unit emphasizes the value of contextualization of both |

| | |probability and statistics in practice as tools for facilitating|

| | |complex everyday decisions, and making connections between |

| | |theoretical and experimental probability |

|12 |Assessment for learning |Effective assessment of mathematics for teaching and learning |

| | |with particular focus on formative assessment |

|13 |Test 2 |

|COURSE LEARNING OUTCOMES |

|At the end of this course students will: |Aligned Programme Learning |

| |Outcomes |

|Demonstrate knowledge and appreciation of appropriate social interaction modes by discussing key |1, 2 |

|mathematics education issues in groups face-to-face and on-line | |

|Demonstrate comprehension of key issues in mathematics education, including how different |1, 2 |

|philosophical and epistemological orientations apply to improving the quality of mathematics | |

|teaching and learning | |

|Demonstrate analytic skills for reflecting on teaching practice by producing lesson plans and |4, 5 |

|demonstrating reflections in and on action critiquing life lesson deliveries | |

|Demonstrate application competency by selecting and utilising available learning resources, |3, 4 |

|including free on-line curricular materials, to illuminate key mathematics concepts and applying | |

|relevant assessment strategies | |

|Demonstrate ability to synthesise key school mathematics concepts, mathematics education theories |3, 4, 5 |

|and teaching strategies by relating different concepts, theories and teaching practice | |

|Demonstrate an ability to evaluate relevant theories and strategies by critiquing the limits and |1, 3, 5 |

|possibilities of different teaching strategies within Lesotho’s education context | |

|COURSE TEACHING AND LEARNING ACTIVITIES |

|Course Teaching and Learning Activities |

|The course is designed with a view to have five contact hours weekly and two interactive and independent learning hours. The two |

|hours will be used for presentations and to work on-line sharing views and experiences. |

|Online discussion and forum |1 |

|Face-to-face lectures |2, 3, 4, 5 |

|Students presentations and critical reading |3, 4 |

|Project work |5 |

|Interactive class discussions |3, 6 |

|COURSE ASSESSMENT METHODS |

|Assessment Method |Description |Weight |Aligned Course Learning Outcome |

|On-line journal |Reflect on-line on the literature on |10% |Analytic and relational |

| |the teaching and learning of | |competencies on effective teaching|

| |mathematics in Lesotho in preparation | |and learning of mathematics in |

| |for a critique of the various teaching| |context while enhancing |

| |strategies and their impact on | |collaborative skills |

| |learning with a short on-line quiz and| |1, 2 |

| |a short piece of writing which should | | |

| |be approximately 750 – 900 words (5 – | | |

| |6 pages) in length to follow. | | |

|Major Project and selected abridged|Prepare a comprehensive file on the |15% |Acquisition of reflective practice|

|presentations |teaching of a school mathematics topic| |and knowledge of mathematics for |

| |drawing on the various resources and | |teaching in the activity of school|

| |techniques discussed in the subject | |mathematics |

| |and showing a full understanding of | |3, 4 |

| |the curricular issues peculiar to | | |

| |Lesotho as well as the various | | |

| |teaching and learning problems the | | |

| |assignment would be addressing. | | |

| |This piece of writing should be | | |

| |approximately 2500 words in length. | | |

| |Participants will also select one | | |

| |aspect of the project to model to | | |

| |colleagues in order to demonstrate how| | |

| |they would put their prepared work | | |

| |into practice in a classroom | | |

| |situation. | | |

|Tests |Based on the school mathematics |20% |Acquisition of competence for |

| |curriculum and assessment issues, | |linking theory to practice; the |

| |student teachers will be assessed on | |test will inform the lecturer and |

| |their ability to link theories and the| |the students about the extent to |

| |practice of school mathematics | |which the content covered has been|

| |teaching and learning. | |understood. |

| | | |1, 2, 5 |

| | | | |

| | | | |

|Examination |All students will write an examination|50% |This is a summative evaluation of |

| |at the end of semester. | |the teaching and learning as |

| | | |revealed through the students’ |

| | | |performance. |

| | | |3, 4, 5 |

| |

|ESSENTIAL READING: JOURNAL, TEXTBOOK, WEBSITE ADDRESSES |

|Referencing |

|At 4th year level you are expected to have acquired referencing skill and that you are, as expected able to reference sources |

|accurately. Please inquire about the referencing guidelines (the APA Manual which is preferred can be made available to you but you|

|are free to use the Harvard style as long as you are consistent) |

| |

|Recommended Readings |

|Stols, G, Kriek, J and Ogbonnaya, U (2008). The relationship between teaching practices and students’ achievement in mathematics in|

|Lesotho. African Journal of Research in SMT Education, Volume 12 Special Edition 2008, pp. 107 – 118. Available on: |

| |

|Mogari, D, Kriek, J, Stols, G and Iheanachor, O (2009). Lesotho’s Students Achievement in Mathematics and their Teachers’ |

|Background and Professional Development. Pythagoras. Volume 70, pp. 3 – 15. Available on: |

|.za/index.php/pythagoras/article/download/33/26 |

|Gwynn, M. (2002-2003). Improving Teaching through Classroom Action Research. Available on the University of Dayton website on |

|Essays on Teaching Excellence: Towards the Best in the Academy: |

| |

|Reed, Y, Davies, H, Nyabanyaba, T (2002). Investigation teachers’ ‘take-up’ of reflective practice from an in-service professional |

