THE AFFECT OF SCHOOL STRUCTURE ON STUDENT ACHIEVEMENT IN
MATHEMATICS
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 Thesis Chair. This thesis does not include
proprietary or classified information.
Lynda Leigh Bingham
Certificate of Approval:
_____________________________
Donald R. Livingston, Ed.D.
Thesis Co-Chair
Education Department
_____________________________
Sharon M. Livingston, Ph.D.
Thesis Co-Chair
Education Department
ii
THE AFFECT OF SCHOOL STRUCTURE ON STUDENT ACHIEVEMENT
A thesis submitted
by
Lynda Leigh Bingham
to
LaGrange College
in partial fulfillment of
the requirement for the
degree of
MASTER OF EDUCATION
in
Curriculum and Instruction
Lagrange, Georgia
May 12, 2011
iii
Abstract
This action research study examined how school structure (self-contained v.
departmentalized) and teacher strengths play a role in student achievement in
mathematics. The study compared 3rd grade CRCT data from two similar Title I schools,
School B (departmentalized) and School A (non-departmentalized). Participants
implemented a mathematics instructional plan at School A (non-departmentalized). Both
qualitative and quantitative data were collected through the use of rubrics, interviews, pre
and post tests, and reflective journals. The quantitative data collected from the pre-post
test was calculated using dependent t-test and an ANOVA. The results showed that
teacher strengths do play a role in student achievement. The CRCT data comparison
showed a higher meets and exceeds percentage for the non-departmentalized School A.
iv
Table of Contents
Abstract……………………….……………………………………………………….….iii
Table of Contents……………………….…………………………………………..…….iv
List of Tables..………………………………………………………………………...…..v
Chapter One: Introduction….……………………………………………………………..1
Statement of the Problem…………………………………………………….……1
Significance of the Problem……………………………………………………….1
Theoretical and Conceptual Frameworks..………………………………………..2
Focus Questions…………………………………………………………………...3
Overview of Methodology………………………………………………………...4
Human as Researcher……………………………………………………………...5
Chapter Two: Review of the Literature…………………………………………………...6
School Structure and the Meaningful Learning Environment……………….……6
Teacher Knowledge and Strengths Affect on Student Outcome…………….……9
Teacher Instructional Efficacy……………………………………………….…. 12
Chapter Three: Methodology…………………………………………………………….14
Research Design………………………………………………………………….14
Setting……………………………………………………………………………15
Subjects and Participants………………………………………………………..15
Procedures and Data Collection Methods………………………………………..16
Validity, Reliability, Dependability, and Bias …………………………………..19
Analysis of Data………………………………………………………………….21
Chapter Four: Results……………………………………………………………………24
Chapter Five: Analysis and Discussion of Results………………………………………33
Analysis………………………………………………………………………….33
Discussion………………………………………………………………………..38
Implications………………………………………………………………………39
Impact on Student Learning……………………………………………………...40
Recommendations for Future Research………………………………………….41
References………………………………………………………………………………42
Appendixes………………………………………………………………………………46
v
List of Tables
Tables
Table 3.1
Data Shell………………………………………………………………17
Table 4.1
t-Test No Treatment-Z..………………………………………..………26
Table 4.2
t-Test Treatment-X…...…………………………………………………27
Table 4.3
t-Test Treatment-Y…...…………………………………………………28
Table 4.4
ANOVA-Pre-Test………………………………………………………29
Table 4.5
ANOVA-Post-Test……………………………………………………..30
THE AFFECT OF SCHOOL STRUCTURE 1
CHAPTER ONE: INTRODUCTION
Statement of the Problem
A common issue in schools is the lack of instructional time allotted for
elementary teachers to implement in-depth, high quality lessons when teaching all
content areas on a daily basis. According to Morton and Dalton (2007), “There has long
been an interest in the use of school time as a means of increasing student achievement.
Prior research has focused on the amount of time allocated to instruction and how that
time is used” (p.1). Elementary teachers who plan and teach all content areas have only
enough time to skim the surface of concepts taught. The goal of this study was to
investigate the effects of how elementary teachers, departmentalizing by content area, can
improve student learning in mathematics.
Significance of the Problem
Due to a lack of in-depth, high quality lesson implementation, students are only
able to get the right answer on standardized testing, rather than internalizing and building
concrete knowledge. The No Child Left Behind [NCLB] legislation pressures states to
show massive gains and growth in standardized test performance each year. This
legislation directly affects each classroom across the nation. As a result, students are
rushed to learn new concepts. Then, whether students have had enough meaningful
learning time or not, the teacher must move on to the numerous other state standards,
resulting in students lacking the foundations of basic knowledge learned in elementary
school.
THE AFFECT OF SCHOOL STRUCTURE 2
Theoretical and Conceptual Frameworks
How do humans learn and acquire knowledge? A philosophy known as
constructivism theorizes about how humans develop knowledge. The constructivist
learning theory, as defined by Cannella and Reiff, is how “individuals create or construct
their own new understandings or knowledge through the interaction of what they already
know and believe and the ideas, events, and activities with which they come in
contact”(as cited by Abdal-Haqq, 1998, p.2). The belief under the constructivist learning
theory is that humans construct and develop their own knowledge through action. This
study directly relates to constructivism, in that it seeks to answer how school structure
influences students learning.
This research is also framed around the notion of enthusiastic engagement in
learning, which is Tenet One of the Lagrange College of Education Department’s (2010)
Conceptual Framework. The third cluster of Tenet One, along with Domain 2 of the
Georgia Framework for Teaching, demands that teachers have a superior knowledge of
how students learn and construct knowledge. This study intended to find the best school
structure method for allowing students to construct their learning and develop a deeper
understanding that is meaningful to the individual student. This study is also related to
Proposition 1 of the National Board for Professional Teaching Standards [NBPTS],
which emphasizes the importance of teachers’ commitment to students and learning.
This study directly relates to Proposition 1, in that, it was designed to investigate the
different school organizations and to procure which school structure is the most
successful in attaining the highest level of student achievement.
THE AFFECT OF SCHOOL STRUCTURE 3
Furthermore, this thesis is linked with creating successful learning environments
to encourage high student achievement and meaningful learning, which correlates to
Tenet Three of the Lagrange College of Education Department’s (2010) Conceptual
Framework, as well as Domain Three of the Georgia Framework for Teaching. Tenet
Three also requires collaboration amongst educators. In this study, educators will work
together to gather and analyze data collected from the two types of schools structure, as
well as use previous research as a guide to find which school structure enables higher
student achievement. Proposition Four in the NBPTS emphasizes the importance of
teachers thinking and reflecting on the practice of teaching and learning from experience.
The study will not only provide meaningful experience for those involved, it will demand
teachers to reflect on their current practices. As demonstrated, this study fully aligns with
standards at the college, state, and national level. The purpose and goal of the study was
to find effective teaching structures that improve the achievement levels in the students,
which closely aligns with the goals and missions of the college, the state, and the national
teaching association.
Focus Questions
There are a number of factors that affect student achievement. This thesis
explores the affects of departmentalization as a factor in student achievement in
mathematics. This study was designed and led by several critical questions.
1. Will an instructional plan designed to teach math content determine teacher
strengths and deficiencies along with the most effective school structure?
2. How do a teacher’s strengths and knowledge affect student outcome?
THE AFFECT OF SCHOOL STRUCTURE 4
3. What are the opinions and attitudes of administrators and third grade teachers
involved in this study, on the effectiveness of departmentalization?
Overview of Methodology
This action research study was designed to explore student achievement in third
grade at two comparable schools. When evaluating the two school populations, the
following factors were deemed closely similar: student enrollment, socio-economic
status, racial make-up, and number of Special Education and Early Intervention Program
students. The variable for this study was the type of school structure implemented and
the teacher teaching in their area of strength. School A used a more traditional school
structure, with self-contained classrooms, where children received all content area
instruction within the one classroom and the teachers do not have a choice on what
subjects they teach. School B used a more unconventional school structure for lower
elementary grades. Students at School B changed classrooms to receive each content
area instruction, where teachers were allowed to choose which subjects they teach based
on their preference and teaching strengths. Participants in the study include three third
grade teachers at School A. Both quantitative and qualitative data were collected from
this study. Archival CRCT data, as well as, pre and post test data from the mathematics
instructional plan were collected and analyzed using various statistical methods.
