DIFFERIENTATING HOMEWORK AND ITS EFFECTS ON …



DIFFERIENTATING HOMEWORK AND ITS EFFECTS ON ACHIEVEMENT: A CASE STUDY OF TWO CLASSESExcept where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my Advisor. This thesis does not include proprietary or classified information.Amanda E KeckCertificate of Approval:___________________________________________________________Donald R. Livingston, Ed. D.Sharon Livingston, Ph. D.Thesis Co-ChairThesis Co-ChairEducation DepartmentEducation DepartmentDIFFERIENTATING HOMEWORK AND ITS EFFECTS ON ACHIEVEMENT: A CASE STUDY OF TWO CLASSESA thesis submittedbyAmanda E KecktoLagrange Collegein partial fulfillment ofthe requirement for the degree ofMASTER OF EDUCATIONinCurriculum and InstructionLagrange, GeorgiaJuly 26, 2011AbstractThis study explores if differentiating math homework has an impact on the engagement and the test scores of seventh grade students. The effectiveness of the differentiated homework was determined through quantitative and qualitative analysis of data produced during the study. The significance of differentiated homework was determined through t-test analysis of the student’s pre-post test. The results were compared to the gains of a control group. Surveys were analyzed using a chi square. The results showed that student’s had positive attitudes about differentiated homework, but it did not provide a significant difference in their gains in their pre-post test. The differentiated homework did not have a statistical significant impact; however the effect size and qualitative analysis show that the homework was beneficial for the students.Table of ContentsAbstract..............................................................................................................iiiTable of Contents...............................................................................................ivList of Tables.......................................................................................................vChapter 1: Introduction......................................................................................1Statement of the Problem..........................................................................1Significance of the Problem.......................................................................2Theoretical and Conceptual Frameworks..................................................2Focus Questions........................................................................................5Overview of Methodology..........................................................................5Human as Researcher...............................................................................6Chapter 2: Review of the Literature...................................................................7History of Homework……..........................................................................7Homework Through-out the Grade Levels.................................................8Different Opinions on Homework………....................................................9Characteristics of Helpful Homework........................................................10Differentiation……………..........................................................................12Student Perspectives and Motivation........................................................14Chapter 3: Methodology...................................................................................16Research Design......................................................................................16Setting......................................................................................................16 Subjects and Participants……..................................................................17Procedures and Data Collection Methods................................................18 Validity, Reliability, Dependability and Bias ...........................................20Analysis of Data.......................................................................................22Chapter 4: Results.............................................................................................25Chapter 5: Analysis and Discussion of Results..................................................33 Analysis..................................................................................................33 Discussion...............................................................................................37 Implications..............................................................................................39 Impact on Student Learning.....................................................................40 Recommendations for Future Research..................................................40References...........................................................................................................43Appendixes..........................................................................................................46List of Tables Table 3.1 Data Shell……………………………………………………………………..18Table 4.1 Independent T-Test Comparing Pre-Tests…………………………..………...26Table 4.2 Dependent T-Test for the Control Group………………………..……………27Table 4.3 Dependent T-Test for Treatment Group …………………………..……….....28Table 4.4 Independent T-Test for Post-Tests………………………………..…………...29Table 4.5 Chi Square for Post Student Survey……..……………………..…………..…30CHAPTER ONE: INTRODUCTIONStatement of the ProblemOne educational tradition that has been prevalent since the beginnings of schooling itself is homework. Long ago in the time when learning consisted of drill, memorization, and recitation, students did much of their preparation at home. Gill and Schlossman describe: a time when students were required to say their lessons in class in order to demonstrate their academic prowess, they had little alternative but to say those lessons over and over at home the night before. Before a child could continue his or her schooling through grammar school, a family had to decide that chores and other family obligations would not interfere unduly with the predictable nightly homework hours that would go into preparing the next day’s lessons. (as cited by Vatterott, 2009, p. 3).It is assumed that homework is a necessary component of success in acquiring new math skills and strengthening existing math knowledge. One would also tend to believe that a student engaged regularly in math homework would have higher test scores compared to a student who does not regularly complete math homework. Although homework is often cited as a necessary strategy when teaching mathematics, it often does not seem to lead to significant gains in student achievement. There is some debate regarding the effectiveness of homework for promoting academic achievement. Cooper, Robinson, and Patall’s (2006) review concluded there is “generally consistent evidence for a positive influence of homework on achievement” (p.1).Consequently, the purpose of this study is to determine if creating differentiated homework assignments can make homework more meaningful, engaging and significant to students’ achievement.Significance of the ProblemAccepted as a normal part of a student’s routine, homework has been generally acknowledged as a positive, necessary practice. However, Vatterrott (2009) describes how “as the culture has changed and as schools and families have changed, homework has become problematic for more and more students, parents and teachers” (p.1). When homework is not meaningful, then it invades social interaction, athletics, scouting, religion and family times. Also, homework can cause stress and lead to arguments amongst children and parents. Wildman explains “whenever homework crowds out social experience, outdoor recreation, and creative activities and whenever it usurps time that should be devoted to sleep, it is not meeting the basic needs of children and adolescents” (as cited in Vatterrott, 2009, p.6).Thus, it would be most advantageous for educators and students to be engaged in meaningful, motivating and stimulating homework assignments. These kinds of assignments offer choices, allow for collaboration, and display creativity and engagement.Theoretical and Conceptual FrameworksThis research is centered among the frameworks of constructivism. Powell and Kalina (2009) explain how the combination of both the cognitive and social methods of constructivism as being the most beneficial way to run an effective constructivist classroom. When students are engaged in homework by way of discovery, creativity, individuality and peer collaboration, the theories of constructivism are being allowed. In the article, Cognitive and Social Constructivism: Developing Tools for an Effective Classroom, Powell and Kalina (2009) describe how cognitive constructivism comes directly from the work of Piaget. Jean Piaget proposed that humans can not simply be given information and immediately understand it. He believed instead that humans must construct their own knowledge through the process of assimilation and accommodation. The authors continue to expound, that Piaget’s beliefs, combined with the work of one of the founders of social constructivism, Lev Vygotsky, fosters effective and engaging classrooms. Social constructivism embeds social interaction as an integral part of learning. These social interactions, combined with a personal critical thinking process, build effective constructivist classrooms (Powell & Kalina, 2009). Powell and Kalina (2009) explain that, “Teachers and students must communicate to convey information and for learning to take place. Constructivism should not only happen sometimes in the classroom, or happen in one or two of the student’s classes, but in all of the student’s classes and in every teaching activity so that true learning can occur” , ( p.247). Differentiating homework assignments fosters this type of experience and will optimistically promote engagement and student achievement.In comparing this research to the LaGrange College Education Department’s (2008) Conceptual Framework, it encompasses parts of all three Tenets. The first subsection of Tenet 1 is titled “Knowledge of Content.” The section describes how teachers need to be resourceful to make the subject matter meaningful to students. Also related is the third subsection of Tenet 1, “Knowledge of Learners.” Addressed in this section is the need of the teacher to understand intelligences, learning styles and exceptionalities of the classroom. All of Tenet 2 is imperative to this study. Considering the study was testing the differentiated planning skills of the teacher, it