Content



ARE MATH JOURNALS EFFECTIVE?

Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my Advisor. This thesis does not include proprietary or classified information.

Christopher Blake Palmer

Certificate of Approval:

_____________________________ ______________________________

Donald R. Livingston, Ed. D. Sharon Livingston, Ph. D.

Thesis Co-Chair Thesis Co-Chair

Education Department Education Department

ARE MATH JOURNALS EFFECTIVE?

A thesis submitted

by

Christopher Blake Palmer

to

LaGrange College

In partial fulfillment of

the requirement for the

degree of

MASTER OF EDUCATION

in

Curriculum and Instruction

LaGrange, Georgia

May 2011

Abstract

This study explores the impact that math journals have on the test scores of third grade students. The effectiveness of the math journals was determined through quantitative and qualitative analysis of data produced during the study. The significance of math journals was determined through t-test analysis of the student’s pre-post test. The results were compared to the gains of a control group. Surveys were analyzed using a chi square. The results showed that student’s had negative attitudes toward journaling, but journals did provide a significant difference in their gains in their pre-post test. The journals did not have a statistical significant impact; however the effect size and qualitative analysis show that the journaling process was beneficial for the students.

Table of Contents

Abstract……………………………………………………………………………..…….iii

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

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

Chapter1: Introduction…………………………………………………………………….1

Statement of the Problem………………………………………………………….1

Significance of the Problem……………………………………………………….2

Theoretical and Conceptual Framework…………………………………………..3

Focus Questions…………………………………………………………………...5

Overview of Methodology………………………………………………………...5

Human as a Researcher……………………………………………………………6

Chapter 2: Review of the Literature………………………………………………………7

Use of Math Journals in the Classroom…………………………………………...7

Positive Effects of Journal Writing for Teachers………………………………….8

Positive Effects of Math Journaling with Students……………….……………….9

Math Journals Effect on Test Scores…………………………………………….10

Positive Student Attitudes Towards Math Journals……………...………………12

Opposing Views on Math Journals……………………………………………....13

Negative Student Attitudes About Journal Writing……………………………...14

Journal Writing and Research……………………………………………………14

Chapter 3: Methodology……………………………...………………………………….16

Research Design………………………………………………………………….16

Setting…...……………………………………………………………………….16

Subjects and Participants…………………………………………………...……17

Procedures and Data Collection Methods……………………………………….17

Validity, Reliability, Dependability, and Bias…………………………….……..20

Analysis of Data……………………………………………………….…………22

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

Chapter 5: Analysis and Discussion of Results………………………………………….36

Analysis……………………………………………………….………………….36

Discussion………………………………………………………………………..43

Implications………………………………………………………………………44

Impact on Student Learning ……………………………………………………..46

Recommendations for Future Research………………………………………….46

References………………………………………………………………………………..48

Appendixes………………………………………………………………………………52

List of Tables

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

Table 4.1 Independent T-Test Comparing Pre-Tests…………………………..………...27

Table 4.2 Dependent T-Test for the Treatment Group……………………..……………28

Table 4.3 Dependent T-Test for Treatment Group ………………………..………….....29

Table 4.4 Independent T-Test for Post-Tests………………………………..…………...30

Table 4.5 Chi Square for Pre-Post Student Survey………………………..…………..…31

Table 4.6 Chi Square for Teacher Survey………………………………..……………....32

CHAPTER ONE: INTRODUCTION

Statement of the Problem

Elementary students are faced with a math curriculum that is constantly growing in difficulty. In recent years, there has been a shift of emphasis to word problems at the early elementary school level. Word problems are very difficult for children of this age, because many children at this development level are still setting the foundation for their language development skills. Plomin (2009) states that third graders arithmetic word problem skills were uniquely predicted by their nonverbal problem solving, concept formation, sight word efficiency, and language skills.

The Georgia Performance Standards (GPS) have forced elementary schools to spend more time focusing on math skills in lower elementary grades, especially third grade, with the presence of the CRCT. The students are facing difficulty with the standards because they do not have the emphasis on language skills necessary to decode and understand the type of word problems required by the standards. According to Fletcher et al. (2008), students with language deficiencies have trouble with word problems because they are unable to decode, analyze, or interrupt the information necessary to perform the calculation required to solve the problem.