Qualitative data were collected using interviews with the third grade teachers at School
A, regarding the teacher’s opinions and attitudes of their teaching ability, in addition to
the reflective journal kept by the researcher. Using these data collected, the two school
structures were compared and analyzed regarding the effectiveness of student
achievement.
THE AFFECT OF SCHOOL STRUCTURE 5
Human as the Researcher
I have taught several years in a self-contained classroom where the students stay
with the teacher for all content areas. I am fully aware of the lack of time for students to
fully understand a concept before it is time to move on to the next state standard. I have
seen many students that have been able to answer the question correctly on a test, but do
not truly have a deep understanding of the concept. I hope to find that departmentalizing
each grade level is the answer to this predicament. I am hoping that departmentalizing
would allow teachers to have a maximum of two content areas to specialize in, which
would in turn allow them to develop lessons that are more meaningful and be able to
nurture a deeper student learning with the appropriate amount of time available.
THE AFFECT OF SCHOOL STRUCTURE 6
CHAPTER TWO: LITERATURE REVIEW
With the start of each new school year, schools begin to form new plans of action
to make improvement in weak areas. Often times these plans for improvement are
centered around creating a high quality learning environment with high quality teachers
along with improved standards based instruction (Beecher & Sweeney, 2008). The
school structure or school organization for each grade level is also frequently considered
when planning ways to improve student achievement. Over the past few decades, many
schools across the country have begun to try various school structures, in the search to
find the one that has the best student outcome. Mainly upper grade levels have
traditionally been departmentalized by subject, however, now grade levels as low as third
grade have begun to try less traditional teaching structures.
School Structure and the Meaningful Learning Environment
School structure has been largely debated since the beginning of the twentieth
century (McGrath & Rust, 2002). The debate centers around the advantages of
departmentalized and self-contained school structures and their effects on student
achievement, as well as other social implications. Prior research indicates the need for
the ongoing effort to find the most effective school structure since student achievement
may directly be affected by the type of school structure implemented. Both
departmentalized school structures and self-contained school structures may be found at
the elementary level. Yet, few of the studies have provided enough concrete evidence to
prove one school structure better than the other.
Several benefits of departmentalization include: increased student flexibility and
adaptability, teacher specialization, teacher retention, and easier transition to middle and
THE AFFECT OF SCHOOL STRUCTURE 7
high school (Chan & Jarman, 2004). When teachers specialize in one or two subject
areas, there is more of an opportunity for increased subject and curricular knowledge.
Teachers must have adequate understanding of the subject matter they are responsible for
teaching (Flick & Lederman 2003). With the vast amount of knowledge now available,
the major disadvantage for the self-contained classroom is that one teacher cannot know
enough to operate effectively in all subject areas. Departmentalization allows teachers to
maximize planning time and resources in addition to being proficient in one or two
content areas. According to McPartland (1987), the intentions behind the creation of
departmentalization is to allow teachers to be experts in a subject area, and produce
higher quality instruction, since they would only have to concentrate on preparing a
limited number of outstanding lessons each day that are offered to several different
classes. McPartland (1990) suggests that school structure can affect teachers’ efforts to
provide high-quality instruction and create positive teacher/student relations.
Departmentalization increases the opportunity for teachers to interact with more
students, which increases the opportunity for students to improve interpersonal skills
through adapting to different teaching styles. More students receive the added advantage
of having a teacher more qualified to teach a particular subject area. Furthermore,
adapting to this flexible school structure of changing classrooms and teachers, is crucial
in easing the transition to the middle and high school settings, where the need for the selfcontained school structure is minimized.
Not only does departmentalizing allow teachers to specialize their knowledge and
improve student interpersonal skills, it also provides each subject area with an equal
amount of time. In many schools, science and social studies are being pushed out of the
THE AFFECT OF SCHOOL STRUCTURE 8
daily schedule, as a result of these subjects not counting towards Annual Yearly Progress
[AYP]. By implementing a departmentalized school structure, each subject is allotted the
same amount of time, thus allowing students to receive a well-rounded education, rather
than solely tested content.
Besides the advantages to departmentalizing, there were a few disadvantages or
pitfalls to the less traditional school structure. Opponents to the less traditional idea of
school structure suggest that by departmentalizing, students lose the safe, secure feeling
of the self-contained classroom. Departmentalizing makes it difficult for teachers to get
to know students well, develop positive student-teacher relationships, create a caring and
supportive environment, and make curriculum connections through integration (Bryk,
Lee, & Smith, 1990; Legters, McDill, & McPartland 1993). Robert Canady and Michael
Rettig have conducted numerous studies and written multiple publications on aspects of
school structure, specifically block scheduling which closely relates to
departmentalization. Canady and Rettig (1995) suggest that by departmentalizing,
schooling becomes similar to an assembly line, depersonalizing the time spent with
students. Self-contained classrooms allow the teacher to really get to know the students’
strengths, weaknesses, and personalities, as they are with the group of students for almost
the entirety of the day; which may allow self-contained teachers to be better prepared to
create instructional time for their students (Irmsher, 1996; McGrath & Rust, 2002).
Another disadvantage to departmentalizing is the amount of time spent in
transition, as students move from classroom to classroom. McGrath and Rust (2002) felt
that self-contained students would perform higher academically because of more
instructional time with one teacher. Through their research, they discovered that the
THE AFFECT OF SCHOOL STRUCTURE 9
instructional minutes did not differ greatly, and the self-contained students did perform
higher in two academic areas.
Supporters of departmentalizing suggest that students are able to move more
frequently during the day in a departmentalized setting, which helps increase attention. A
connection between physical activity and academic performance has been explored
through several studies conducted by researcher Terrence Dwyer, suggesting that
movement supports success in school. His research found that movement improves
classroom behavior and academic performance (Dwyer, Sallis, Blizzard, Lazarus, &
Dean, 2001).
Teacher Strengths and Knowledge Affect on Student Outcome
If teaching were as simple as using the “one best way” to teach everything, it
would be considered more of a science. However, there isn't just “one best way” to teach
everything and that is why teaching is considered an art. If teaching meant simply
following a text book and using the “same size fits all” approach, then anyone could
teach. Long ago, teachers knew that individual needs, strengths and weaknesses must
drive instructional and assessment practice.
When Howard Gardner created the Multiple Intelligences theory, he shaped the
awareness of the fact that children come in their own individual packages and that no two
children learn the same way even though the curriculum may be the same (Gardner,
1991). This same knowledge applies to the teacher too. Various research points to the
remarkable fact that while teaching styles and approaches may differ, all great teachers
make the most of their natural strengths and talents.
THE AFFECT OF SCHOOL STRUCTURE 10
Research consistently shows that teachers have the greatest potential to influence
children's education. "The major research finding is that student achievement is related
to teacher competence in teaching," noted by Kemp and Hall (1992, p. 4). Proof from
teacher-effectiveness studies indicates that student engagement in learning is to be valued
above curriculum plans and materials. Research on teacher effectiveness has yielded a
wealth of understanding about the impact that teacher ability has on student growth.
According to Michael Schiro (2008), a researcher of teacher’s beliefs and
philosophies, under the scholar academic ideology, teachers should be knowledgeable
people. Schiro found that learning best occurs when the teacher clearly and accurately
presents knowledge which the student is to acquire. Teachers should have a thorough
understanding of the discipline they teach. Schiro also suggests that in order to promote
the highest academic achievement in students, teachers should earn academic degrees in
the subjects they teach. In order to implement standards and curriculum effectively,
school systems depend upon the work of expert teachers who understand the subject
matter they teach and have an organized body of knowledge readily available. For
example, how well teachers know mathematics is directly related to their ability: to use
instructional materials wisely, to continuously assess students’ progress, and to create and
implement meaningful lessons. The teacher’s aptitude and interest in a subject can
influence how the students will perform (Ackerlund, 1959).