only seems logical that the subgroup titled “Planning Skills” would be incorporated. In this category, teachers must foster learning environments where responsibility, decision making, individual and group work is enforced with an understanding of motivations and behavior. In short, all needs are met by all learners. One of the forms of collecting data for the study is going to be looking at pre and post- tests. Therefore, logically the third sub group of Tenet 2, “Assessment Skills” cluster was implemented. Finally, the last cluster to be considered for this study is the subgroup of Tenet 3, “Action.” Towards the end of the study, the students were surveyed to provide some feedback about the differentiated homework. Naturally I used the surveys to reflect on the input from the students. With regards to the National Board for Professional Teaching Standards’, Core Propositions for Experienced Teachers, four of the five domains, were addressed in this study. Proposition 1 relates with the third subgroup of Tenet 1. The Tenet 1.1, “Knowledge of Content”, correlates with Proposition 2. Both Proposition 2 and 3 are addressed by Tenet 2.1 while only Proposition 3 relates to Tenet 2.3, “Assessment Skills”. The last correlation is between Proposition 4 and the third subgroup of Tenet 3. They both relate to teachers reflecting and learning from their experience.The domains of the Georgia Framework for teaching addressed in this study include: Domain 1, Content and Curriculum, Domain 3, Learning Environments, and Domain 5, Planning and Instruction.Focus QuestionsIn doing action research it is important to choose questions to guide the research in optimal directions. These questions are referred to as focus questions. There are three main focus questions; number one refers to executing the study, number two is to determine student outcomes, and number three helps to determine the attitudes and experiences of the students during and after the study. The focus questions for my study are as follows: What differentiated assignments can be created to promote student engagement and achievement?How do differentiated homework assignments increase mathematics test scores as compared to more traditional assignments?What were the students’ attitudes about the differentiated homework?Overview of MethodologyThe purpose of the study is to determine if implementing differentiated homework increases engagement and significantly impacts test scores. Data for the study were collected using mixed methods; which are composed of qualitative and quantitative data. The action research study took place in a seventh grade middle school class room in a rural setting in Coweta, Georgia. For about a three week period (one unit of standards), students were divided into two groups. The study did obtain validity, reliability, dependability, and an absence of bias. The data gathered in the study was analyzed holistically by the focus question to which it applied. The holistic analysis focused on the concepts of validation, credibility, transferability, and transformational qualities. Human as ResearcherI am qualified to conduct this case study because I have been teaching for twelve years. In my experience I have encountered all types of learners. In Fulton County, where I taught for ten years, my career began in the alternative school. For two years there, I faced the most reluctant of learners. Six of the ten years spent in Fulton County was served at a south suburban middle school setting where I taught seventh grade math. My last two years in Fulton County were served in a fourth grade classroom at a brand new south county elementary school. Two school years ago, I moved to teach in the county in which I lived. I have been teaching seventh grade math at rural Coweta County middle school for two years now. Over three-fourths of my career has been in a middle school math classroom. In that time, I have encountered many battles with homework. It is my assumption that students who complete their homework are more prepared, practiced, positive and productive in his/her math class. Engaging students in completing homework assignments has been an underlying battle in every school setting that I have experienced. That is why it is my hope to improve student involvement, and success by creating stimulating, exciting and productive homework assignments in this study.CHAPTER TWO: LITERATURE REVIEWHistory of HomeworkHomework, defined as tasks assigned to students by school teachers that are meant to be carried out during non-school hours has been a key component of American schooling for many years. Throughout the latter part of the 20th century, trends have swayed in opposite directions about homework and its place in American schooling (Cooper & Valentine, 2001; Hong & Milgram, 2000; Simplicio, 2005). The opinions even extended to the national government. In 1957, the National Defense Education Act (NDEA) was established. Feeling threatened by the launching of the Russian satellite Sputnik, the United States government passed NDEA which was designed to enhance the Science and Math curriculums (Buell, 2004). It was assumed that deepening the rigor of the curriculum, assigning more homework and making students more academically accountable would help to produce more globally competitive students. Since the 1960s education had been on the forefront of concerns in governmental issues, and there have been several studies done on the topic of homework related to student achievement, studies which are both for and against homework. There have been several studies about homework. Most research found can support whichever idea an educator believes about homework.Homework is an integral part of the instruction. It provides reinforcement, practice, application, transference, and enrichment of what is taught in class. In addition, homework places demands on students that help them to develop mental skills such as concentrating, following directions, organizing materials, solving problems, and working independently. Homework can develop a sense of competency and independence. It can be a tool to transfer new knowledge into becoming long lasting or a new skill to becoming second nature. According to Willingham (2002), distributed and sustained practice is necessary in obtaining extensive learning. Homework is just one avenue for this practice to occur.Homework in Elementary, Middle and High SchoolThe amount and types of homework differ at different age levels. Its impact is also distinguished. Research indicates varying effects of homework for different age levels. The benefit of homework at the elementary level is to assist students in developing time organization, independent problem solving, and information processing skills. Homework helps children develop beliefs about achievement and study habits, including the value of effort and the ability to cope with mistakes and difficulty (Bempechat, 2004). Conversely the effects of homework on students by the time they reach high school are much more impressive. According to Cooper & Valentine (2001), a typical homework completing high school student will outperform students who do not do homework by 69% on standardized tests. Research also shows homework can raise a student’s G.P.A. by one-half point for 30 extra minutes of homework per night (Marzano, 2001). Students doing no homework end up with 1.2 years less education and 19% lower earnings than average. Students doing 15 hours or more a week of homework attain almost 1.5 year of education and attain 16% higher earnings than average (Rosenbaum, 2004). Time guidelines are not readily enforced and differ from school to school. A common recommended formula is for students to complete approximately ten minutes of homework per grade level (Vatterott, 2009). Different Opinions on HomeworkData can sometimes be skewed to show the researcher’s bias. For example, there was a study which showed the correlation of time spent on homework and achievement by Cooper and Valentine (2001). Cooper and Valentine found that the correlation of time spent on homework and achievement is higher at higher grade levels. Cooper and Valentine reported this in 2001:For high school students (grades 10-12), a sizable average correlation was found (r = +.25), whereas for students in grades 6-9, the average correlation was small (r = +.07), and for elementary school students, it was nearly nonexistent (r = +.02). (p.26)Later in 2007, Cooper and Valentine combined the data differently to make it appear that students in grades 7 through 9 benefited as much from homework as students in grades 10 through 12. Here is the contrasting data:We grouped correlations into those involving elementary students (grades kindergarten - 6) and those involving secondary school students (grades 7 - 12). This was the best we could do given the precision of the data. The average correlation between time spent on homework and achievement was substantial for secondary school students, averaging about +.25 across 23 samples. For elementary school students, it hovered around zero for the average of 10 samples. (p. 29-30).According to Vatterott (2009), the latter interpretation makes it appear that students in the 7-9 grade group gained as much from homework as the students in the 10-12 grade group. This is a grave difference from his earlier findings when he broke down the data into three groups instead of just two. The data could be displayed differently to placate Cooper and Valentine’s (2001) bias about homework in the early grades. Cooper and Valentine feel that homework is not necessary for elementary students. Cooper and Valentine contend, “there is no evidence that any amount of homework improves the academic performance of elementary school students” (p.109). In 2000 Kralovec and Buell co-authored a book titled, The End of Homework: How Homework Disrupts Families, Overburdens Children, and Limits Learning. This surely fueled the homework debate. The majority of the book discusses the possible negative connotations that homework could create. Kralovec and Buell (2000) contend that,Beyond the academic achievement, many teachers and parents see other benefits in homework. Its proponents claim that homework fosters self-discipline, good work habits, and responsibility, while at the same time providing accountability, enabling parents to know what is happening during the school day. Researchers even proponents of homework, point out, however that for each potentially positive impact of parental involvement in homework there is a corresponding potentially negative effect. (p. 