Can the use of math journals positively affect standardized math test scores? This study will implement journals into the math curriculum in a third grade classroom in order to bridge the gap between the two subjects. Math journals have proven to be effective in studies by Moore (1991) and Lauritzen (1992). The use of math journals will help the students to receive personal feedback and strengthen essential language skills, leading to a better understanding of word problems.

Significance of the Problem

The correlation between language deficiencies and math deficiencies has also been linked at the genetic level, according to Hart, Petrill, and Thomson (2009). Their study also noted that the relationships between the genes that are related to math and reading skills “are significant at .94” (p.389). Even though the two subjects have been shown to have correlations at the genetic level and on standardized tests, the two subjects remain independent from each other in classrooms. Writing in math class is a rarity for most children at the primary level (Koirala, 2002).

Language and math deficiencies have been proven to have a correlation as early as first grade (Fletcher, 2008). A study by Fletcher (2008) shows reading fluency and the number of basic addition problems answered in a three minute time span to be statistically significant. The lack of reading fluency often leads the student to have a poor self-image negatively affecting the motivational level of the student. When this problem occurs motivational problems carry over to math due to the correlation between the subjects.

Students have a hard time linking the two subjects together because of the wall put up between the two subjects. Math is viewed as a means to calculate numbers and the students do not always know why the calculations work, or the real life applications of the problem (Dusterhoff, 1995). It is almost impossible for higher level thinking to occur when the basic levels of the concept are not fully attained. When higher level thinking does not occur, it makes it difficult for the educator to plan future lessons, because of the inability to build off the previous lesson.

Theoretical and Conceptual Frameworks

This thesis is firmly grounded in the ideals of the constructivist theory of learning. In the article, Performance Assessment Design Principles Gleaned from Constructivist Learning Theory (Part 1), Zane (2009) discusses the guidelines for assessment under the constructivist theory. According to Zane (2009),”Constructivist theory clearly suggests

that domains should define real-world, integrated tasks as opposed to listing a series of content topics or decontextualized knowledge components or a series of individual decontextualized behaviors” (p.83). This directly relates with the usage of math journals. Math journals are an authentic assessment in which the students can relate concepts through their life experiences. Vygotsky (1978) believes that language is the outward expression of thinking, the way one makes meaning out of one’s thoughts (p.72).

This thesis also directly aligns with the tenets of the Conceptual Framework of the LaGrange College Education Department (2008), which are (1) Enthusiastic engagement in learning, (2) Exemplary professional teaching practices, and (3) Caring and supportive classrooms and learning environments. This thesis directly relates to Competency Cluster 1.2: knowledge of curriculum where it states “Candidates relate content areas to other subject areas and connections in everyday life to make subject matter meaningful” (LaGrange College Education Department, 2008, p.4). Math journals are an effective way to promote writing across the curriculum, and they also help students relate curriculum to daily life experience. This thesis also aligns with Cluster 2.3, assessment skills, where it states “Candidates monitor and adjust strategies in response to student feedback” (LaGrange College Education Department, 2008, p.7). According to Kiorala (2002), math journals are an effective way for teachers to provide feedback and make appropriate future plans for lesson in response to the students understanding. The LaGrange College Education Department’s (2008) Conceptual Framework Competency Cluster 3.1, covering reflection, states “Candidates reflect on the effects of choices and actions on others (students, parents, and other professionals) to improve their own practice. This study will have a strong relationship with this element. Dusterhoff (1995) elaborates on how math journals can be used for students to interview parents and members of the community in order to build relationships and show how math does have a bearing in the everyday lives of people they know and can relate.

This study also aligns with NBPTS Proposition Three that states, “Teachers are responsible for managing and monitoring student learning” (LaGrange College Education Department, 2008, p.12). Journals are an effective way to track student progress, and simultaneously provide essential feedback to students who are scared to ask questions in front of the class (Koirala, 2002). Student learning reaches a high point when a risk taking environment can be established, and this also leads to students having a higher self-esteem and self image.

An alignment between this study and the Georgia standards for teachers as outlined in The Conceptual Framework (LaGrange College Education Department, 2008) which is defined as “professional dispositions for candidates.” This standard is relevant because teacher attitudes can positively or negatively affect the classroom. There is empirical evidence that suggests that teacher input has an impact on student performance (Singh & Stoloff, 2008). Journaling is an effective way to foster relationships with students through written communication.