|development teacher education programme in South Africa. |

|Kazima, M, Pillay, V, Adler, J, (2008). Mathematics for teaching: observations from two case studies. South African Journal of |

|Education. Vol. 28: 283 – 299. |

|MEANS/PROCESSES FOR STUDENT FEEDBACK ON CAMPUS |

| |

|While understanding that marking essays is highly subjective, I have developed criteria for marking essays as an attempt to reduce |

|bias (see annexure) |

|Feedback will be provided in class so that all students can benefit from the general feedback. |

|Feedback will be provided as soon as marking has been completed. |

| |

|It is my understanding that more often than not students require feedback as soon as marking has been completed. It is important |

|for you to understand that group work assignment and objective tests are quicker to mark compared to individual essays and short |

|answer forms of assessment. |

|COURSE POLICY (Including plagiarism, academic honesty, attendance etc. |

| |

|Expectations |

| |

|Underpinning my dealings with students is a deep belief in your active participation in the course and a deep respect for your |

|knowledge and expectations. Feel free to e-mail me or call me at the numbers provided above. While your expectations and |

|experiences will be respected, the following policies are important for maintaining a professional collegial interaction. |

| |

|Attendance |

|You will be greatly disadvantaged if you miss any session as assessments are directly linked to sessional content. At minimum, |

|there is a requirement of a least 80% attendance. |

| |

|Referencing |

|At this level you are expected to reference sources accurately according to one of the standard forms of referencing. If you are |

|unsure about how to do this, please ask for an explanation. |

| |

|Plagiarism and cheating |

|You may have read media reports about increased plagiarism in universities worldwide, particularly but not only from the web. NUL |

|treats cheating and plagiarism very seriously and it is an offence subject to disciplinary action. Plagiarism means the theft of |

|ideas from others; copying or using others’ ideas without acknowledging them. NUL is in the process of developing a policy on |

|cheating and plagiarism. Meanwhile, here are some principles that can help you to avoid plagiarism: |

| |

|No person works alone, we all get ideas from others. However, in an academic context, it is important to: |

|1. Explicitly acknowledge your sources, using appropriate referencing conventions; |

|2. Re-work ideas into your own thinking. |

| |

|It is not acceptable to copy long tracts from another text, unless it is as a quote and appropriately cited and acknowledged. Too |

|many quotes suggest that you are not doing enough of your own thinking. |

| |

|Plagiarism applies to ideas that you get from colleagues as well. You are encouraged to work together, but assignments must be |

|produced individually. If you make use of an idea you got from someone else, you should acknowledge this (Mofolo, personal |

|communication, 2002). Ideas from colleagues that have been reworked into your own thinking can be presented as your own. |

| |

|Both groups (myself and students) should as much as possible adhere to this contract |

|ADDITIONAL COURSE INFORMATION |

|Mode of instruction |

| |

|A mixture of face-to-face sessions and on-line material and interaction will be used in this course. No textbook is prescribed for |

|the course, but students will benefit from having technology in the form of tablets or laptops to access on-line materials. The |

|acquisition of these materials (especially the tablets) at affordable rates is currently being enabled and all attempts will be |

|made to ensure that no one is disadvantaged by the use of the on-line mode. |

|FACULTY COMMITTEE APPROVAL |

| |

|Signature Dr N Liphoto Date 22/8/2013 |

|. |

Annexure

Assessment criteria for the major project[2]

1 Written work

|Level 1 |Level 2 |Level 3 |Level 4 |

|0 - 3 |4 - 7 |8 - 11 |12 - 15 |

|The project is sloppy and laden with |The project shows basic knowledge and |The project flows well and applies the knowledge |The project extends the knowledge and understanding of the |

|misconceptions and shows limited knowledge |understanding of the theories in |and understanding of the various theories |mathematics education theories and consistently and |

|and understanding of the main theories in |mathematics education and attempts to |underpinning mathematics education and effectively|creatively applies the knowledge in order to support high |

|mathematics education, with some gaps, and |support student learning, with some |uses them to support student learning drawing on a|quality student learning experience, shows deep reflections |

|the proposed activities are not designed to |exciting innovations as well as some |wide variety of material for an illuminating |of possible constraints and is of high academic standards in |

|support student learning |evident gaps |perspective to the subject. |terms of referencing and engaging with debates |

2 Presentation

|Level 1 |Level 2 |Level 3 |Level 4 |

|0 - 2 |3 - 5 |6 - 8 |9 - 10 |

|The presenter demonstrates poor preparedness|The presenter is properly poised and |The presentation is well designed, clear and |The presentation is ground-breaking in the its innovative |

|and low enthusiasm as well as a weak |demonstrates a solid grasp of concepts |engaging and shows a through grounding in the |nature and is set at the right level for the imagined |

|knowledge of basic concepts and is unable to|and does not constantly refer to notes |concepts and theories of secondary mathematics |audience while taking into account the varying nature of the |

|hold the attention of the audience. | |education with a good summary at the end |individuals within the audience |

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[1] Will be explained further in class but, simply put, is about learning aspects

[2] Note: These criteria are aimed at guiding the students and are aimed at supporting quality and effectiveness for professional teacher preparation and have been derived from various international programmes including the California Teacher Preparation Program.

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