12)Characteristics of helpful homeworkRegardless of your bias about homework, there is evidence that well-designed homework assignments that relate directly to what is being taught in the classroom, and are meaningful, can extend students’ learning beyond the classroom. According to Connors (1992) homework has many advantages: Homework teaches students how to organize their time, homework helps teachers cover more material throughout the year, helps students promote creativity, teaches students how to learn, motivates students and promotes learning, satisfies parents who believe in homework, encourages positive school-home communication, reinforces the content presented in class, promotes responsibility, independence, and decision-making skills, and improves grades. (pp.16-20).Considering this study was about how differentiating homework effects the engagement and achievement of students, this is the research of most validity. The first variable in creating meaningful, engaging homework is the teacher’s behavior and attitude towards homework itself. The teacher’s homework behavior relates to the quality and quantity of homework assigned the discussing of homework in class, and the methods of checking or grading (Epstein & Van Hoohris, 2001). If the teacher has a negative attitude about homework, checking homework or discussing homework, the students will feel it is not important and generally will not do it. Perception is everything, and students infer a lot from the attitude the teacher displays about homework. How teachers describe homework tasks and how they defend the purpose of the assignment tends to reveal their attitude about the homework. Teacher feedback is another important variable. It can encourage or discourage a student from completing a homework assignment. According to Vatterott (2009),Nonthreatening feedback with no grades attached provides positive information to students and keeps the focus on checking for understanding and learning. Detailed feedback is more effective than simple numbers or letters. When students receive no feedback on homework, is sends a message that homework is not important and not related to classroom learning ( p.75).Parental involvement can also be an imperative variable. When parents are interested in their student’s homework, they are more likely to complete their homework assignments successfully (Cooper & Valentine 2001). Unfortunately this variable is not controlled by the student. They have no bearing on how concerned their parents may or may not be in their education. Generally, more affluent and middle – income parents are more involved in the student’s homework. Also parental involvement affects much more than just homework completion. Designing meaningful, relevant homework assignments that complement the curriculum can be an effective instructional technique that can serve as a vital link between the school and the family.DifferentiationExperienced teachers know that children differ in their readiness and development level and that all children do not learn in the same way, yet homework is often a one-size-fits all, with all students being assigned the same assignment for homework (Eisner, 2003). The current trend is for teachers to implement differentiated instruction in to their classroom. However, many are unsure how to incorporate this philosophy into their current teaching methodologies. Although the first step in implementation is the hardest, Tomlinson (1999) states that “we have to know where we want to end up before we start out-and plan to get there”; therefore, “we must have a solid curriculum and instruction in place before we can differentiate them” ( p.13 ). Tomlinson (2005) puts it best when she states “our success as teachers in helping students see themselves as competent in the subjects we teach will affect the rest of their lives” ( p.12). In the article Differentiating Instruction in Response to Student Readiness, Interest and Learning Profile in Academically Diverse Classroom: A Review of Literature, Tomlinson et al. (2003) noted that students achievement gains in effectively differentiated classrooms were demonstrated across economic lines through pre and post-test and on state standardized tests. In order for differentiated instruction to be implemented into classrooms, staff development programs must be conducted. Teacher readiness levels, interests, and knowledge will need to be assessed so that training can be tailored toward individual needs. The training needs to be structured into flexible groups to provide a time for practicing, extending, and refining skills. Administrators will need to be patient and conduct the training over time so that teachers can implement the practices in their classroom in small steps. As Tomlinson (2003) explains, “It is not a lack of desire on the part of teachers, but a time issue. Differentiation is a wonderful concept if you supply staff development. Hess adds, “But to leave teachers high and dry-they’re dying out there with so much on their plate” (Hess, 1999, p.67). Tomlinson (1999) also states that “teachers are at different points in their professional journey, and we need to accommodate them” (p.15). As training takes place and differentiation becomes part of the school’s culture and climate, it is important to remember that it will take time to evolve. Tomlinson estimates that differentiation can take as long as seven to ten years to really institutionalize.Student Perspectives and MotivationA study by Xu (2005) revealed that some students understood the role and reason of homework. Xu (2005) explains “a majority of them were aware of the role that homework played in helping them better understand their lessons” ( p.47). As mentioned earlier there are many types of homework. According to Cooper and Valentine (2001), students were more engaged and willing to work on homework that was meant to practice past lessons and prepare for future ones. If students understand and agree on the reason for the homework assignment, the more likely they are to do the assignment. Many students are motivated for many reasons. A select few are intrinsically driven, some are competitive, some are motivated by a teacher or a parent and some might even be intrigued by an interesting assignment. Creating homework assignments that allow students a choice and a voice in how to process the information helps to engage learners in activities. This can begin to provide a practice and to establish independence (Dodge, 2005). According to Tomlinson and Allan (2000), not only is student interest a key in ongoing motivation, but also helps to continue student engagement in work that is not interesting. Differentiated homework assignments allow students a choice in processing the information that seems comfortable and makes sense. Students will be exposed to many different teaching methods and philosophies throughout their school careers. One thing that may be an underlying constant in all grades and all teachers is, more than likely, homework assignments. Unfortunately they will probably continue to be the one size fits all or a drill and skill type of assignment. Maybe this study can influence some to change by extending the practice of differentiation in designing homework in effort to continue to increase engagement and hopefully some achievement as well. Tomlinson (2000) describes differentiated instruction as “tailoring instruction to meet individual needs” (p.14). It is important to note that differentiated instruction is not a strategy to use in the classroom, but a way to think about teaching and learning. Tomlinson describes differentiated instruction as a philosophy. Although homework has been in debate over the years and continues to remain a source of controversy, homework is as much a part of school as lunch. As the literature revealed, the opinions are as diverse as the population. One fight that may continue is whether or not homework is necessary. However, with today’s societal view being that homework is expected, it is not going away anytime soon. Educators have a responsibility to their students to try different strategies to meet the needs of their students. According to Vatterott (2009), “at its best, homework in reasonable amounts can support and enhance learning, provide feedback to teachers about learning, allow students to practice skills and deepen their knowledge, and instill confidence within students when they successfully complete tasks on their own” (p. 158). Considering homework is a staple in education one might be inclined to think that the time spent on the debates about whether or not homework is necessary, would better be spent on arguments about how to improve homework practices and/ or how to implement homework effectively.CHAPTER THREE: METHODOLOGYResearch DesignAction research was the design I selected for my study. According to Best and Kahn (2003), action research is focused on immediate application, not on the development of theory or on generalization of applications. Its purpose is to improve school practices and at the same time improve those who try to improve the practices. Subsequently, by combining the research processes, habits of thinking, ability to work harmoniously with others, and professional spirit lends itself to positive improvements in school practices. According to Hendricks (2009), “the purpose of action research is for practitioners to investigate and improve their practices” (p.3). I plan to implement what I learned from the direct involvement with the research. I was able to see some of the major reasons contributing to students not completing homework. I chose two comparable classes that totaled fifty-two students, twenty-six in each class. The students took a pre and post-test that produced two even sets of data. According to Salkind (2010) when examining the differences between groups on one or more variable, the t-test is best used to show statistical comparisons. SettingThis research took place in a 7th grade classroom located in west Georgia. The school was a traditional middle school with grades six through eight. Each grade level was logistically located on its own wing of the building. There were two seventh grade teams and two seventh grade math teachers. My fifth and sixth period on- level math classes were the focus of my study. The two classes were comparable in their demographic and math ability make up. At the time of the study, I worked at this school for three years and the demographics have remained almost the same over that time period. There were 767 students enrolled and only 