Tak Cheung Chan and Delbert Jarman, two professors at Kennesaw State
University wrote an article that appeared in the September 2004 issue of Principal
magazine. Through their findings in literature, they concluded that elementary teachers
are expected to be a “jack-of-all-trades” who are masters of all content areas of the
THE AFFECT OF SCHOOL STRUCTURE 11
curriculum (Chan & Jarman, 2004). Richard Anderson conducted research in the East
Bruinswick public schools concerning teacher specialization in one or two subject areas.
Anderson found that the most commonly used elementary organization of self-contained
classes did not take into account that it is rare for a teacher to have extensive competence
in more than one or two subjects (Anderson, 1962).
Ackerlund (1959) also felt that although the self-contained school structure
maintains a better student-teacher relationship, it is difficult for the teacher to be
knowledgeable and prepared to teach all subjects. Ackerlund suggests that when a
teacher is teaching in a content area they are the most knowledgeable in, they are more
able to focus on other aspects of teaching, like applying creative insight to problems that
arise, as well as planning, evaluating, and monitoring their students. To investigate his
theory Ackerlund (1959) surveyed a large school district in Quakertown, Pennsylvania.
Teachers were asked about training in the areas of “knowledge of subject” and “methods
of teaching”. Responses showed that 109 teachers felt self-contained was the best
classroom organization and 122 felt that was it not. In grades K-2, many teachers
favored self-contained classroom, but in 3-5 grades teachers opposed self-contained
classes because of the higher demand of content knowledge. In Ackerlund’s (1959) study
is was revealed that out of 260 teachers surveyed, only four teacher considered
themselves well prepared to teach all subjects. The results show that there is an increased
need for departmentalization with the increase of content knowledge that a higher grade
level requires. Ackerlund’s study also displays a need for further exploration as to why
only four teachers felt prepared enough to teach all subjects.
THE AFFECT OF SCHOOL STRUCTURE 12
Teacher Instructional Efficacy
Since a teacher’s beliefs can have a significant influence on what teachers do in
their classroom, this action research study will explore how teachers feel about the
quality and success of their instruction in the classroom. A well-known education
theorist, Albert Bandura (1986), suggests that teacher instructional efficacy has to do with
a teacher’s perception of his or her own capabilities and effectiveness in a classroom, as
well as their perception of their ability to implement instruction that leads to the desired
outcomes of student engagement and learning. Teacher instructional efficacy plays a
significant role in knowledge development, and has been suggested by many researchers
to be strongly related to student achievement on standardized tests (Henson, 2001).
Robin Henson conducted a year long study in a large school district in the southwestern
United States to find out how collaboration in research affected teacher’s instructional
efficacy. Henson found that teachers who see themselves as capable of teaching certain
subjects challenge themselves and persist in their efforts to succeed, which, in turn,
influences their students.
Teacher instructional efficacy can assist a teacher in many meaningful educational
outcomes. When teachers have high instructional efficacy, they can directly influence
student achievement. Research reviewed by Muijs and Reynolds (2002), suggests that
students who have teachers with high efficacy, attain better scores on achievement tests
than students who are taught by teachers with low efficacy. Muijs and Reynolds (2002)
also suggest that low teacher efficacy has also been linked to low expectations of student
achievement.
THE AFFECT OF SCHOOL STRUCTURE 13
The purpose of this review of literature was to provide background information
that is essential for understanding this action research study. The focus questions
provided the structure for the basis of the literature review. The review of literature
examined school structure, teacher knowledge, and teacher instructional efficacy. While
there is a growing amount of research on school structure and teacher specialization, this
action research study seeks to fill in the research gaps and further our understanding of
teacher specialization.
As noted in the literature review, there were several advantages and disadvantages
related to departmentalizing that were discovered in prior research studies, however many
studies mentioned the lack of data to support departmentalization. Although selfcontained and departmentalized school organizations have been debated for many years,
research has still not proven that departmentalization will significantly improve academic
achievement in elementary schools. Findings in the literature provided a framework for
this action research study in examining school organization’s affect on student
achievement. As reviewed in the literature, some changes are in progress in order to
meet the needs of all students. There is a continued need for exploration between student
achievement and its relationship to the different organizational structures for the
elementary school students with an insight into teacher instructional efficacy.
THE AFFECT OF SCHOOL STRUCTURE 14
CHAPTER THREE: METHODOLOGY
The purpose of this chapter is to explain the methods used to complete the
action research study. As previously mentioned this study examined which
organizational structure, traditional (self-contained, one teacher for all academic subjects)
or departmentalized (each subject taught by a different teacher), had the greatest affect on
general third-grade students’ math achievement as measured by the Georgia CRCT.
Research Design
This was an action research study that encompassed the use of a variety of data
collection methods. According to Cher Hendricks (2009), the author of Improving
Schools Through Action Research, the purpose of action research is to allow inquiry,
discussion, and collaboration as components in the research process. Action research
searches to find answers/solutions to problems experienced in education (Hendricks,
2009). The authors of the article, Sustaining Teachers' Growth and Renewal through
Action Research, suggest that action research begins with a question or inquiry, then data
is gathered, next the data is analyzed with the goal of improving a component of the
educational practice (Gilles, Wilson, & Elias, 2010). This action research study began
with the inquiry of whether or not the type of school structure can affect student
achievement in mathematics. Next, an intricate mathematics instructional plan was
designed and data was collected and meticulously analyzed in order to promote growth
and awareness on the educational topic of departmentalization.
The researcher examined the archival data of two different classroom
organizational instruction techniques—traditional (self-contained, one teacher) and
departmentalized formats (each subject taught by a different teacher). For School B, a
THE AFFECT OF SCHOOL STRUCTURE 15
portion of this study was accomplished by analyzing the 2009 and 2010 CRCT
mathematical achievement data of the third-grade students to investigate the cause-andeffect relationships of the two different types of instructional techniques, as measured by
the Georgia CRCT. The second portion of this study involved three teachers from School
A, using the traditional self-contained school structure, implementing a mathematics
instructional plan and collecting data from a summative common assessment. Other
variables involving teachers’ experiences, perceptions, and opinions about the classroom
organization were also researched. These variables were addressed using data collection
through an interview. The goal of this design was to discover whether or not teacher
strengths play a role in student achievement
Setting
This action research study took place in a Title I school in west Georgia; this
school was coded as school A. School B, is a rural Title I school also in west Georgia,
located in close proximity to School A. The schools were selected based on a set criteria.
The study required a school that implemented the traditional self-contained school
structure—School A. The study also required a school that implemented a less traditional
school structure, departmentalization—School B. Permission and approval from the
county and principal at School A, where the mathematics instructional plan would be
implemented, along with the Lagrange College IRB were granted in order to proceed
with the study.
Subjects and Participants
School A had approximately 460 students enrolled, with 87 of those students
being in three third grade classes. School B had a total school enrollment of 621 and
THE AFFECT OF SCHOOL STRUCTURE 16
approximately 93 of those students are third graders. Both schools were Title I schools
and had distinction (meeting Annual Yearly Progress for three or more consecutive
years). School A had 56 % White population, while School B had 75% White
population. Both School A and B served 64% economically disadvantaged students who
qualify for free and reduced lunches. The subjects in this study were the third grade
students at school A, who were administered the mathematics instructional plan.
Active participants in this study were the third grade teachers at School A who
implemented the mathematics instructional plan and participated in interviews conducted
by the researcher. Teacher Z had twenty-three years of teaching experience. Teacher Y
had one year of teaching experience. Teacher X had three years of teaching experience.
