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.
Thesis Co-Chair
Education Department
______________________________
Sharon Livingston, Ph. D.
Thesis Co-Chair
Education Department
Differentiating Homework
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
ii
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
Table of Contents
Abstract..............................................................................................................iii
Table of Contents...............................................................................................iv
List of Tables.......................................................................................................v
Chapter 1: Introduction......................................................................................1
Statement of the Problem..........................................................................1
Significance of the Problem.......................................................................2
Theoretical and Conceptual Frameworks..................................................2
Focus Questions........................................................................................5
Overview of Methodology..........................................................................5
Human as Researcher...............................................................................6
Chapter 2: Review of the Literature...................................................................7
History of Homework……..........................................................................7
Homework Through-out the Grade Levels.................................................8
Different Opinions on Homework………....................................................9
Characteristics of Helpful Homework........................................................10
Differentiation……………..........................................................................12
Student Perspectives and Motivation........................................................14
Chapter 3: Methodology...................................................................................16
Research Design......................................................................................16
Setting......................................................................................................16
Subjects and Participants……..................................................................17
Procedures and Data Collection Methods................................................18
Validity, Reliability, Dependability and Bias ...........................................20
Analysis 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
iv
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).
Differentiating Homework
2
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,
Differentiating Homework
3
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
Differentiating Homework
4
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.
Differentiating Homework
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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.
Differentiating Homework
6
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.
Differentiating Homework
7
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
Differentiating Homework
8
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).
Differentiating Homework
9
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
Differentiating Homework
10
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:
Differentiating Homework
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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
Differentiating Homework
12
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-sizefits 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
Differentiating Homework
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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.
Differentiating Homework
14
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
Differentiating Homework
15
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.
Differentiating Homework
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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
Differentiating Homework
17
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.
Differentiating Homework
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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
What
differentiated
assignments can
be created to
promote student
engagement and
achievement?
How do
differentiated
homework
assignments
increase test
scores as
compared to
more traditional
homework
assignments?
Does the use of
differentiated
assignments
make homework
more meaningful,
engaging and
significant to
student
achievement?
Literature
Sources
Dodge, J.
(2005)
Tomlinson &
Mctighe
(2006)
Cooper,
Robinson, &
Patall (2006)
Data
Sources
Tomlinson, C.
(2005).
How are data
analyzed?
Instructional
plan and
rubric
Coded for themes:
Reoccurring
Dominant
Emerging
Coded for themes
aligned with focus
question
Pre-Post Test
Shows difference
between 2 groups
and within groups
It was base line data
and then showed the
results of
implementing the
instrument.
Descriptive and
Inferential
Statistics
Use of prompt
questions reward
daily student
engagement with
lessons
Coded for themes
aligned with focus
question
Chi Square
Cronbach’s alpha
Cooper,
Lyndsey, Nye
& Greathouse
(1998)
Vatterott, C.
(2009).
Why do these
data answer the
question?
Student
Survey
Reflective
Journal?
Trautwein, U.,
et al. (2006)
Instructional
plan and
rubric
As observations are
made, I was able to
determine which
strategies work best
for the students
dependent t test
within groups
Independent t test
between groups
Effect size
calculations
Differentiating Homework
19
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).
Differentiating Homework
20
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/posttest 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
Differentiating Homework
21
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
Differentiating Homework
22
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.
Differentiating Homework
23
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.
Differentiating Homework
24
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.
Differentiating Homework
25
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.
Differentiating Homework
26
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
Mean
Variance
Observations
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Control Treatment
21.741 18.57692308
94.123 102.0938462
27.000
26
0.000
51.000
1.162
0.125
1.675
0.251
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.
Differentiating Homework
27
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
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Pre
21.741
94.123
27.000
0.143
0.000
26.000
-16.511
0.000
1.706
0.000
2.056
post
72.630
201.704
27.000
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 testretest 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.
Differentiating Homework
28
Table 4.3 Pre/Post Treatment
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Pre
18.577
102.094
26.000
0.284
0.000
25.000
-17.381
0.000
1.708
0.000
2.060
post
67.692
183.182
26.000
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 testretest indicator of reliability. There were significant differences present between the pretest 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.