279 were seventh graders. In the seventh grade, there were 165 White students, 95 Black students and 19 students that are in the other category. The population comprised of sixty percent White, thirty-eight percent Black and two percent other. This was a Title I school with over half the students receiving free and/or reduced lunch. Title I is a program in which the federal government grants money in order to improve the quality of education in low income areas. In this county, permission to perform this study was given by the county’s lead psychologist. Permission was also granted by the principal of Smokey Road Middle School, Dr. Laurie Barron as well as LaGrange College’s Institutional Review Board.Subjects and ParticipantsStudents in my 7th grade classes were chosen for the study. Students in 7th grade average from 12 years old to 14 years old. The two classes chosen for this study were comparable. Each class had twenty-six students with fifteen girls and eleven boys, fourteen whites and twelve blacks. The classes were heterogeneously grouped with everyone in on-level math. There were also the same number of students in each class who did, and did not, pass the math portion of last year’s CRCT. Neither class had a student who receives any special services. At our school, the seventh grade math scores have averaged eighty-six percent meeting or exceeding expectations in math my last three year tenure.Procedure and Data Collection MethodsAccording to Bruce (2010), mixed methods refer to the use of quantitative and qualitative to acquire data in a study. In order to better answer and collect data for the focus questions, the action research study used mixed methods. Table 3.1 demonstrates the use of the mixed methods.Table 3.1 Data ShellFocus QuestionsLiterature SourcesData SourcesWhy do these data answer the question? How are data analyzed?What differentiated assignments can be created to promote student engagement and achievement?Dodge, J. (2005)Tomlinson & Mctighe (2006)Instructional plan and rubricCoded for themes: Reoccurring DominantEmergingCoded for themes aligned with focus questionHow do differentiated homework assignments increase test scores as compared to more traditional homework assignments? Cooper, Robinson, & Patall (2006)Cooper, Lyndsey, Nye & Greathouse (1998)Pre-Post TestShows difference between 2 groups and within groupsIt was base line data and then showed the results of implementing the instrument.Descriptive and Inferential Statisticsdependent t test within groupsIndependent t test between groupsEffect size calculationsDoes the use of differentiated assignments make homework more meaningful, engaging and significant to student achievement?Vatterott, C. (2009). Tomlinson, C. (2005).Trautwein, U., et al. (2006)Student SurveyReflective Journal?Instructional plan and rubricUse of prompt questions reward daily student engagement with lessonsAs observations are made, I was able to determine which strategies work best for the studentsCoded for themes aligned with focus questionChi SquareCronbach’s alphaThe first focus question was answered through a peer review of the instructional plan. The plan (see Appendix A) was evaluated using a rubric (see Appendix B), which allowed helpful responses for areas that needed improvement by three colleagues. The peer review of the instructional plan was performed in order to ensure the instructional plan was not biased, dependable and reliable in nature. The second focus question was answered through the use a control and a treatment group. Students involved in this research study and that attend this school are hand scheduled into classes according to their previous years math CRCT score. Generally, each class is formed with students that fall within a thirty to forty point interval of his/her math scores in each class period. At the beginning of the unit a pre-test was given (see Appendix C). After the pre-test, a t-test was performed to show that there was no significant difference among the groups. Throughout the unit, students in one class were given traditional book or work book page homework assignments. The other class was assigned homework that offered some choice and was differentiated. At the end of the unit, a post-test was given. The third focus question was answered using a survey. After the post-test, students completed a homework survey (see Appendix D). The survey questions were from a survey designed by Trautwein, Ludtke, Schnyder & Niggli,(2006) and the questions were same or very close to the same wording. Quantitative data gathered from the five point Likert-scale survey responses ranging from strongly agree to strongly disagree were analyzed to determine if the type of homework assigned affected the student attitudes and/or achievement. The student attitudes were measured by collecting the same survey and some journal reflections (see journal prompts in Appendix E).Validity, Reliability, Dependability and BiasThe data for Focus Question One was answered through a peer review of the instructional plan. The plan was evaluated using a rubric which allowed helpful responses for areas that needed improvement by three colleagues. This feedback was gathered as qualitative data; which requires accuracy and consistency. To help ensure dependability the data collection and treatment was consistent throughout the study, the control and treatment groups were carefully selected and all raw data were well organized. According to Popham (2008), “content-related evidence of validity refers to the adequacy with which the content of a test represents the content of the curricular aim about which inferences are to be made” (p. 89). In order to maximize content validity another middle grades math teacher read over the test to access if it directly related to the 7th grade Georgia Performance Standards. To ensure reliability the strategy implemented was the test-retest reliability. The same pre-test and post-tests were given to two groups. The test revealed pertinent data that as indicated by Salkind (2010), showed how much more post-test scores were when compared to the pre-test by using interval scales. The threat of bias was minimized by having others read over the test checking for offensiveness and fairness. The data for Focus Question Two was measured using test scores. The pre/post-test directly related to the standards addressed in the unit. Therefore the quantitative scores collected displayed content- related evidence of validity and were compared using several statistical tests. According to Popham (2008), “content-related evidence of validity refers to the adequacy with which the content of a test represents the content of the curricular aim about which inferences are to be made” (p. 89). In order to maximize content validity another middle grades math teacher read over the test to access if it directly related to the seventh grade Georgia Performance Standards. To ensure reliability the strategy implemented was the test-retest reliability. The same pre-test and post-tests were given to two groups. Reliability is defined by Popham (2008) as, “the consistency of results produces by measurement devices” (p.503). Reliability is used to make sure that research is consistent and can be repeated. The test revealed pertinent data that as indicated by Salkind (2010), showed how much more post-test scores when compared to the pre-test by using interval scales. Dependability was ensured by controlling the data setting, selecting relevant study groups, and consistently collecting data. The threat of bias was minimized by having others read over the test checking for offensiveness and fairness.Focus Question Three was measured using a five point Likert-type scale that analyzes attitude survey results. These results were categorized to ensure a nominal level of measurement. Salkind (2010) says that when an outcome fits into only one category, it can be a nominal level of measurement. To assess internal consistency, a Cronbach’s alpha was computed to match the scores for each item to the total for each participant. This showed which items on the survey function homogenously. This revealed the internal consistency of reliability because as Popham (2008) suggests, “it shows the extent to which the items in an educational assessment instrument are functioning in a consistent fashion. In addition a reflective journal was kept by the researcher throughout the study. The date from the reflective journal was coded for themes and analyzed to determine dispositions and attitudes. The dependability from the data collected from the reflective journal is measured by the consistency in recording events, and the length of time for the data collection being persistent and prolonged. Construct validity was obtained by showing a correlation between positive student attitudes about math homework and student achievement. The threat of bias was minimized by checking the survey questions for offensiveness and fairness.Analysis of Data The data for Focus Question One was measured using an instructional plan and rubric that was evaluated by three respected colleagues. The peers focused in on assuring that the pre/post-tests, and essential questions were aligned with the Georgia Performance Standards and reflected higher order thinking skills. Qualitative feedback from these peers was then coded for reoccurring themes. Those themes were then analyzed to see if any changes need to be made to increase the effectiveness of the plan. This was done by looking for categorical and repeating data that might form patterns of behavior.The data for Focus Question Two were analyzed inferential statistics. Dependent t-tests were used to describe the pre-test and post-test data to determine if there are significant differences between the means of one group tested twice to see if there is a significant difference between the two groups. The null hypothesis, there is no significant difference in the pre-test and post-test scores, was rejected at the .05 significance level. Then the Independent T-test was used to determine if there was a significant difference between the means of an independent group after the implementation of the treatment. An effect size calculation (Effect Size r for dependent and Cohen’s d for independent) was also necessary to analyze the magnitude of the treatment effect on the group. The purpose is to find statistical significance between the gains in the pre and post test scores of the treatment group. Focus Question Three was measured using surveys and journals. The students took a survey that offered choices displayed