Procedures and Data Collection
Prior to institutional review board (IRB) application, the researcher requested
permission from School A’s principal to conduct the action research study, through the
implementation of the mathematics instructional plan. After approval from the
institutional review board (IRB) and School A’s principal, the researcher sought approval
of the third grade teachers at School A as participants in implementing the mathematics
instructional plan. After all approvals were granted, the following data shell in Table 3.1
was used to guide the action research study.
THE AFFECT OF SCHOOL STRUCTURE 17
Table 3.1 Data Shell
Focus Question
Literature
sources
Will an
Canady &
instructional plan Rettig
designed to teach (1995)
math content
determine teacher McPartland
strengths and
(1990)
deficiencies along
with the most
McGrath &
effective school
Rust (2002)
structure?
How does teacher
strength and
knowledge affect
student outcome?
Ackerlund
(1959)
Gardner
(1991)
Chan &
Jarman
(2004)
Type: Method,
Data , Validity
Type of Method:
Instructional Plan
rubric and
interview
Type of Data:
Qualitative
Type of Validity:
Content
How are data
analyzed
Coded for themes
Recurring
Dominant
Emerging
Rationale
Type of Method:
Teacher made –
pre /post test &
Standardized CRCT
Type of data:
Interval
Type of Validity:
Content
Dependent T
Independent T
ANOVA
Type of Method:
Reflective
Journal and
interviews
Type of Data:
Qualitative
Type of Validity:
Construct
Coded for themes
Recurring
Dominant
Emerging
To determine if
there are
significant
differences:
-between means
from one group
tested twice
-between means
from two
independent
groups
-among the
means from
three or more
independent
groups
Looking for
categorical and
repeating data
that form
patterns of
behaviors
Kemp &
Hall (1992)
What are the
opinions and
attitudes of third
grade teachers
involved in this
study, on the
effectiveness of
teaching in
capital strength
areas?
Muijs &
Reynolds
(2002)
Bandura
(1986)
Henson
(2001)
Looking for
categorical and
repeating data
that form
patterns of
behaviors
THE AFFECT OF SCHOOL STRUCTURE 18
The mathematics instructional plan (see Appendix A) was created and used as a
data source for focus question one. The instructional plan consisted of ten mathematics
lessons which were aligned to the third grade Georgia Performance Standards concerning
the concepts of area and perimeter. During the creation of the ten lessons, the diverse
student population was kept in mind through the consideration of Howard Gardner’s
(1991) multiple intelligence theory. The lessons and activities were the constant, while
the teachers teaching in their strengths areas were the variable. Two teachers, Teacher X
and Y, felt their teaching abilities were strong in the area of mathematics, while Teacher
Z did not express a feeling of strength in teaching ability in this content area. Throughout
the implementation of the ten lesson Instructional Plan, the researcher and colleague
participants kept meticulous notes on various aspects concerning the Instructional Plan
and implementation process, this was documented in a reflective journal using the
reflective journal prompts found in Appendix C. Feedback regarding the Instructional
Plan’s integrity and quality was sought from experienced colleagues through the use of a
rubric and interview. From the rubric and interview, suggestions were made to include a
pre and post test to show each teacher’s student sample growth. Experienced colleague
reviewers also thought the instructional plan included a variety of lessons that would
meet all students learning needs.
According to James Popham (2010), the author of Classroom Assessment: What
Teachers Need to Know, multiple choice assessments measure a student’s knowledge and
can allow students to employ higher order thinking skills. In an effort to answer focus
question two, a multiple choice pre assessment was administered prior to implementation.
After implementation of the mathematics instructional plan, a post assessment was
THE AFFECT OF SCHOOL STRUCTURE 19
administered in an effort to measure whether teaching in strength areas affects student
achievement. In addition, all of the third grade students who served as subjects in this
action research study, where administered the Georgia Criterion Referenced Competency
Test [CRCT]. In order to compare the two different school structures, the researcher
obtained archival test data from the Georgia Report Card from the GaDOE website for
both School A, and School B. School A and B archival test data was compared to prove
that school structure along with teachers teaching in strength areas affect student
achievement.
The data collection instruments used in this action research study to measure
focus question three, concerning student achievement and teacher experiences,
perceptions, and opinions were the interviews conducted with the three third grade
teachers who implemented the instructional plan along with the reflective journal kept by
the researcher. The interview was conducted to gain a better understanding of how
teacher strengths affect student outcome, see Appendix B for questions used during the
interviews.
Validity, Reliability, Dependability, and Bias
Qualitative data were gathered for focus question one through the instructional
plan rubric and interviews. The instructional plan provides content validity. The
researcher sought construct validity by conducting interviews and collecting feedback
from experienced colleagues concerning the instructional plan. Hendricks (2009) refers
to this process as “peer debriefing”, which is employed to increase validity. In order to
increase dependability of these data the following actions took place: interviewees
checked transcripts for accuracy, data were accurately recorded with the use of protocols,
THE AFFECT OF SCHOOL STRUCTURE 20
audio and/or videotaping, and data collection and treatment were kept consistent. In an
effort to eliminate bias, all instruments: the instructional plan, pre and post assessments
and interview questions—have all been checked for unfairness, offensiveness, and
disparate impact.
Quantitative, interval data were collected for focus question two through the pre
and post assessment in order to achieve test-retest reliability. In addition, archival CRCT
mathematics data were collected. Content validity refers to how well an assessment
matches the curriculum taught (Popham, 2010). Through the collection of the post test
data, content validity was achieved. Variance will be measured, to ensure reliability of
the ANOVA. In an effort to eliminate bias, all instruments: the instructional plan, pre
and post assessments and interview questions—have all been checked for unfairness,
offensiveness, and disparate impact.
Qualitative data were collected for focus question three using the reflective
journal and interviews conducted with the third grade teachers. Hendricks (2009)
suggests that through the use of the reflective process and journaling, educators can
identify issues and seek resolutions to such issues, which is a crucial aspect of improving
an educator’s professional development. Construct validity was achieved through the
collection of feedback from experienced colleagues on their beliefs and attitudes. In
order to increase dependability of these data, the following actions took place:
interviewees checked transcripts for accuracy, data were accurately recorded with the use
of protocols, audio and/or videotaping, and data collection and treatment were kept
consistent. In an effort to eliminate bias, all instruments: the instructional plan, pre and
THE AFFECT OF SCHOOL STRUCTURE 21
post assessments and interview questions—have all been checked for unfairness,
offensiveness, and disparate impact.
Analysis of Data
Qualitative data were collected for focus question one. These data were analyzed
and coded for reoccurring, emergent, and dominant themes. The rationale for this type of
analysis was to detect categorical and repeating data that form patterns for behavior.
Quantitative data were collected for focus question two, and then analyzed using
various statistical tests. The hypothesis being, that there is a significant difference
between the pre and post test scores or amongst the three classes implementing the
instructional plan. The pre and post data collected from each of the three classes
implementing the instructional plan, were also analyzed in three dependent t-tests. These
results addressed focus question two. Effect size, r test, was also used to calculate the
magnitude for the pre and post test data for each teacher. Effect size is categorized as
small, medium, or large. Reliability was also calculated from the 3 dependent t-tests,
using the Pearson’s coefficient correlation, to calculate the relationship between the pre
and post test results. An analysis of variance-ANOVA test was used to compare the
mean scale scores differences between the three classes that were administered the pre
test prior to implementing the instructional plan, with the null hypothesis being that there
is no significant difference among the three classes. Another ANOVA test was used to
analyze the mean scale scores difference between the three classes post assessment after
the instructional plan was implemented, with the research hypothesis that there would be
a significant difference between the groups. These results also addressed focus question
two. This test was used to determine if there were significant differences among the
THE AFFECT OF SCHOOL STRUCTURE 22
means from three groups of students who were administered the post test. The null
hypothesis being that there is a no significant difference between the groups. The
decision to reject the null hypothesis has been set at p < .05.
