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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. Sharon M. Livingston, Ph.D.Thesis Co-Chair Thesis Co-Chair Education Department 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….……………………………………………………………..1Statement of the Problem…………………………………………………….……1Significance of the Problem……………………………………………………….1Theoretical and Conceptual Frameworks..………………………………………..2Focus Questions…………………………………………………………………...3Overview of Methodology………………………………………………………...4Human as Researcher……………………………………………………………...5

Chapter Two: Review of the Literature…………………………………………………...6School Structure and the Meaningful Learning Environment……………….……6Teacher Knowledge and Strengths Affect on Student Outcome…………….……9Teacher Instructional Efficacy……………………………………………….…. 12

Chapter Three: Methodology…………………………………………………………….14Research Design………………………………………………………………….14Setting……………………………………………………………………………15 Subjects and Participants………………………………………………………..15Procedures and Data Collection Methods………………………………………..16Validity, Reliability, Dependability, and Bias …………………………………..19Analysis of Data………………………………………………………………….21

Chapter Four: Results……………………………………………………………………24

Chapter Five: Analysis and Discussion of Results………………………………………33Analysis………………………………………………………………………….33Discussion………………………………………………………………………..38Implications………………………………………………………………………39Impact on Student Learning……………………………………………………...40Recommendations 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.


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.


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?


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.


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.


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


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 self-

contained 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


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


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.


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


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.


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 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 self-

contained 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.


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


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-and-

effect 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


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.


Table 3.1 Data ShellFocus Question Literature

sources Type: Method, Data , Validity

How are data analyzed

Rationale

Will an instructional plan designed to teach math content determine teacher strengths and deficiencies along with the most effective school structure?

Canady & Rettig (1995)

McPartland (1990)

McGrath & Rust (2002)

Type of Method:Instructional Plan rubric and interviewType of Data:QualitativeType of Validity:Content

Coded for themesRecurringDominantEmerging

Looking for categorical and repeating data that form patterns of behaviors

How does teacher strength and knowledge affect student outcome?

Ackerlund (1959)

Gardner (1991)

Chan & Jarman (2004)

Kemp & Hall (1992)

Type of Method:Teacher made –pre /post test & Standardized - CRCT Type of data:IntervalType of Validity:Content

Dependent TIndependent TANOVA

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

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)

Type of Method: Reflective Journal and interviewsType of Data:QualitativeType of Validity:Construct

Coded for themesRecurringDominantEmerging

Looking for categorical and repeating data that form patterns of behaviors


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


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,


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


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


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


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.


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


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.


Table 4.1T-Test: Paired Two Sample for MeansNo treatment-Teacher Z

Pre-test Post-testMean 50.47368 81.42105Variance 320.8187 89.70175Observations 19 19Pearson Correlation 0.51914Hypothesized Mean Difference 0Df 18t Stat -8.81119P(T<=t) one-tail 3.02E-08t Critical one-tail 1.734064P(T<=t) two-tail 6.03E-08t Critical two-tail 2.100922

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.


Table 4.2 T-Test: Paired Two Sample for MeansTreatment-Teacher X

Pre-Test Post-testMean 54.65217 86.82609Variance 213.2372 98.51383Observations 23 23Pearson Correlation 0.334505Hypothesized Mean Difference 0Df 22t Stat -10.5284P(T<=t) one-tail 2.35E-10t Critical one-tail 1.717144P(T<=t) two-tail 4.69E-10t Critical two-tail 2.073873

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.


Table 4.3T-Test: Paired Two Sample for MeansTreatment-Teacher Y

Pre-test Post-testMean 61.85714 86.42857Variance 476.8286 133.5571Observations 21 21Pearson Correlation 0.78367Hypothesized Mean Difference 0Df 20t Stat -7.68184P(T<=t) one-tail 1.08E-07t Critical one-tail 1.724718P(T<=t) two-tail 2.17E-07t Critical two-tail 2.085963

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, treatment-

Teacher X-0.82, and treatment-Teacher Y-0.62.


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 FactorPre-TestSUMMARY

Groups Count Sum Average VarianceTeacher X 23 1257 54.65217 213.2372Teacher Y 21 1299 61.85714 476.8286Teacher Z 21 1003 47.7619 362.1905

ANOVASource of Variation SS df MS F P-value F crit

Between Groups 3208.522868 2 1604.261 4.632362 0.013336 3.145258Within Groups 21471.59834 62 346.3161

Total 24680.12121 64


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 FactorPost-TestSUMMARY

Groups Count Sum Average VarianceTeacher X 23 1997 86.82609 98.51383Teacher Y 21 1815 86.42857 133.5571Teacher Z 19 1547 81.42105 89.70175

ANOVASource of Variation SS Df MS F P-value F crit

Between Groups 362.6672 2 181.3336 1.68602 0.193913 3.150411Within Groups 6453.079 60 107.5513

Total 6815.746 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

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

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.


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


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


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


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


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


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


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


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


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.


References

Abdal-Haqq, I., & ERIC. (1998).Constructivism in teacher education: Considerations for

those who would link practice to theory. ERIC Digest. Clearinghouse on Teaching

and Teacher Education. Retrieved from ERIC database.(ED426986)

Ackerlund, G. (1959). Some teacher views on the self-contained classroom. Phi Delta

Kappan, 15, 283-285.