in a five point Likert-type scale format. The results from the survey were analyzed statistically using a Chi square. The Chi Square was able to determine if the survey questions were statistically significant at one of three levels. The three levels were p<.05, p<.01, and p<.001. According to Salkind (2010), “the Chi-square test involves a comparison between what is observed and what is expected by chance” (p.313). In addition, the researcher kept a reflective journal that was coded for themes. The themes reflected the attitudes and ideas of the researcher during the study. As a whole, the study was analyzed on the concepts of validation, credibility, transferability, and transformation versus breaking down the elements of the study by each focus question. By analyzing the study holistically, the above concepts are all included.There were two types of validation used in this study, consensual validation and epistemological validation. Consensual validation was met by having the study reviewed by the LaGrange College Educational department. Epistemological validation was obtained through the literature review found in chapter two of the thesis.Triangulation of data is related directly to the credibility. Eisner (1991) says that ‘structural corroboration’, is where a convergence of evidence comes together to from a convincing whole. This thesis has obtained credibility through structural corroboration. Structural corroboration was acquired by using multiple sources of data from mixed methods. Fairness is evident in the literature review where opposing points of view of homework are presented, and rightness-of-fit is presented in Chapter Five of this thesis where all the data are discussed holistically.This study has transferability and is transformational. Transferability is where the study can be recreated by others or when your study can be applied to other situations and can only occur if credibility has been established. Referential adequacy refers to the research being able to be replicated easily by others. This has been acquired in this study through the details outlined in the methodology section. Catalytic validity as described by Khinchloe & McLaren (1998) is when a study causes a positive change or transformation in the researcher or others. Due to some of the responses, suggestions and attitudes gathered in this study, I plan on transforming how homework is assigned at least from time to time from now on.CHAPTER FOUR: RESULTSThe results of this study on differentiating homework and its effects on student achievement were collected and analyzed by focus question. The outcomes are organized and presented by focus question throughout this chapter. Focus question one, “What differentiated assignments can be created to promote student engagement and achievement?” produced qualitative data that was measured using a rubric critiqued by two fellow 7th grade math teachers and the curriculum assistant principal to determined if the instructional plan was based on the Georgia Performance Standards (GPS) and if higher order thinking skills were reflected throughout the unit of instruction. Data were gathered using a rubric from two perspective colleagues that critiqued the instructional plan. These data were coded for recurring, dominant and emerging themes. Most of the feedback was positive and in agreement with the plan. In the open ended section of the rubric both colleagues commented that the plan was very student centered and presented all levels of thinking skills. However, there were two reoccurring themes that evolved from the other open-ended question that asked for suggestions. The time might be a constraint and the assessment is too long. Teacher 1 with ten years experience suggested that some of the activities might take longer than predicted. The assistant principal recommended that the unit may take longer than just 3 weeks. Teacher 1 with ten years experiences commented, “You might want to consider making the assessment a little shorter considering it is open ended.” The assistant principal observed, the exam might take longer than one class period.” From the feedback of my colleagues, I made minor adjustments to the specific items mentioned in the instructional plan.The second focus question was created to determine if a unit assessment score would show a significant difference in a group of students that were assigned differentiated types of homework assignments versus a group of students that were assigned more traditional types of homework. The data for focus question two, “Do differentiated homework assignments increase test scores compared to more traditional homework assignments?” were collected using pre and post-test scores of a control and treatment group. First to show that there was no significant difference at the a = .05 significance level among the two groups in the study, an independent t-test was conducted. The pre-test scores of the control group were compared to the pre-test scores of the treatment group. Table 4.1 shows that the null statement, that there are no significant differences between the two groups, was accepted at the p < .05 level.Table 4.1 – Treatment and Control Group Pre-Test Scorest-Test: Two-Sample Assuming Unequal Variances?ControlTreatmentMean21.74118.57692308Variance94.123102.0938462Observations27.00026Hypothesized Mean Difference0.000Df51.000t Stat1.162P(T<=t) one-tail0.125t Critical one-tail1.675P(T<=t) two-tail0.251t Critical two-tail2.008?As shown in Table 4.1, t(51) = 1.16, p > .05; therefore, since the obtained value, failed to exceed the critical value, the null hypothesis failed to be rejected. Consequently, there is no significant difference among the two groups in the study. After the treatment period, two t-tests for dependent means were conducted using the scores from the pre and post assessments of the treatment and control groups. Salkind (2010) says the purpose of the dependent t-test was to compare the means of the pre and post- tests to help discover if there were any significances in the differences. The null hypothesis, there is no significant difference in the pre-test and post-test scores, was rejected at the .05 significance level. The findings in the dependent t-tests are presented in the following tables.Table 4.2 Pre/Post Control t-Test: Paired Two Sample for Means?PrepostMean21.74172.630Variance94.123201.704Observations27.00027.000Pearson Correlation0.143Hypothesized Mean Difference0.000Df26.000t Stat-16.511P(T<=t) one-tail0.000t Critical one-tail1.706P(T<=t) two-tail0.000t Critical two-tail2.056?According to Table 4.2, the obtained t-value exceeded the corresponding critical value at the a = .05 confidence level. The results of the pre-test and post-test scores showed that t(26) = - 16.511, p < .05; therefore the null hypothesis was rejected. A test-retest indicator of reliability is the Pearson correlation. You can see from the table it measured .143. There were four outliers in this group. Four students only answered one question on the pre-test. There were significant differences in the pre-test and post-test scores of the control group.Table 4.3 Pre/Post Treatmentt-Test: Paired Two Sample for Means?PrepostMean18.57767.692Variance102.094183.182Observations26.00026.000Pearson Correlation0.284Hypothesized Mean Difference0.000Df25.000t Stat-17.381P(T<=t) one-tail0.000t Critical one-tail1.708P(T<=t) two-tail0.000t Critical two-tail2.060?In Table 4.3, the obtained t-value exceeded the corresponding critical value at the a = .05 confidence level. The results show that t(25) = - 17.381, p < .05; therefore the null hypothesis was rejected. The table shows the Pearson Correlation at .284. This is a test-retest indicator of reliability. There were significant differences present between the pre-test and post-test scores of the treatment group.To compare the post-test scores of the treatment group and the control group, an independent t-test was done at confidence level of a =.05. Table 4.4 displays the obtained t-value is less than the corresponding critical value at the a = .05 confidence level.Table 4.4 Post-Testst-Test: Two-Sample Assuming Unequal Variances?ControlTreatmentMean72.63067.69230769Variance201.704183.1815385Observations27.00026Hypothesized Mean Difference0.000Df51.000t Stat1.296P(T<=t) one-tail0.100t Critical one-tail1.675P(T<=t) two-tail0.201t Critical two-tail2.008?The results of the control and treatment post-test comparisons show that t(51) = 1.296, p > .05; therefore the null hypothesis was accepted. There were no significant differences among the control and treatment groups post test scores. According to Salkind (2010), the effect size measures the magnitude of a treatment effect. An effect size calculation was computed on both the treatment and control group. Considering a dependent t-test was calculated on the control and treatment groups, effect size (r) was determined from the mean (21.74) and standard deviation (9.7) from the pre-test score and the mean (72.63) and standard deviation (14.2) from the post test score of the control group. Thus resulting in an effect size of r = -.902 which shows a large size. In addition, an effect size calculation was computed on the mean (18.58) and standard deviation (10.1) from the pre-test score and the mean (67.7) and standard deviation (13.5) from the post test score of the treatment group. Thus resulting in an effect size of r = -.9 which also shows a large size. A Cohen’s d effect size calculation was ran using the control mean of 72.63 and standard deviation of 14.20 and the treatment mean of 67.69 and standard deviation of 13.53 to measure differences among the treatment and control groups. The effect size measured .36, which is a small difference.The results of focus question three, “Does the use of differentiated assignments make homework more meaningful, engaging and significant to student achievement?” were collected from anonymous student surveys and a reflective journal kept by me. The ten question student attitude survey was answered on a Likert scale by a total of forty-four students.From the results of these surveys, a Chi Square statistical test was calculated for each variable based on the sample size. Salkind (2010) explains that by determining the statistical evaluation of probability reflects if results of the survey occurred by chance or are a meaningful response. The results of the survey are displayed in Table 4.5.Table 4.5 Student Attitude SurveysTable 4.5: Chi Squaren=44χ?(Treatment)χ?(control)Item 1: Doing math homework allows me to continue to learn about things that interest me. 7.565.45Item 2: I often copy math homework from others. 