Qualitative data were collected for focus question three. These data were
analyzed and coded for reoccurring, emergent, and dominant themes. The rationale for
this type of analysis was to detect categorical and repeating data that form patterns for
behavior.
The entirety of the study was analyzed holistically. The study was approved by
the faculty, as a result, the study obtained consensual validity. Through the incorporation
of prior research through the literature review this study attained epistemological
validation. As a result of presenting opposing opinions in the literature review in
addition to selecting participants who have opposing views, this study achieved fairness.
By including a variety of data sources, as seen in Table 3.1, structural corroboration and
triangulation have been achieved. Eisner (1991) calls this process ‘structural
corroboration,’ where all evidence comes together to form a compelling whole. Immense
consideration has been taken to ensure accuracy in reporting research findings, data
collection, and data analysis. A coherent and logical case has been made through
presenting strong evidence which has been collected and presented through a variety of
methods in order to assert judgments, thus achieving rightness of fit. According to Eisner
(1991), a tight argument, coherent case, and strong evidence to assert judgments are all
necessary components of research precision, also referred to as ‘rightness of fit’. To
ensure the ease of transferability to future similar studies, referential adequacy has been
achieved through the details and precise instruction of the procedures and methods of the
THE AFFECT OF SCHOOL STRUCTURE 23
complete study. As this is an action research study seeking to find whether school
structure can affect student achievement, it seeks to answer and improve the education
realm, therefore exuding catalytic validity.
THE AFFECT OF SCHOOL STRUCTURE 24
CHAPTER FOUR: RESULTS
The focus questions guided this action research process. The results for this
action research study are organized by focus question. Embedded data tables will be
used to display quantitative data results, while qualitative data results were coded for
themes.
Focus question one was, will an instructional plan designed to teach math content
determine teacher strengths and deficiencies along with the most effective school
structure? Qualitative data were gathered through an instructional plan rubric along with
interviews regarding the design of the instructional plan. These data were analyzed and
coded for reoccurring, dominant, and emerging themes.
Prior to the implementation of the mathematics instructional plan, through
interviews, feedback was sought from collaborating colleagues regarding the design of
the instructional plan. The following factors as related to the design of the area and
perimeter mathematics instructional plan emerged from the interviewees’ responses in the
interviews and on the rubric. The first interviewee, Teacher 1, a ten year veteran teacher,
reported after reviewing the ten day mathematics plan on the concept of area and
perimeter, “the plans included a wide variety of activities that would help accommodate a
wide variety of learning styles”. Teacher 1 also reported that entirety of the instructional
plan was “clear, concise, and easy to follow”. Teacher 1 suggested offering the students
more choices throughout the instructional plan through the use of choice boards and
choice menus, as a means of differentiating. After much thought and consideration of the
suggestion, the researcher wanted to keep each teacher and their students as controlled as
allowable by minimizing the activity choices each day. The second interviewee, Teacher
THE AFFECT OF SCHOOL STRUCTURE 25
2 with less than five years experience, suggested the use of a pre and post assessment,
rather than only testing the students at the end of the instructional plan. Teacher 2 stated,
“The use of a pre and post test would help track classroom progress.” Teacher 2 also
liked the incorporation of technology throughout the instructional plan. Teacher 2
commented, “Week one is hands-on learning tasks, and week 2 is more application and
extension tasks.” Both teachers interviewed reported that the instructional plan was
closely aligned with Georgia Performance Standards, essential questions were clearly
stated along with lesson expectations and learning goals. The instructional plan was
revised and aligned to the feedback and suggests given by the interviewees and collected
from the instructional plan rubric.
The second focus question guiding this action research study was, how does
teacher strength and knowledge affect student outcome? The data gathered to answer this
focus question were the scores from the three classrooms implementing the mathematics
instructional plan, both pre and post test data. Three dependent t-tests were used to
calculate the pre and post test data. In Table 4.1,for the no treatment group-Z, the
obtained value of 8.81 is greater than the critical value of 1.73, t(18)=8.81, p<.05, therefore
rejecting the null hypothesis. There is a significant difference between the pre and post
test results of the no treatment group. There is a statistically significant relationship
between the pre and post test. Reliability, reported as Pearson Correlation, was .51, r (17)
= .51.
THE AFFECT OF SCHOOL STRUCTURE 26
Table 4.1
T-Test: Paired Two Sample for Means
No treatment-Teacher Z
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
Pre-test
50.47368
320.8187
19
0.51914
0
18
-8.81119
3.02E-08
1.734064
6.03E-08
t Critical two-tail
2.100922
Post-test
81.42105
89.70175
19
In Table 4.2 the treatment group-Teacher X, shows that the obtained value of
10.52 is greater than the critical value of 1.71, t(22)=10.52, p<.05, therefore rejecting the
null hypothesis. There is a significant difference between the pre and post test results of
the no treatment group. Therefore accepting the null hypothesis that there is no
significant relationship between the pre and post test. Reliability, reported as Pearson
Correlation (r), was .33, r(21)= .33.
THE AFFECT OF SCHOOL STRUCTURE 27
Table 4.2
T-Test: Paired Two Sample for Means
Treatment-Teacher X
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
Pre-Test
54.65217
213.2372
23
0.334505
0
22
-10.5284
2.35E-10
1.717144
4.69E-10
t Critical two-tail
2.073873
Post-test
86.82609
98.51383
23
In Table 4.3, the treatment group-Teacher Y, shows that the obtained value of
7.68 is greater than the critical value of 1.72, t(20)=7.68, p<.05, therefore rejecting the
null hypothesis. There is a significant difference between the pre and post test results of
the no treatment group. There is a statistically significant relationship between the pre
and post test. Reliability, reported as Pearson Correlation (r), was .78, r(19)= .78.
Therefore rejecting the null hypothesis.
THE AFFECT OF SCHOOL STRUCTURE 28
Table 4.3
T-Test: Paired Two Sample for Means
Treatment-Teacher Y
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
Pre-test
61.85714
476.8286
21
0.78367
0
20
-7.68184
1.08E-07
1.724718
2.17E-07
t Critical two-tail
2.085963
Post-test
86.42857
133.5571
21
The effect size was calculated for all three groups. All three groups are
categorized as having a large effect size: no treatment-Teacher Z- 0.79, treatmentTeacher X-0.82, and treatment-Teacher Y-0.62.
THE AFFECT OF SCHOOL STRUCTURE 29
An Analysis of Variance was also used to calculate the results amongst the three
groups. Table 4.4 shows the results of the ANOVA using the pre test data from all
groups. The obtained value of 4.63 is greater than the critical value of 3.14, F(2,62)=4.63,
P<.05, therefore rejecting the null hypothesis. There is a significant difference between
the pre tests of the three groups.
Table 4.4 ANOVA: Single Factor
Pre-Test
SUMMARY
Groups
Count
Teacher X
23
Teacher Y
21
Teacher Z
21
ANOVA
Source of Variation
Between Groups
Within Groups
SS
3208.522868
21471.59834
Total
24680.12121
Sum
Average Variance
1257 54.65217 213.2372
1299 61.85714 476.8286
1003 47.7619 362.1905
df
MS
F
P-value
F crit
2 1604.261 4.632362 0.013336 3.145258
62 346.3161
64
THE AFFECT OF SCHOOL STRUCTURE 30
Another Analysis of Variance was used to calculate the results of the post-test
data from all three groups. Table 4.5 shows the obtained value of 1.68 is less than the
critical value of 3.15, F(2,60)=1.68, P>.05, therefore accepting the null hypothesis. There
is no significant difference among the results of the post test data from the three groups.