Anderson, R. C. (1962). The case for teacher specialization in the elementary school.

Elementary School Journal, 62, 253-260.

Bandura, A. (1986). Social foundations of thought and action: A social cognitive

theory.Englewood Cliffs, NJ: Prentice Hall.

Beecher, M., & Sweeny, S. (2008). Closing the Achievement Gap with Curriculum

Enrichment and Differentiation: One School's Story. Journal of Advanced

Academics, 19(3), 502-530. Retrieved from ERIC database. (DOI #EJ810785)

Bryk, A., Lee, V., & Smith, J. (1990). High school organization and its effects on

teachers and students. In W. Clune & J. Witte (Eds.), Choice and control in

American education, Vol 1: The theory of choice and control in American

education (pp. 135-225). Bristol, PA: Falmer Press.

Canady, R., & Rettig, M. (1995). Block scheduling: A catalyst for change in high

schools. Retrieved from ERIC database. (ED387930)

Chan,T.C., & Jarman, D. (2004). Departmentalize Elementary Schools. Principal

Magazine, (84)1, p. 70. Retrieved October 26, 2010 from the National

Association of Elementary School Principals. Link:

http://www.naesp.org/resources/1/Principal/2004/S-Op70.pdf

http://www.naesp.org/resources/1/Principal/2004/S-Op70.pdf


Dwyer, T., Sallis, J. F., Blizzard, L., Lazarus, R., & Dean, K. (2001). Relation of

Academic Performance to Physical Activity and Fitness in Children. Pediatric

Exercise Science, 13, 225-238.

Eisner, E. (1991). The enlightened eye. New York: MacMillan.

Flick,L., & Lederman,N. (2003). The matter of subject matter. School Science and

Mathematics.103(8).

Gardner, H. (1991). The unschooled mind: How children think and how schools

should teach. New York: BasicBooks.

Gilles, C., Wilson, J., & Elias, M. (2010). Sustaining Teachers' Growth and Renewal

through Action Research, Induction Programs, and Collaboration. Teacher

Education Quarterly, 37(1), 91-108. Retrieved from EBSCOhost.

Hendricks, C. (2009). Improving schools through action research: A comprehensive

guide for educators (2nd ed.). Boston: Allyn& Bacon.

Henson, R. (2001). Teacher self-efficacy: Substantive implications and measurement

dilemmas. Retrieved from ERIC database.(ED452208)

Irmsher, K. (1996). Block Scheduling. ERIC Digest, Number 104. Retrieved from ERIC

database. (DOI# ED393156)

Kemp, L., & Hall, A. H. (1992). Impact of effective teaching research on student

achievement and teacher performance: Equity and access implications for quality

education. Jackson, MS: Jackson State University. (DOI # ED 348 360)

LaGrange College Education Department.(2010). Conceptual framework. LaGrange, GA:

LaGrange College.


Legters, N., McDill, E., & McPartland, J. (1993, October). Section II: Rising to the

challenge: Emerging strategies for educating students at risk. In Educational

reforms and students at risk: A review of the current state of the art (pp. 47-92).

Washington, DC: U.S. Department of Education, Office of Educational Research

and Improvement. Available online (1994, January):

www.ed.gov/pubs/EdReformStudies/EdReforms/chap6a.html

McGrath, C., & Rust, J. (2002). Academic achievement and between-class transition time

for self-contained and developmental upper-elementary classes. Journal of

Instructional Psychology, 29(1), 40-43.

McPartland, J. (1987). Balancing high quality subject-matter instruction with positive

teacher-student relations in the middle grades: Effects of departmentalization,

tracking and block scheduling on learning environments. (Report No. SP028925).

Washington, DC: U.S. Department of Education, Office of Educational Research

and Improvement. Retrieved from ERIC database. (DOI# ED291704)

McPartland, J. (1990). Staffing decisions in the middle grades: Balancing quality

instruction and teacher/student relations. Phi Delta Kappan 71(6), 465-469.

Retrieved October 29, 2010, from ERIC database. (DOI# EJ402386)

Morton, B.A. & Dalton, B. (2007). Changes in instructional hours in four subjects by

public school teachers of grades 1 through 4 (Report No. NCES 2007-

305).Retrieved from ERIC database. (ED497041)

Muijs, D. & Reynolds, D. (2002). Teachers’ beliefs and behaviors: What really matters?,

Journal of Classroom Interaction, 37(2), 3-15 Retrieved November 1, 2010 from

ERIC database.

http://www.ed.gov/pubs/EdReformStudies/EdReforms/chap6a.html


Popham, W. J. (2010). Classroom assessment: What teachers need to know. Boston, MA:

Pearson College Div.

Schiro, M. (2008). Curriculum theory: Conflicting visions and enduring concerns.

Thousand Oaks, CA: Sage Publications, Inc.


Appendix A

Instructional PlanSUBJECT TOPIC STANDARDS ESSENTIAL

QUESTIONSVOCABULARY

Math Measurement: Area & Perimeter

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

MONDAY(Week 1) *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/

TUESDAYReview 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 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.

WEDNESDAYWhole 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.

FRIDAYRectangles 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. 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 pointless than 6 correct: 0 points

TUESDAYSmall 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.

WEDNESDAYWhole 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. 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.


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 ofstudents for an entire school year)_____DEPARTMENTALIZATION (more than one teacher for core subjectswhere 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?


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?

Documents

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