6.444.74Item 3: I often do my math homework during homeroom or breaks at school. 1.58.78Item 4: I often write down random answers on the homework in order to just earn credit. 3.725.41Item 5: I work hard on my math homework every time it is assigned. 7.566.85Item 6: I don’t learn much from our math homework.23.67***3.93Item 7: When I am trying to do my math homework, I often feel completely lost. 7.069.85Item 8: My math homework takes a lot of time. 6.59.03Item 9: My math homework helps me better understand what was taught in class. 9.289.11Item 10: I wish my math homework was more interesting. 12.61*22.45**** = p < .05, ** = p < .01, *** = p < .001The results of the Chi Square test revealed that two questions in the survey were of significance. According to the treatment group, questions 6 and 10 were found to be significant. The significance of question 6 showed a p < .001, which means that a high percentage of students agreed with the question stating that not much is learned from the math homework. Also indicated by the treatment group, question 10 showed a p < .05. This shows a good percentage of the students agreed with the question stating that homework should be more interesting. Referring to the results of the control group, only question 10 shows a significance with a p < .001. This indicates that a high percentage of students agreed with the question stating that homework should be more interesting. In addition, the survey for treatment group included three open-ended questions in order to collect opinions about the treatment. The questions were basically related to what was liked, what was not liked and which homework was preferred. The reoccurring opinions were that the differentiated homework was preferred but it sometimes took longer than traditional. On student marked, “I liked it because it gave you a choice of what to do.” A similar comment was recalled be another student, “I loved it because we got to make up our own problems.” For this portion of the study the purpose of the Cronbach’s Alpha test is to show aggregate trends in the overall responses of a survey. This test regulates internal consistency reliability of the items on the attitude surveys. The test for the attitude survey for the treatment group resulted a Cronbach’s Alpha score of α = .42. The test for the attitude survey for the control group resulted a Cronbach’s Alpha score of α = .48. Therefore, the survey for both groups demonstrates a medium level of reliability.Throughout this research process, consistency in the reflective journal was obtained by using writing prompts. Each day the positive and negative attitudes about the lesson and main topics were recorded along with any interesting facts or possible changes to be made. I recalled at the beginning of the study the students in the treatment group were excited and eager to do their homework. I wrote, “I can not believe how excited everyone seems to be about homework, especially in this class. This group of students not doing their homework is exactly why I choose them for the treatment group. I hope this eagerness appears in the grade book on Friday.” Later in the first week the observations reflected that the attitudes were the same but students had still not completed their homework. I recall, “Today as I checked the homework, the students seemed to be really disappointed that they had not done the homework assignments.” Even though the work had not been completed the attitudes still remained positive about the differentiated homework. “I am definitely going to do my homework next week”, I remembered being mentioned by a couple of students who had not completed the homework. However, the habits did not change. It seemed as though the same students were still not completing their homework. The next couple of weeks of the study produced the same outcome as the first week. Recalled from the second week, “I was hopeful that the students would follow through with the promises to do their homework this week.” The last week of the study was still showing no changes. The following quote was taken from the journal during the last week of the study, “I guess old habits are hard to break. Maybe next year I will incorporate the differentiation in during class time to ensure that it is attempted. Some students just don’t do homework no matter how exciting it might seem to be.” In the upcoming chapter, these reported results are analyzed and discussed in detail. In addition, any interpretation, implications and/or recommendations for future study are expressed.CHAPTER FIVE: ANALYSIS AND DISCUSSION OF RESULTSAnalysisThis study was designed to determine if differentiating homework assignments would increase students’ academic achievements. The results were organized by focus question and compared with information discovered and reported in the literature review. The scores from unit assessments of the treatment and control groups were used to perform statistical tests to determine if differentiating the homework helped students’ assessment scores increase. A homework attitude survey was given to both groups to gather common views about doing homework. Also, a reflective journal was kept to record any interpretations, considerations and/or modifications that might have occurred.The data for focus question one were gathered through faculty review, the instructional plan rubric, and feedback provided by three colleagues, the curriculum assistant principal and two fellow seventh grade math teachers. The type of data used to answer focus question one is was qualitative data. The data were then analyzed by coding for recurring themes. The coded results were then examined to determine the changes that may occur in order to make the instructional plan more effective. The reoccurring issue that arose with the plan was timing. One issue in particular was the original pre/post-test was too long and would possibly take more than one class period considering it was 25 open-end questions. This issue was addressed by making the assessment shorter. It was narrowed down to sixteen open-ended questions. The second focus question was answered through the collection of data from pre-post tests for both the treatment and the control groups. The pre-post tests were analyzed using inferential statistics. The two forms of statistical analysis that were used were dependent t-tests and independent t-test. The independent t-test determines if there are significant differences among groups being examined. The analysis of the independent t test performed using pre-test scores on both groups produced obtained values that did not exceed the critical values. Therefore, at the a = .05 confidence level, the null statement was accepted. According the pre-test scores, there was no significant difference among the groups. According to Salkind (2010), two groups that show no significant difference are similar in nature and able to be compared. The dependent t-test measures if there are statistically significant gains in a group after some intervention. For this study, the intervention was to differentiate student’s homework throughout the unit. Instead of assigning the typical workbook page, an alternate, engaging, number of choices were given to complete for the week’s homework was given to one group. The group chosen was a class that most students, for some reason, chose to just not do their homework. The differentiation and student choice hopefully would peak some student interest in doing homework. As previously reported in the literature review, according to Tomlinson and Allan (2000), not only is student interest a key in ongoing motivation, but also helps to continue student engagement in work that is not interesting. At the end of the unit the treatment group’s scores were compared to a control group that throughout the unit were assigned the typical workbook page homework assignments. The post test scores were analyzed to see if there were statistically significant gains after the unit’s completion. The reliability between the pre-post tests was determined using the Pearson Correlation. Both the treatment group and control group showed significant gains throughout the study. The means for both groups showed dramatic increases on the post tests as opposed to the pre-test scores. Finally, the two group’s post-tests scores were compared using an independent t-test. This was to see if significant differences were present in the post test scores of the treatment and control groups. The results indicated that t(51) = 1.162, p > .05; therefore the null hypothesis was accepted. There were no significant differences among the control and treatment groups post test scores. An effect size was also calculated to show the magnitude of the difference and it too was a low .36. These results show that even though both groups post test scores greatly improved, the treatment group did not score higher that the control group. Therefore the study did not show that assigning differentiated homework instead of traditional homework does not help increase test scores. I believe that this is mostly due to the fact that most of the students, even though they seemed excited about the different homework assignments as reported in the researcher reflective journal, still did not complete their homework assignments any more than usual. As previously mentioned the group of students chosen, were so because they were very inconsistent in completing homework assignments. I had hoped to change their habits in addition to the unit assessment score. I found in the research discovered in the literature review that homework is a pretty important component especially in high school. According to Cooper and Valentine (2001), a typical homework completing high school student will outperform students who do not do homework by 69% on standardized tests. Research also shows homework can raise a student’s G.P.A. by one-half point for 30 extra minutes of homework per night (Marzano, 2001). Students doing no homework end up with 1.2 years less education and 19% lower earnings than average. Students doing 15 hours or more a week of homework attain almost 1.5 year of education and attain 16% higher earnings than average (Rosenbaum, 2004). The research in the literature review never really confirmed that homework would raise test scores. There were arguments for and against homework. One opinion I found to agree with was that homework can be helpful if it is meaningful and engaging. However the number one variable in the effectiveness of homework, classwork or