Table 4.5 ANOVA: Single Factor
Post-Test
SUMMARY
Groups
Count
Sum
Average Variance
Teacher X
23
1997 86.82609 98.51383
Teacher Y
21
1815 86.42857 133.5571
Teacher Z
19
1547 81.42105 89.70175
ANOVA
Source of
Variation
Between Groups
Within Groups
SS
362.6672
6453.079
Total
6815.746
Df
MS
2 181.3336
60 107.5513
F
P-value
F crit
1.68602 0.193913 3.150411
62
The archival CRCT data collected from Georgia Report Card portion of the
Georgia Department of Education website showed School A as having 85 total students
tested with 21 students not meeting standards (DNM), 42 students meet the standard, and
36 students exceed the standards for the mathematics portion of the 2010 CRCT. Of the
99 students tested at School B, 29 students did not meet the standards, 42 students meet
the standards, and 28 students exceeded the standards for the 2010 CRCT mathematics
test. The percentage of meets and exceeds for School A (not departmentalized) was 92%,
while 71% meet and exceed at School B (departmentalized).
The third focus question used to guide the study was concerned with the opinions
and attitudes of third grade teachers involved in this study about the effectiveness of
THE AFFECT OF SCHOOL STRUCTURE 31
teaching in capital strength areas. Data were gathered through reflective journals and
interviews. These data were analyzed and coded for reoccurring, dominant, and
emerging themes. Over the course of the instructional plan implementation, a few
reoccurring themes were noted in the reflective journals kept by the teachers participating
in this action research study. One reoccurring theme was the availability of time allotted
to teach the instructional plan. It was noted several times throughout all three journals,
each participant struggled with the time allotted for teaching the instructional plan. An
emergent theme that all teachers noted in their journals was the successfulness of the
hand-on activities throughout the instructional plan. An emergent theme in Teacher Z’s
journal was difficulty managing the various grouping situations and ensuring that all
students were constructing the appropriate knowledge and understanding of area and
perimeter. In the fifth journal entry for the fifth lesson in the instructional plan, Teacher
Y noted, “working with a small group was a huge success.”, while Teacher Z noted the
importance of differentiating for all levels, Teacher Z experienced difficulty setting aside
time to hold such small group sessions. Thus, making the dominant theme found in all
journals the difficulty with appropriate time allotment to the subject.
During the interview held with the participating teachers multiple differences in
prior experience and training were discussed, however a few dominant themes were
presented. The participants expressed similar opinions of departmentalizing. The
participants felt positive about the idea of a teacher being an expert in one or two subject
areas, rather than trying to master the art of successfully implementing all subjects. The
participants also expressed feelings of low efficacy when discussing how prepared they
felt to successfully teach all subjects. Teacher Y expressed that the best training she
THE AFFECT OF SCHOOL STRUCTURE 32
received in college occurred during fieldwork at participating elementary schools.
Teacher Z described how her years of teaching experience better prepared her than her
undergraduate program. Teacher Z and Teacher Y both agreed that a teacher teaching the
subject they had specialized training in, could better serve their students. The
participants suggested that students taught by teachers with special training, would have a
more successful learning experience.
THE AFFECT OF SCHOOL STRUCTURE 33
CHAPTER FIVE: ANALYSIS AND DISCUSSION OF RESULTS
Analysis
This action research study was designed to further investigate teacher strengths
and school structure, and their affects on student achievement in mathematics. The study
was guided by a few leading research questions. Both quantitative and qualitative data
were collected and analyzed statistically and coded for themes. In order to achieve
epistemological validity, the results of this action research study were compared with the
current published literature and research findings.
Will an instructional plan designed to teach math content determine teacher
strengths and deficiencies along with the most effective school structure? In order to
collect data for focus question one, an instructional plan rubric was used in addition to an
interview with experienced colleagues in regards to the integrity of the ten day
mathematics instructional plan. Qualitative data were collected and coded for themes.
The feedback from experienced colleagues reported in chapter four, was used to modify
the instructional plan. After reviewing the qualitative data collected, it could be argued
that any teacher could easily implement the instructional plan. While any teacher could
implement the plan, the plan may yield different results based on teacher strengths and
deficiencies. The data collected from the rubric and interview directly relates to Howard
Gardner’s (1991) theory of multiple intelligences, as cited in the literature review.
Teachers, like students, have multiple intelligences. It is nearly impossible to be an
expert in all subject areas. According to Flick and Lederman (2003) , it is necessary for
teachers to have an adequate understanding of the subject matter they are responsible for
teaching. Through collecting feedback to improve the quality and integrity of the
THE AFFECT OF SCHOOL STRUCTURE 34
instructional plan, along with the uniform implementation and analysis of student results,
it could be argued that the instructional plan was successful in identifying teacher
strengths and weaknesses. Through careful analysis of the class post test means, in
addition to the reflective journals, it could be argued that Teacher X exhibited a strength
in mathematics instruction.
Through the uniform implementation of the ten day area and perimeter
instructional plan, a few themes were uncovered. One theme uncovered was that Teacher
Z, who had no specialization or preference for teaching mathematics, struggled with
setting aside time to give small group instruction in order to differentiate for all ability
levels. Could this be a result of a lack of confidence, subject-matter knowledge, or
motivation towards teaching mathematics? Kemp and Hall (1992). noted, “…student
achievement is related to teacher competence in teaching” (p. 4). As noted in the
reflective journals, Teacher Y and Teacher X consistently reported feeling confident and
prepared throughout the instructional plan implementation, while Teacher Z reported on
various occasions throughout the journal, feeling “unprepared” and “unsure” of herself.
From the qualitative data collected for focus question one and the coinciding review of
literature, it can be concluded that this portion of the study reinforces the current
literature findings related to teacher strengths and abilities playing a role in the
implementation of the ten day instructional plan.
The second focus question guiding this action research study was, how does
teacher strength and knowledge affect student outcome? The methods used to gather data
were the pre and post test for the ten day area and perimeter instructional plan, and the
archival CRCT math results from School A (non departmentalized structure) and School
THE AFFECT OF SCHOOL STRUCTURE 35
B (departmentalized structure). The data were analyzed through three dependent t-tests
using pre and post test data collected from the three third grade classes that implemented
the ten day instructional plan. Through administering the same pre and post assessment
at two different times throughout the implementation process, this portion of the study
achieved test-retest reliability. The reliability was calculated for all three t-tests. The
results showed no significant (weak ) relationship between the pre and post test results for
Teacher X, while Teacher Y and Teacher Z’s results showed a (strong and moderate)
significant relationship between the pre and post test results. The three dependent t-test
results showed a significant difference between the pre-test results and the post-test
results for all three classes. This type of outcome was expected, as a result of student
knowledge before the unit was taught and an expected growth in knowledge constructed
after the unit was taught. In addition, the effect size was also expected to be medium to
large, and when calculated was considered large for all three classes, due to the increase
in student knowledge. The pre and post assessment tool used, proved to be a valid
assessment of student knowledge and understanding of area and perimeter. An Analysis
of Variance (ANOVA) test used to calculate the results among the three classes pre tests.
A significant difference was found amongst the three groups of pre-test scores. By
looking at the averages of the three classes pre test data listed in Table 4.4, it could be
argued that Teacher Z’s students started out with less knowledge about area and
perimeter than Teacher X and D’s students. Teacher Z’s pre-test average was 47.7%,
while Teacher X’s class average was 54.6%, and Teacher Y’s class average was 61.8%.
A second ANOVA test was run to calculate the post test results among the three classes.
The results from the second ANOVA showed no significant difference among the three
THE AFFECT OF SCHOOL STRUCTURE 36
groups. The three classes post-test results range from 81% to 86%: Teacher X- 86.8%,
Teacher Y-86.4%, and Teacher Z-81.4%. From such results, it could be argued that
teacher strengths do affect student achievement. Teacher X and Teacher Y both
expressed high instructional efficacy when teaching mathematics, feeling that this subject
area was a strength for them. While Teacher Z, reported mathematics as a weak area of
her teaching ability. Teacher X and Teacher Y’s students achieved a higher class average
on the post test, than Teacher Z’s students. Muijs and Reynolds (2002) suggest that
students who are taught by teachers with high efficacy, attain better scores on tests than
students who are taught by teachers with low efficacy.
