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DIFFERIENTATING HOMEWORK AND ITS EFFECTS ON ACHIEVEMENT: A CASE STUDY OF TWO CLASSES

Except 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 Keck

Certificate of Approval:

_____________________________ ______________________________Donald R. Livingston, Ed. D. Sharon Livingston, Ph. D.Thesis Co-Chair Thesis Co-ChairEducation Department Education Department

Differentiating Homework ii

DIFFERIENTATING HOMEWORK AND ITS EFFECTS ON ACHIEVEMENT: A CASE STUDY OF TWO CLASSES

A thesis submitted

by

Amanda E Keck

to

Lagrange College

in partial fulfillment of

the requirement for the

degree of

MASTER OF EDUCATION

in

Curriculum and Instruction

Lagrange, Georgia

July 26, 2011

Differentiating Homework iii

Abstract

This 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.

Differentiating Homework iv

Table of Contents

Abstract..............................................................................................................iii

Table of Contents...............................................................................................iv

List of Tables.......................................................................................................v

Chapter 1: Introduction......................................................................................1Statement of the Problem..........................................................................1Significance of the Problem.......................................................................2Theoretical and Conceptual Frameworks..................................................2Focus Questions........................................................................................5

Overview of Methodology..........................................................................5Human as Researcher...............................................................................6

Chapter 2: Review of the Literature...................................................................7History of Homework……..........................................................................7Homework Through-out the Grade Levels.................................................8

Different Opinions on Homework………....................................................9Characteristics of Helpful Homework........................................................10

Differentiation……………..........................................................................12Student Perspectives and Motivation........................................................14

Chapter 3: Methodology...................................................................................16Research Design......................................................................................16Setting......................................................................................................16

Subjects and Participants……..................................................................17Procedures and Data Collection Methods................................................18

Validity, Reliability, Dependability and Bias ...........................................20Analysis of Data.......................................................................................22

Chapter 4: Results.............................................................................................25

Chapter 5: Analysis and Discussion of Results..................................................33 Analysis..................................................................................................33 Discussion...............................................................................................37 Implications..............................................................................................39 Impact on Student Learning.....................................................................40 Recommendations for Future Research..................................................40

References...........................................................................................................43

Appendixes..........................................................................................................46

Differentiating Homework v

List of Tables

Table 3.1 Data Shell……………………………………………………………………..18

Table 4.1 Independent T-Test Comparing Pre-Tests…………………………..………...26

Table 4.2 Dependent T-Test for the Control Group………………………..……………27

Table 4.3 Dependent T-Test for Treatment Group …………………………..……….....28

Table 4.4 Independent T-Test for Post-Tests………………………………..…………...29

Table 4.5 Chi Square for Post Student Survey……..……………………..…………..…30

Differentiating Homework 1

CHAPTER ONE: INTRODUCTION

Statement of the Problem

One 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 Problem

Accepted 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 Frameworks

This 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 Questions

In 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:

1. What differentiated assignments can be created to promote student

engagement and achievement?

2. How do differentiated homework assignments increase mathematics test

scores as compared to more traditional assignments?

3. What were the students’ attitudes about the differentiated homework?

Overview of Methodology

The 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 Researcher

I 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 REVIEW

History of Homework

Homework, 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 School

The 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 Homework

Data 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 homework

Regardless 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.

Differentiation

Experienced 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 Motivation

A 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: METHODOLOGY

Research Design

Action 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.

Setting

This 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 Participants

Students 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 Methods

According 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 Shell

Focus Questions

Literature Sources

Data Sources

Why 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 rubric

Coded for themes: ReoccurringDominantEmerging

Coded for themes aligned with focus question

How 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 Test Shows difference between 2 groups and within groupsIt was base line data and then showed the results of implementing the instrument.

Descriptive and Inferential Statistics

dependent t test within groups

Independent t test between groups

Effect size calculations

Does 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 rubric

Use of prompt questions reward daily student engagement with lessons

As observations are made, I was able to determine which strategies work best for the students

Coded for themes aligned with focus questionChi SquareCronbach’s alpha


The 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 Bias

The 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: RESULTS

The 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 Scores

t-Test: Two-Sample Assuming Unequal Variances

Control Treatment

Mean 21.74118.5769230

8

Variance 94.123102.093846

2Observations 27.000 26Hypothesized Mean Difference 0.000Df 51.000t Stat 1.162P(T<=t) one-tail 0.125t Critical one-tail 1.675P(T<=t) two-tail 0.251t Critical two-tail 2.008


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

Pre postMean 21.741 72.630Variance 94.123 201.704Observations 27.000 27.000Pearson Correlation 0.143Hypothesized Mean Difference 0.000Df 26.000t Stat -16.511P(T<=t) one-tail 0.000t Critical one-tail 1.706P(T<=t) two-tail 0.000t Critical two-tail 2.056

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 Treatment

t-Test: Paired Two Sample for Means

Pre postMean 18.577 67.692Variance 102.094 183.182Observations 26.000 26.000Pearson Correlation 0.284Hypothesized Mean Difference 0.000Df 25.000t Stat -17.381P(T<=t) one-tail 0.000t Critical one-tail 1.708P(T<=t) two-tail 0.000t Critical two-tail 2.060

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-Tests

t-Test: Two-Sample Assuming Unequal Variances

Control TreatmentMean 72.630 67.69230769Variance 201.704 183.1815385Observations 27.000 26Hypothesized Mean Difference 0.000Df 51.000t Stat 1.296P(T<=t) one-tail 0.100t Critical one-tail 1.675P(T<=t) two-tail 0.201t Critical two-tail 2.008

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 Surveys

Table 4.5: Chi Square

n=44χ²

(Treatment)χ²

(control)Item 1: Doing math homework allows me to continue to learn about things that interest me. 7.56 5.45Item 2: I often copy math homework from others. 6.44 4.74Item 3: I often do my math homework during homeroom or breaks at school. 1.5 8.78Item 4: I often write down random answers on the homework in order to just earn credit. 3.72 5.41Item 5: I work hard on my math homework every time it is assigned. 7.56 6.85Item 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. 7.06 9.85Item 8: My math homework takes a lot of time. 6.5 9.03Item 9: My math homework helps me better understand what was taught in class. 9.28 9.11Item 10: I wish my math homework was more interesting. 12.61* 22.45**** = p < .05, ** = p < .01, *** = p < .001

The 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 RESULTS


Analysis

This 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).