Differentiating Homework
29
Table 4.4 Post-Tests
t-Test: Two-Sample Assuming Unequal
Variances
Mean
Variance
Observations
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Control
72.630
201.704
27.000
0.000
51.000
1.296
0.100
1.675
0.201
2.008
Treatment
67.69230769
183.1815385
26
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
Differentiating Homework
30
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 fortyfour 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
χ²
χ²
n=44
(Treatment)
(control)
Item 1: Doing math homework allows me to continue to learn about things that interest
me.
7.56
5.45
Item 2: I often copy math homework from others.
6.44
4.74
Item 3: I often do my math homework during homeroom or breaks at school.
Item 4: I often write down random answers on the homework in order to just earn
credit.
1.5
8.78
3.72
5.41
Item 5: I work hard on my math homework every time it is assigned.
7.56
6.85
Item 6: I don’t learn much from our math homework.
23.67***
3.93
Item 7: When I am trying to do my math homework, I often feel completely lost.
7.06
9.85
Item 8: My math homework takes a lot of time.
6.5
9.03
Item 9: My math homework helps me better understand what was taught in class.
9.28
9.11
Item 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
Differentiating Homework
31
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
Differentiating Homework
32
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.
Differentiating Homework
33
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 prepost 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
Differentiating Homework
34
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.
Differentiating Homework
35
Finally, the two group’s post-tests scores were compared using an independent ttest. 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 onehalf 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).
Differentiating Homework
36
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
Differentiating Homework
37
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
Differentiating Homework
38
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
Differentiating Homework
39
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.
Differentiating Homework
40
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
Differentiating Homework
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.
41
Differentiating Homework
42
References
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perspective. Theory into Practice, 43(3), 189-196.
Best, J. W. & Kahn, J. V. (2003). Research in Education. Boston: Library of. Congress
Cataloguing-in-Publication data.
Bruce, S. (2010). Action research in special education: An inquiry approach for effective
teaching and learning. New York: Teachers College Press.
Buell, J. (2004). Closing the book on homework: Enhancing public education and
freeing family time. Philadelphia: Temple University Press.
Cooper, H., Lindsay, J., Nye, B., & Greathouse, S. (1998). Relationships among attitudes
about homework, amount of homework assigned and completed and student
achievement. Journal of Educational Psychology, 90(1), 70-83.
Cooper, H., Robinson, J. C., & Patall, E. A. (2006). Does homework improve academic
achievement? A synthesis of research, 1987-2003. Review of Educational
Research, 76, 1-62.
Cooper, H., & Valentine, J. C. (2001). Using research to answer practical questions about
homework. Educational Psychologist, 36(3), 143-153.
Connors, N. (1992). 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), 2328
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Epstein, 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: Pearson
Hess, M. A. (1999). Although some voice doubts, advocates say differentiated instruction
can raise bar for all learners. Retrieved from
http://www.weac.org/Home/Parents_Community/differ.aspx
Hong, E., & Milgram, R. (2000). Homework: Motivation and learning preference.
Westport, CT: Greenwood Press.
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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.
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works: Research-based strategies for increasing student achievement.
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Pearson Education, Inc.
Powell, K., & Kalina, C. (2009). Cognitive and social constructivism: Developing tools
for an effective classroom. Education, 130(2), 241-250.
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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.
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Differentiating Homework
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Appendix A
Instructional Plan
Keck’s 7th Grade Math, Unit 6: Values That Vary
Established 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):
Essential Question(s):
Students will understand that…
Double number lines, models and
manipulatives are helpful in recognizing
and describing proportional relationships.
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
The equation y = kx describes a
proportional relationship in which y varies or inversely?
directly as x.
In what real world situations can I find
The equation y = k/x describes a
direct and inverse variation?
proportional relationship in which y varies
How can I determine the constant of
inversely as x.
proportionality in a proportional
Proportional relationships can be
relationship by looking at a table, graph, or
represented using words, rules, tables and equation?
graphs.
Many problems encountered in everyday
life can be solved using proportions
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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 graph
Surprise Birthday Party
Other Evidence:
pre-assessment and post-assessment.