In addition, the 2010 archival mathematics CRCT data collected for focus
question two, show that 92% meet and exceed at School A (not departmentalized), while
71% meet and exceed at School B (departmentalized). Much of the prior literature that
was reviewed for this study coincides with these results. While research was found to
support departmentalization, more research was found that did not support
departmentalizing in the lower grades. Those who advocate for the self-contained school
structure, claim that it promotes instruction that is more child centered than subject
centered (McGrath & Rust, 2002). Research suggests that this type of setting is the most
effective in allowing teachers to truly know their students’ abilities. According to
Canady and Rettig (1995), self-contained school structure allows teachers to not only
know their students’ personalities, but also their strengths and weaknesses, allowing
those teachers to be better prepared when planning instruction for their students. The
CRCT data collected for this study supports previous research findings comparing
departmentalized and self-contained school structures. While there is still a lack in proof
THE AFFECT OF SCHOOL STRUCTURE 37
for which school structure is more effective than another, this study showed that the
school the is not departmentalized (School A) did have higher CRCT mathematics scores
than the departmentalized school (School B).
The final research question guiding the study was, what are the opinions and
attitudes of third grade teachers involved in this study, on the effectiveness of teaching in
capital strength areas? Qualitative data were collected through the reflective journals
kept by the study participants and the interview conducted with the study participants.
Data were coded and analyzed for themes. The dominant theme from the interview was
the positive attitude the teachers shared about departmentalizing. While the teachers
reported that they had never actually taught in a departmentalized setting, they both felt
that each subject would be given the fair amount of time and emphasis. They also felt
that teachers would observe more student success, due to the teacher being able to share
his/her specialized knowledge of the subject. Such results align with previous research
conducted by Michael Schiro (2008), who found that learning best occurs when the
teacher clearly and accurately presents knowledge. Through the reflective journaling
process a few themes were uncovered. Teacher Z expressed feelings of low efficacy and
difficulty meeting with all students. While Teacher Y reported feeling well prepared and
organized each day. These results directly related to the research found on self-efficacy
and how it relates to effective teaching. Teacher instructional efficacy plays a significant
role in knowledge development, and has been suggested by many researchers to be
strongly related to student achievement on standardized tests (Henson, 2001). Robin
Henson (2001) found that teachers who see themselves as capable of teaching certain
THE AFFECT OF SCHOOL STRUCTURE 38
subjects challenge themselves and persist in their efforts to succeed, which, in turn,
influences their students.
Discussion
The findings in this study may be limited due to the short amount of time to
implement the action research instructional plan (10 days). The study yielded results that
coincide with previous research studies. This study produced results that could be argued
to prove teacher strengths to be beneficial in improving student learning, numerous
studies in the past also proved teacher strengths to be beneficial. Such studies were much
more extensive and longitudinal than this study.
Similar studies centered mainly around school structure also aligned with this
action research study. It could be argued from the CRCT data comparison, that school
structure does play an important role in student achievement and success on standardized
testing. Much of the previous research proved to be true for this study. Prior studies
conducted by Canady and Rettig (1995), as well as McGrath and Rust (2002), have
yielded results that support self-contained school structure and prove departmentalizing
to entail many less desirable side effects than the usage of self-contained organization in
the younger grade levels.
Through the incorporation of various data collection sources and prior research,
credibility for this study has been established and maintained throughout its entirety. In
an attempt to attain fairness, this study has incorporated both supporting and opposing
research whenever possible. Through the use of careful organization and effective
research questions, this study has maintained rightness of fit. While the results from this
THE AFFECT OF SCHOOL STRUCTURE 39
study and previous studies do not yield a simple right or wrong answer, it does help build
interest and amplify the need for further in depth research in this area of education.
Implications
This study was based on the participation of three third grade teachers
implementing the ten day mathematics instructional plan. The seventy-five third grade
students at School A served as the subjects. This action research study was minuscule in
comparison to previous published studies, for instance in Ackerlund’s 1959 study, he
surveyed a total of 260 teachers on their prior training and knowledge of subject. Would
the results of this study remain the same had more teachers been able to participate?
Considering the methods of collecting quantitative data, the probability that the results
would remain the same is very likely regardless of the population size.
This study brought effective school structure to the forefront of the research
location. Participants became interested in further investigation of the most effective
school structure. Participants were considering using current research to construct a
proposal for departmentalizing at their school. The teachers who participated in this
study felt departmentalizing is an effective way to ensure meaningful learning, which is
significantly different from ensuring successful standardized test takers.
Through the reflective journaling process “referential adequacy” was ensured in
this study. Through the journaling process several themes were identified and can be
transferred to other areas in education. The reflective journal kept by the researcher and
other participants in the study, was used as a method for gathering qualitative data. A
theme uncovered in the reflective journal was elementary school teachers’ struggle with
time constraints. This is a common conversation amongst many teachers, there seems to
THE AFFECT OF SCHOOL STRUCTURE 40
never be enough time in the day to fit in everything that needs to be taught. Another
theme that could be applied to various teaching situations was the feeling of instructional
efficacy. Often, teachers may not experience high efficacy in everything they do each
day. It can be beneficial in improving to identify times of low instructional efficacy, and
make an effort to improve in such areas. It can also be beneficial to identify times of
high instructional efficacy and use these times to highlight natural teacher strengths to
benefit student learning.
Due to the reflective nature of the study, catalytic validity was ensured. The
researcher began the study as a supporter of departmentalizing in elementary school,
through this research process the researcher’s views have been modified as a result of the
study. After completing the literature review and implementation of the instructional
plan, the researcher believed teacher strengths can be beneficial to students, however, the
researcher is not convinced that departmentalizing is the answer to improving student
learning at the elementary level.
Impact on Student Learning
The purpose of this action research study was to find out which school structure
produces the highest levels of student achievement. While the participating teachers’
strengths and efficacy were different, after reviewing the results collected from focus
question two, , the end results showed no significant difference in student achievement
amongst the three classes. From these results, it could be argued that teacher strengths
did not greatly affect student achievement in this action research study. The CRCT data
collected also yielded a larger meets and exceed percentage of the student population for
the traditional self-contained third grade at School A. Such results suggest that
THE AFFECT OF SCHOOL STRUCTURE 41
departmentalizing may not increase student achievement on standardized tests. From the
results of this study, it may also be argued that the traditional self-contained school
structure may yield better outcomes for student achievement on standardized tests.
Recommendations for Future Research
A suggestion for similar future research would be to examine archival CRCT data
for an extended period of time for the two different school settings. Perhaps comparing
several years of data may result in more accurate analysis of school structure. It may also
be interesting to have both schools-one departmentalized and one traditional- implement
the exact same instructional plan, then calculate and analyze those data.
THE AFFECT OF SCHOOL STRUCTURE 42
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Appendix A
Instructional Plan
MONDAY(Week 1)
SUBJECT
Math
TOPIC
 Measurement:
Area &
Perimeter
STANDARDS
ESSENTIAL
QUESTIONS
VOCABULARY
M3M3. Students will
understand and
measure the perimeter
of simple geometric
figures (squares and
rectangles).
M3M4. Students will
understand and
measure the area of
simple geometric
figures (squares and
rectangles).
 How are the
perimeter and
area of a
shape related?
 area: a
measurement of the
region enclosed by
the sides of a
polygon Area is
always expressed in
squared units.
 perimeter: the
distance around the
outside of a shape
*Watch the BrainPopJr. Perimeter and Area cartoons
*The teacher will have the students feel the difference between perimeter and area by
having the students close their eyes and use their touch to examine two cardboard
polygons, one of which has pompons glued around the edge (perimeter) and the other
which has pompons glued all over its surface (area). The teacher will say, “We can
measure perimeter using many different things. We can use pompons, toy cars, inches,
centimeters, even our hands.”