any work is the teacher. The behavior presented by the teacher towards the students is the most impressionable variable. The teacher’s homework behavior relates to the quality and quantity of homework assigned the discussing of homework in class, and the methods of checking or grading (Epstein & Van Hoohris, 2001). If the teacher has a negative attitude about homework, checking homework or discussing homework, the students will feel it is not important and generally will not do it. Perception is everything, and students infer a lot from the attitude the teacher displays about homework. How teachers describe homework tasks and how they defend the purpose of the assignment tends to reveal their attitude about the homework. Teachers that feel homework is important need to display that in their behavior. If teachers tend to feel as if homework is not such an important component for learning, their students will probably display the same attitude in their homework behavior.Focus question three was answered using both qualitative and quantitative data. The qualitative data for focus question three was collected through a reflective journal and a student homework attitude survey. I recorded daily entries in the reflective journal to record events I considered important, wanted to change, or interesting in terms of the study. The journal entries were analyzed by coding for recurring themes. The reoccurring opinions were that the differentiated homework was preferred but it sometimes took longer than traditional. Tomlinson (2003) describes, as training takes place, and differentiation becomes part of the school’s culture and climate, it is important to remember that it will take time to evolve. Tomlinson estimates that differentiation can take as long as seven to ten years to really institutionalize. Nevertheless I recorded in the researcher reflective journal that the students’ attitudes and excitement did not relate to the number of students who were completing homework assignments. Unfortunately, this chosen treatment group still had low homework completion scores. One student remarked, “I can not wait to do my homework on the internet, I love working on the computer.”The minimal quantitative data collected came from the results of the Chi Square test that highlighted only two significant statements answered on a Likert scale survey. Both the treatment and control groups found significance in statement number 10, “I wish my math homework were more interesting.” The control group also found significance in statement number 6, “I don’t learn much from my math homework.” This was interesting to me because this is the same group that the majority of them don’t do their homework in the first place. Creating homework assignments that allow students a choice and a voice in how to process the information helps to engage learners in activities. This can begin to provide a practice and to establish independence (Dodge, 2005). DiscussionThis study did not produce the results that I was hoping to achieve. Both groups made significant gains from the pre to the post test, which was an expected outcome. However, the treatment groups’ mean score on the post test was actually five points lower than the control groups mean. This was a surprising result because it turned out the exact opposite of what I had expected. There could be at least three factors that could have contributed to this unexpected outcome. First the students at my school are scheduled based on their math state standardized test score. The control group was a class having averaging scores that range about fifteen to thirty points higher than the treatment groups average state standardized test scores. This could also be an indicator subsidizing the other variable that could have altered the expected test results. As mentioned before, the treatment group was chosen because they seemed to be a less motivated in completing their homework assignments. Also as previously explained, this group’s state standardized test scores ranged about fifteen to thirty points lower than the control group. I was hoping to increase student motivation and engagement along with unit assessment scores. This is the reason I chose this group as the treatment cluster for the study. The final impacting variable could be the timeline. Three weeks is a very short period of time to try to incorporate a change on a group of people. Had I begun the study when school started continued to implement the differentiated activities throughout the year, the students would been more comfortable with my expectations and types of assignments given. They were much more student centered and involved than the mere traditional workbook page homework assignment.Credibility was obtained by assuring structural corroboration through the use of multiple sources. The opposing views presented in the review of the literature ensured the fairness. Part of being fair is making sure opinions are expressed in an unbiased manner. The fair, unbiased presentation helps to make sure the argument was coherent and tight.Validity and reliability were considered when determining data collection methods for the study. Both qualitative and quantitative data were gathered and analyzed as accurately as possible. This study was conducted with great care and attention. The groups were carefully selected to confirm rightness of fit. Even though the desired results were not achieved, student’s attitudes about homework were positively affected. Referring to the comments on the survey, some excitement and curiosity was raised about doing homework. One student remarked, “I can’t wait to try my homework.” Another comment was, “I was so excited about the homework, I finished mine for the whole week on Monday.”ImplicationsThis study could be applied to any class in any discipline. Differentiation is a current popular trend in education. In my experience in the area where I teach, it is an extremely widespread method to ensure that student accommodations are met. One drawback however, to differentiation is it can take some time to implement. Tomlinson (1999) states that “teachers are at different points in their professional journey, and we need to accommodate them” (p.15). As training takes place and differentiation becomes part of the school’s culture and climate, it is important to remember that it will take time to evolve. Tomlinson estimates that differentiation can take as long as seven to ten years to really institutionalize. The quantitative results of this study showed that both groups made significant gains. Even though the expected results were not achieved, the qualitative data showed some changes in attitudes and opinions about homework. In achieving referential adequacy, one would merely have to create differentiated assignments for his/her content and/or grade level and then simply follow the steps for the rest of the study.In doing this study I became aware of the hunger for alternative types of homework assignments. Students get bored doing the same type of assignment over and over again and again. There is a definite need for diversity in assignments. The issue of student engagement involving homework is going to continue to be an ongoing battle. The planning of the diverse lessons offering student choice was fun to create. Also, checking homework once a week versus my usual everyday check off was much more time effective. It allowed for me to be more thorough in my feed back and check for more accuracy and mastery of a particular topic. I want to try to incorporate that aspect of the homework check off in my routine for next year for sure, even if assignments are not differentiated every week. I did enjoy planning them and do plan on using them, however they do take quite a bit of time to plan.Impact on Student LearningThe quantitative data revealed that there was a minimal impression made on the student’s learning. Even though the post tests comparisons showed that the treatment did not work, the significant gains made in both the treatment and control groups from the pre to post test indicate that the treatment did not hinder any learning. The qualitative data exposed unexpected differing attitudes about homework. Hopefully some initiatives were stirred and some homework habits will be altered.Recommendations for Future ResearchWhen replicating this study in the future, there are two recommendations I would suggest incorporate. First, the study would produce more concise, coherent results if it were presented to more than merely two groups and last for more than just one unit of study. The unit of study chosen for this study was one of the more challenging introduced in 7th grade. Some students might do better with material in other units introduced. I suggest the study to last through at least two units of seventh grade instruction. Lasting the entire school year would probably be best.The second suggestion I would recommend implementing is consistency and consideration. Consistency relates to assessing throughout the study. If you give multiple choice assessments as pre and post tests at the beginning of the study, it must remain the assessment method throughout the study. Consideration should be given to the discipline, the environment and especially the student. ReferencesBempechat, J. (2004). The motivational benefits of homework: A social-cognitive perspective. 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Homework: A new direction. Columbus, OH: National Middles School Association.Dodge, J. (2005). Differentiation in action. New York: Scholastic Teaching Resources.Eisner, E. (1991). The enlightened eye. New York: MacMillan.Eisner, E. (2003). Giving students what they need. Educational Leadership, 61(1), 23- 28Epstein, J. L., & Van Voorhis, F. L.(2001). More than minutes: Teachers’ roles in designing homework. Educational Psychologist, 36(3), 181-193.Hendricks, C. (2009). Improving schools through action research: A comprehensive guide for educators. Upper Saddle River, NJ: PearsonHess, M. A. (1999). Although some voice doubts, advocates say differentiated instruction can raise bar for all learners. Retrieved from , E., & Milgram, R. (2000). Homework: Motivation and learning preference. Westport, CT: Greenwood Press.Kinchloe, J., & McLaren, P. (1998) Rethinking critical theory and qualitative research. In N. Denzin & Y. Lincoln (Eds.), The landscape of qualitative research: Theories and issues (pp. 260-299). Thousand Oaks, CA: Sage Publications.Kralovec, E., & Buell, J. (2000). The end of homework: How homework disrupts families, overburdens children and limits learning. Boston: Beacon Press.LaGrange College Education Department . (2008). The conceptual framework. Lagrange, GA: Lagrange College.Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA: ASCD.Popham, W. (2008). Classroom assessment: What teachers need to know. Boston: Pearson Education, Inc.Powell, K., & Kalina, C. (2009). Cognitive and social constructivism: Developing tools for an effective classroom. Education, 130(2), 241-250.Rosenbaum, J. (2004, Spring). It’s time to tell the kids: If you don’t do well in high school, you won’t do well in college (or on the Job). American Educator. Retrieved from , N. (2010). Statistics for people who (think they) hate statistics: Excel 2007 2nd edition. Thousand Oaks, CA: SAGE Publications, IncSimplicio, J. (2005, Fall). Homework in the 21ST Century: The antiquated and ineffectual implementation of a time honored educational strategy. Education. 126, 138-142Tomlinson, C. A. (1999). Mapping a route toward differentiated instruction. Personalized Learning, 57(1), 12-16. Tomlinson, C. A. (2000). What is differentiated instruction? Retrieved from , C. (2003). Fulfilling the promise of the differentiated classroom. Alexandria, VI: Association for Supervision and Curriculum Development.Tomlinson, C. A. (2005). Differentiating Instruction: Why Bother? Middle Ground, 9(1), 12-14. Tomlinson, C., & Allan, S. (2000). Leadership for differentiating schools and classrooms. Alexandria, VA: Association for Supervision and Curriculum DevelopmentTomlinson, C. A., Brighton, C., Hertberg, H., Callahan, C. M., Moon, T. R., Brimijoin, K., et al. (2003). Differentiating instruction in response to student readiness, interest, and learning profile in academically diverse classrooms: A review of literature. Journal for the Education of the Gifted, 27(2/3), 119-145. Trautwein, U., Ludtke, O., Schnyder, I.,& Niggli, A. (2006). Predicting homework effort: Support for a domain-specific, multilevel homework model. Journal of Educational Psychology, 101 (1), 176-189.Vatterott, C. (2009). Rethinking homework: Best practices that support diverse needs. Alexandria, VI: Association for Supervision and Curriculum Development. Willingham, D. (2002, Summer). Allocating student study time, American Educator. Retrieved from http: pubs-reports/american_educator/ authors5.html Xu, J (2005). Purposes for doing homework reported by middle and high school students. The Journal of Education Research, 99 (1), 46-55.Appendix AInstructional PlanKeck’s 7th Grade Math, Unit 6: Values That VaryEstablished Goals (Standards):M7A3. Students will understand relationships between two variables.a. Plot points on a coordinate plane.b. Represent, describe, and analyze relations from tables, graphs, and formulas.c. Describe how change in one variable affects the other variable.d. Describe patterns in the graphs of proportional relationships, both direct (y=kx) and inverse (y=k/x).M7P5. Students will represent mathematics in multiple ways. a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical phenomena Enduring Understanding(s):Students will understand that…? Double number lines, models and manipulatives are helpful in recognizing and describing proportional relationships.? The equation y = kx describes a proportional relationship in which y varies directly as x.? The equation y = k/x describes a proportional relationship in which y varies inversely as x.? Proportional relationships can be represented using words, rules, tables and graphs.? Many problems encountered in everyday life can be solved using proportionsEssential Question(s):? How can I tell the difference between an inverse proportion and a direct proportion?? In an inverse proportion, how do quantities vary in relation to each other?? How can I decide if data varies directly or inversely?? In what real world situations can I find direct and inverse variation?? How can I determine the constant of proportionality in a proportional relationship by looking at a table, graph, orequation?Students will know… Students will be able to…draw pictures and use manipulatives to demonstrate a conceptual understanding of proportion; ? solve problems using proportional reasoning; ? represent and recognize direct proportions and inverse proportions graphically, numerically, and symbolically; ? determine and interpret the constant of proportionality in direct and inverse relationships; and ? explain how a change in one variable affects another variable. Stage 2: Assessment EvidencePerformance Task(s)Name that graph Surprise Birthday PartyCulminating Task: Decorating for the DanceOther Evidence: pre-assessment and post-assessment.Checkpoint quizzes along the wayStage 3: Learning PlanDuration: 3 weeksTechnology: Smartboard and student computersLearning Activities:Pre-assessment/ VocabularyRead “And the Doorbell Rang” Intro activityDetermining from a table, graph and an equation the characteristics of a direct relationshipGroup practice: 10 examples determining the characteristics with group of 4Quiz on direct variationMini-lesson: inverse relationship characteristicsLearning Task: Surprise Birthday Begin the name that graph activityQuiz on inverse variationFinish name that graph activityCreate variations flipbookCompare and contrast two types of tables, graph, and equations Cumulative task: Decorating for the DanceFinish and present dance tasks Post testAccommodationsSeveral of the assignments will be tieredFlex grouping Quiz retakes until students have shown masteryDifferentiation based upon student choiceAppendix BInstructional Plan Evaluation RubricKECK?4321CommentsStandards/ Learning ObjectivesThe learning objectives relate to the standards and reflect higher order thinking.The learning objectives relate to the standards.Contains both standards and learning objectives, but the objectives do not necessarily relate to the standards.Applicable standards are listed in the plan.Essential QuestionsThe essential questions correlate with the given standards, are open ended, and tie the content to real-world applicationThe essential questions correlate with the given standards. EQs are open ended.The essential questions correlate with the given standards, but have very specific answers.The essential questions are given but do not apply to the listed standards.Learning ActivitiesThe learning plan is mostly student centric. The activities are directly related to the elements of the unit.The learning activities are mostly student centric. The activities are mostly related to the elements of the unit.The learning activities are somewhat student centric and somewhat related to the elements of the unit. The learning activities are very teacher centric and do not seem to be related to the elements of the unit.AssessmentPracticesAssessment is well balanced and reflects higher order thinkingAssessment is well balancedStudent assessment practices are not balancedThere is no evidence of effective assessment practicesWhat seems to work well in this instructional plan? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________How could this plan be improved? ________________________________________________________________________________________________________________________________________________________________________________________________________________________Appendix CUnit 6 DiagnosticName _______________________ Date _______________ Class Period _________M7A3dDetermine if the following equations represent direct variation, inverse variation, or neither. Identify the constant (k).1. x + 4 = y2. xy = 103. 4x + y = 04. x = 3y5. y = 76. 4x + 3y = 12Tell whether the table represents direct variation, inverse variation, or neither. Identify the constant (k).x1234y5678 7. K= _______ _____________ x23412y6431 8. K =_______ ______________x4567y8101214 9. K=________ ______________x2468y-2-4-6-810. K=________ ______________11. If y varies directly with x, and y = 2 when x = 8, what is the value of y when x = 5?12. If y = 4 and x = 5, using inverse variation, what is the value of y when x = 2?13. If y = 50 and x = 10, what is the value of y when x = 8? Use direct variation to solve.14. Ashley waters 25 plants in 5 minutes. At this same rate, how many plants can he water in 15 minutes?15. Would the following graph represent direct variation, inverse variation, or neither?Bonus Question:In the following equation: 2x +y = 6, what does the 6 do to the graph?________________________________________________________________________________________________________________________________Appendix DStudent Homework SurveyThis survey is to simply provide some information about your homework habits and attitude. Please be honest in your responses. No one will know your responses because this survey is anonymous. Please do not write your name. Place an X next to the best answer that describes you. Doing math homework allows me to continue to learn about things that interest me.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___Strongly disagreeI often copy math homework from others.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeI often do my math homework during homeroom or breaks at school.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeI often write down random answers on the homework in order to earn the credit.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeI work hard on my math homework every time it is assigned.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeI don’t learn much from our math homework.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeWhen I am trying to do my math homework, I often feel completely lost.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeMy math homework takes a lot of time.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeMy math homework helps me better understand what was taught in class.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ Strongly disagreeI wish my math homework was more interesting.____ Strongly Agree___ Agree___ Slightly Agree___ Disagree___ StronglydisgreeAppendix EReflective Journal QuestionsWhat were three main things I learned from this session?What did we not cover that I expected we should?What was new or surprising to me?What have I changed my mind about, as a result of this session?One thing I learned in this session that I may be able to use in the future is…..I am still unsure about….Ideas for action, based on this session….What I most liked about this session was…..What I most disliked about this session was…..Miscellaneous interesting facts I learned in this session….. ................
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