Checkpoint quizzes along the way
Culminating Task:
Decorating for the Dance
Stage 3: Learning Plan
47
Differentiating Homework
Duration: 3 weeks
Technology: Smartboard and student computers
Learning Activities:
1. Pre-assessment/ Vocabulary
2. Read “And the Doorbell Rang” Intro activity
3. Determining from a table, graph and an equation the characteristics of a
direct relationship
4. Group practice: 10 examples determining the characteristics with group
of 4
5. Quiz on direct variation
6. Mini-lesson: inverse relationship characteristics
7. Learning Task: Surprise Birthday
8. Begin the name that graph activity
9. Quiz on inverse variation
10. Finish name that graph activity
11. Create variations flipbook
12. Compare and contrast two types of tables, graph, and equations
13.
Cumulative task: Decorating for the Dance
14. Finish and present dance tasks
15.
Post test
Accommodations
1.
2.
3.
4.
Several of the assignments will be tiered
Flex grouping
Quiz retakes until students have shown mastery
Differentiation based upon student choice
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Appendix B
Instructional Plan Evaluation Rubric
KECK
4
3
The learning objectives
The learning objectives
relate to the standards and relate to the standards.
reflect higher order thinking.
2
Contains both standards
and learning objectives,
but the objectives do not
necessarily relate to the
standards.
1
Comments
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 realworld application
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 The learning activities are The learning activities are
mostly student centric. The somewhat student centric
student centric.
activities are mostly related and somewhat related to
The activities are directly
to the elements of the unit. the elements of the unit.
related to the elements of the
unit.
Assessment
Assessment is well balanced Assessment is well
and reflects higher order
balanced
thinking
Standards/
Learning
Objectives
Practices
The essential questions
correlate with the given
standards. EQs are open
ended.
The learning activities are
very teacher centric and
do not seem to be related
to the elements of the
unit.
Student assessment
There is no evidence of
practices are not balanced effective assessment
practices
What seems to work well in this instructional plan?
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
How could this plan be improved?
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
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Appendix C
Unit 6 Diagnostic
Name _______________________ Date _______________ Class Period _________
M7A3d
Determine if the following equations represent direct variation, inverse variation, or
neither. Identify the constant (k).
1. x + 4 = y
2. xy = 10
3. 4x + y = 0
4. x = 3y
5. y = 7
6. 4x + 3y = 12
Tell whether the table represents direct variation, inverse variation, or neither. Identify
the constant (k).
7. K= _______
_____________
12
1
8. K =_______
______________
6
12
7
14
9. K=________
______________
6
-6
8
-8
10. K=________
______________
x
y
1
5
2
6
3
7
4
8
x
y
2
6
3
4
4
3
x
y
4
8
5
10
x
y
2
-2
4
-4
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?
________________________________________________________________
________________________________________________________________
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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.
____ Strongly Agree ___ Agree
___ Slightly Agree ___ Disagree
___ Strongly
disagree
4. I often write down random answers on the homework in order to earn the credit.
____ Strongly Agree ___ Agree
___ Slightly Agree ___ Disagree
___ Strongly
disagree
5. I work hard on my math homework every time it is assigned.
____ Strongly Agree ___ Agree
___ Slightly Agree ___ Disagree
___ Strongly
disagree
6. I don’t learn much from our math homework.
____ Strongly Agree ___ Agree
___ Slightly Agree
___ Disagree
___ Strongly
disagree
7. When I am trying to do my math homework, I often feel completely lost.
____ Strongly Agree ___ Agree
___ Slightly Agree ___ Disagree
___ Strongly
disagree
8. My math homework takes a lot of time.
____ Strongly Agree ___ Agree
___ Slightly
Agree
___ Disagree
___ Strongly
disagree
9. My math homework helps me better understand what was taught in class.
____ Strongly Agree ___ Agree
___ Slightly Agree ___ Disagree
___ Strongly
disagree
10. I wish my math homework was more interesting.
____ Strongly Agree ___ Agree
___ Slightly Agree
___ Disagree
___ Stronglydisgree
Differentiating Homework
Appendix E
Reflective 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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