•
Practice: Have the students work in pairs and measure the perimeter of 4 or 5
different objects around the room using different units: hands, feet, pencils, in, ft, etc.
•
Monitor the students' progress.
•
Have a couple of students share their examples.
•
Discuss why it might be necessary to have a standard unit like: inches, feet, or
meters.
•
Discuss why someone might need to know the perimeter of something. (Example:
fencing a yard)
Use the Area/Perimeter Explorer to practice
http://www.shodor.org/interactivate/activities/PerimeterExplorer/ (I always emphasize
RIM in peRIMeter. I say that we are measuring the outside RIM of our shape.)
http://www.shodor.org/interactivate/activities/AreaExplorer/
TUESDAY
Review what perimeter means and real-world situations that may use perimeter
measurements. Pass out the 1 centimeter square paper to each student along with one red
fraction bar, two green fraction bars, and one purple fraction bar. The students are to
arrange the fraction bars into a shape on the centimeter paper. It is necessary that when
the student traces around their shape, they draw only on the black lines and their shape
must remain in one piece if it were to be cut out. (In other words, corners touching are not
THE AFFECT OF SCHOOL STRUCTURE 47
allowed.) The students must find a way to arrange the fraction bars in order to make the
smallest and largest possible perimeter. Have them trace their shapes and count the
perimeter of each before making the next one.
*To add an extra challenge, increase the number of fraction bars. You may also want to
ask students if they can find a given perimeter ("Can you make a perimeter of 20?").
*Students can work in groups or individually.
WEDNESDAY
Whole group--Review perimeter and area concept by using painters tape to tape off
the tiles on the floor—making various size rectangles and squares. Have students come
stand on each side to show the perimeter. Note-there must be a student standing on each
of the line segments that make up the whole side of each rectangle/square. If you tape
the outside of 3 tiles to make a rectangle, there will be 3 students, 1 student, 3 students, 1
student—that will stand on the outside to model perimeter. The area for the 3 tile
rectangle could be modeled with 3 students.
Partners/small groups (before the activity- using index cards, write a specific perimeter or
area on at least 20 cards) Students will be given a flashcard programmed with either area
or perimeter. Using painter’s tape, they will tape off the figure on their flashcard.
Assessment After all figures have been taped and checked, the students will complete the
Perimeter/Area scavenger hunt sheet.
THURSDAY How big is a desk? (GPS Framework)
Choose from the units available to measure the area of the top of your desk.
• Estimate how many of the units it will take to cover your desktop with no pieces
overlapping.
• Measure the desk using your chosen unit of measure and record your measurements
accurately.
• Explain how you arrived at your answer using numbers, pictures, and words.
• Choose a different measurement unit.
• Estimate how many of the 2nd unit it will take to cover your desk. Will you need more
or less of the 2nd unit than of the 1st unit?
• Measure the area of your desk with this 2nd unit and record your measurements
accurately.
• Compare the two measurements.
• Explain your observations and whether or not your predictions were or were not correct.
FRIDAY
Rectangles Rule (GPS Framework)
On your dot paper, draw all the rectangles you can with a perimeter of 24. Determine the
area of each rectangle and record it inside the rectangle. Now, count to check the
perimeter of each rectangle. Write a paragraph that explains how the shape of the
rectangle and its area are related.
Discussion, Suggestions, Possible Solutions
All students should have had prior experience in determining area and perimeter.
They will need dot paper or may prefer using 10 x 10 geoboards if available.
THE AFFECT OF SCHOOL STRUCTURE 48
There are 6 possible rectangles: a 1 x 11, 2 x 10, 3 x 9, 4 x 8, 5 x 7, and 6 x 6. All should
be drawn and labeled accurately.
Students should note that the more narrow the rectangle, the smaller the area. Exemplary
work will note that the sum of the length and width must equal twelve.
Extension: Given a rectangle with a perimeter of 36 units, what is the smallest possible
area it could have? The largest?
The smallest area of a rectangle with a perimeter of 36 units would be 17 square units.
The largest area would be 81 square units.
MONDAY (Week 2)
Area and Perimeter Quiz Quiz Trade
Pass out a cup of 1-inch foam squares to each student along with a pre-programmed
index card that has a set area or perimeter. The students may want to place the flashcard
in the cup with the foam pieces. All students will stand up, put their hand up, and find a
partner to high-five and pair up. One partner will read their flashcard, while the other
partner will make the figure with the foam squares. Then, the partner that read the card
will check the figure that the other partner made. Next, the partners will switch jobs.
Once the pair finishes quizzing each other. They must trade cards. They will then raise
their hand to find a new partner to quiz.
Assessment: Given ten random shapes on a grid, the students will be able to calculate the
area and perimeter.
Rubric for scoring:
•
9–10 correct: 5 points
•
7–8 correct: 3 points
•
6 correct: 1 point
less than 6 correct: 0 points
TUESDAY
Small Group day—work with students who scored a 0 or 1 on the assessment from
yesterday.
Rest of the class—students will complete the area and perimeter cut and paste activity
from the mailbox magazine.
WEDNESDAY
Whole group- student will use the interactive whiteboard to manipulate the shapes to
find the area and perimeter, using the following website
http://illuminations.nctm.org/LessonDetail.aspx?ID=L650
-ues area and perimeter workbook page to assess students
THURSDAY Perimeter Mall (GPS Framework)
Use pentomino pieces to create a map of a new shopping mall.
Design the mall by tracing the pieces onto white paper to make a map of the mall.
Label the stores that are in your shopping mall.
Add details to your map such as a parking lot, trees, and benches.
Determine the number of units in the area and perimeter (in each building if your mall
has separate buildings) of your mall.
THE AFFECT OF SCHOOL STRUCTURE 49
Record that data on your map.
Write a few sentences that describe the choices you made as you designed your mall.
Explain how you found the perimeter and area of your mall.
You may want to bring in an actual map of a shopping mall.
Discuss how maps help us to find our way around and how we can look at a mall map
directory to see how far we would have to walk.
Each student needs to have access to pentominos.(Pieces are included in the appendix at
the end of this unit framework.) Student work should reflect student preferences for
stores and should be varied. .
All work should have perimeters and areas that are accurately figured. Work should be
neat and legible.
Extension: Pretend each unit on the pentomino is 10 yards. What is the perimeter of your
mall?
FRIDAY: finish Perimeter Mall (GPS Framework) culminating activity and give
area/perimeter multiple choice test in order to collect data.
THE AFFECT OF SCHOOL STRUCTURE 50
Appendix B
Interview Questions
How many years of experience do you have?
How long have you taught third grade?
What is the highest degree you’ve earned?
Do you have any endorsements?
Have you had any specific college level training in the area of math?
What subjects do you prefer to teach? What subjects do you prefer not to teach?
What subject do you feel most qualified to teach? What subject do you feel least
qualified to teach?
What is your preference for the classroom organizational structure for third-grade
students?
_____TRADITIONAL (one teacher who teaches all core subjects to a group of
students for an entire school year)
_____DEPARTMENTALIZATION (more than one teacher for core subjects
where students change classes among teachers)
Do you feel that your initial college training adequately trained you to teach all subjects
at the third- grade level?
Do you believe teachers who have specialized training in a specific subject area can
better serve students through some type of departmentalization at the 3rd grade level?
THE AFFECT OF SCHOOL STRUCTURE 51
Appendix C
Reflective Journal Prompts
 Did you feel confident and prepared in your ability to successfully implement this
lesson?
 Were additional skills or information needed to successfully implement this lesson?
 What outcomes did you hope you or your students would achieve through this lesson?
 What were the actual outcomes you or your students achieved through this lesson?
 What worked well?
 What would you do differently next time? What do I need to do to improve the quality
of what I do?
 What is the most important thing I have learned about student learning?
 What is the most important thing I have learned about my teaching?
 What is the most important thing I have learned about my students?
 How can I use my learning to improve student learning in my classes?
 What professional development activities should I be seeking?