Discussion

This 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.”

Implications

This 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 Learning

The 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 Research

When 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.


References

Bempechat, J. (2004). The motivational benefits of homework: A social-cognitive

perspective. Theory into Practice, 43(3), 189-196.

Best, J. W. & Kahn, J. V. (2003). Research in Education. Boston: Library of. Congress

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Appendix A

Instructional Plan

Keck’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 proportions

Essential 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 Evidence

Performance Task(s)Name that graphSurprise Birthday Party

Culminating Task:Decorating for the Dance

Other Evidence:

pre-assessment and post-assessment.

Checkpoint quizzes along the way

Stage 3: Learning Plan


Duration: 3 weeksTechnology: Smartboard and student computersLearning Activities:1.Pre-assessment/ Vocabulary2. Read “And the Doorbell Rang” Intro activity3.Determining from a table, graph and an equation the characteristics of a

direct relationship4.Group practice: 10 examples determining the characteristics with group

of 45.Quiz on direct variation6.Mini-lesson: inverse relationship characteristics7.Learning Task: Surprise Birthday8. Begin the name that graph activity9.Quiz on inverse variation10. Finish name that graph activity11. Create variations flipbook12. Compare and contrast two types of tables, graph, and equations13. Cumulative task: Decorating for the Dance14. Finish and present dance tasks15. Post test

Accommodations

1. Several of the assignments will be tiered2. Flex grouping3. Quiz retakes until students have shown mastery4. Differentiation based upon student choice


Appendix B

Instructional Plan Evaluation Rubric

KECK 4 3 2 1 Comments

Standards/ Learning Objectives

The 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 Questions

The essential questions correlate with the given standards, are open ended, and tie the content to real-world application

The 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 Activities The 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.

Assessment

Practices

Assessment is well balanced and reflects higher order thinking

Assessment is well balanced

Student assessment practices are not balanced

There is no evidence of effective assessment practices

What seems to work well in this instructional plan? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


How could this plan be improved? ________________________________________________________________________________________________________________________________________________________________________________________________________________________


Appendix C

Unit 6 Diagnostic

Name _______________________ Date _______________ Class Period _________M7A3dDetermine if the following equations represent direct variation, inverse variation, or neither. Identify the constant (k).1. x + 4 = y 2. xy = 103. 4x + y = 0 4. x = 3y5. y = 7 6. 4x + 3y = 12Tell whether the table represents direct variation, inverse variation, or neither. Identify the constant (k).

7. K= _______ _____________

8. K =_______ ______________

9. K=________ ______________

10. 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?________________________________________________________________________________________________________________________________

x 1 2 3 4y 5 6 7 8

x 2 3 4 12y 6 4 3 1

x 4 5 6 7y 8 10 12 14

x 2 4 6 8y -2 -4 -6 -8

http://images.google.com/imgres?imgurl=http://www.staff.vu.edu.au/mcaonline/units/graphs/imagesgraph/graph5.gif&imgrefurl=http://www.staff.vu.edu.au/mcaonline/units/graphs/linear.html&usg=__c1LxAUHy8sNsii9LNBu-vieCIqA=&h=322&w=300&sz=4&hl=en&start=26&um=1&itbs=1&tbnid=OcdRR2ELBZANGM:&tbnh=118&tbnw=110&prev=/images?q=linear+graph&start=20&um=1&hl=en&safe=strict&sa=N&rls=com.microsoft:en-us:IE-SearchBox&rlz=1I7SUNA_en&ndsp=20&tbs=isch:1


Appendix D

Student Homework Survey

This 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.

1. Doing math homework allows me to continue to learn about things that interest me.

____ Strongly Agree ___ Agree ___ Slightly Agree ___ Disagree ___Strongly disagree

2. I often copy math homework from others.

____ Strongly Agree ___ Agree ___ Slightly Agree ___ Disagree ___ Strongly disagree

3. I often do my math homework during homeroom or breaks at school.


4. I often write down random answers on the homework in order to earn the credit.


5. I work hard on my math homework every time it is assigned.


6. I don’t learn much from our math homework.


7. When I am trying to do my math homework, I often feel completely lost.


8. My math homework takes a lot of time.


9. My math homework helps me better understand what was taught in class.



10. I wish my math homework was more interesting.

____ Strongly Agree ___ Agree ___ Slightly Agree ___ Disagree ___ Stronglydisgree

Appendix EReflective Journal Questions

1. What were three main things I learned from this session?2. What did we not cover that I expected we should?3. What was new or surprising to me?4. What have I changed my mind about, as a result of this session?5. One thing I learned in this session that I may be able to use in the future is…..6. I am still unsure about….7. Ideas for action, based on this session….8. What I most liked about this session was…..9. What I most disliked about this session was…..10. Miscellaneous interesting facts I learned in this session…..

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