Focus Questions

The effects that journals have when incorporated into math class were researched in this study. There are several aspects between reading and writing that can impact math scores, but this study will focus on three questions. The following focus questions were used in this study:

1. How can math journals be successfully implemented in a third grade classroom?

2. Can the use of math journals positively affect test scores?

3. How will writing during math class affect the attitudes of teachers and students about math?

Overview of Methodology

The purpose of the study is to determine if implementing journals in mathematics classroom will significantly impact test scores. Mixed methods were used in order to collect data for the study. Mixed methods are composed of qualitative data and quantitative data. The study was conducted in the third grade classroom of a low socioeconomic school in LaGrange, GA. The study did obtain validity, reliability, dependability, and an absence of bias. The data gathered from the study was analyzed by the focus question in which it was gathered for and the data was analyzed holistically. The holistic analysis focused on the concepts of validation, credibility, transferability, and transformational qualities.

Human as Researcher

The qualifications and credentials of the researcher are important to the success and validity of the study. I am a recent graduate from LaGrange College with a B.A. in Early Childhood Education. I teach third grade at a low socioeconomic school in Troup County. I believe that the incorporation of reading and writing across the curriculum is essential in developing higher level thinking skills. The teachers’ willingness to differentiate instruction and interweave reading and math can greatly impact the success of students on state mandated standardized tests.

CHAPTER TWO: REVIEW OF THE LITERATURE

Use of Math Journals in the Classroom

Utilizing writing in the mathematics classroom is a practice that is becoming more common in schools today. Burns and Silbey (2001) state, “It [math journal] helps students stretch their thinking and make sense of problems that can sometimes leave them confused or frustrated” (p.18). The marriage of mathematics and writing is not yet fully ordained by the entire community of educators in the field, but the two disciplines are starting to be merged in many school systems. There are several studies that show writing can have a positive effect on one’s ability to learn in the math classroom. According to Carter (2009), students should be precise with mathematical language and be able to analyze other people’s mathematical strategies, and the use of math journaling is an effective way to meet both skills.

There are several ways that writing can be implemented in the mathematics classroom, but journal writing is the most common method. Math journals help students to better grasp both the concepts and vocabulary centered on mathematics education. The use of math journals as diagnostic tool in determining student understanding of concepts is amazing (Moore, 1991, p.7). The use of math journals help students to understand the idea that math is all around them, and not a subject limited to the classroom. The study of Burns (1998) was able to turn real life problems into activities through the use of journaling giving students greater understanding that mathematics will be used in the student’s daily life.

Another study by Lauritzen (1992) details a benefit of math journals in the classroom. The study explains that stories are the most effective way that children make content meaningful. When students are able to write about their mathematical knowledge they demonstrate they have a higher understanding of mathematical concepts and vocabulary. According to the study there are three important ideas to monitor about each prompt response. The three ideas are relevance, reality, and expressiveness. Relevance being is the response relevant to the prompt, reality being was the response true, and expressiveness being the student’s ability to successfully communicate their ideas to the reader.

Positive Effects of Journal Writing for Teachers

The use of math journals allows students the opportunity to reflect their understanding of concepts obtained in mathematics class. This allows teachers to have an authentic assessment for each student, and better prepare lessons to ensure each student’s success. The writing prompts also help to feed classroom discussion by allow student adequate to reflect upon a given problem or situation (Burns, 2001). The teachers also benefit from the students use of math journals. The teachers are able to give individualized feedback to every student, and they are able to diagnose problems or misconceptions early in the learning process. This allows more time for students to have remediation or interventions on concepts that are troubling to a struggling student. Manning and Manning (1996) state, “When teachers observe students' writing, they can make an evaluation of students' thinking that may be useful for supporting future learning” (p.107).

Math journaling also allows teachers the ability to quickly diagnose problem areas for students before the final assessment. The use of math journals allows for quick remediation (Moore, 1991). The ability to give quick remediation helps to keep the students in equilibrium. The longer the student is in disequilibrium the more likely the student is to become frustrated and stop trying to obtain the concept. The proper implication with constant feedback will help to support the student’s attainment of knowledge.

Positive Effects of Math Journaling with Students

Math journals are being instituted in classrooms all across the county with much success, and journal writing in math has been supported by several research studies (Koirala, 2002). These benefits include critical thinking, better understanding of mathematical concepts, increased problem solving skills, and increased vocabulary of the subject. According to Manning and Manning (1996), journaling is a powerful tool for thinking in math, and it will also improve the students writing abilities.

Critical thinking is a very important part of the math learning process, and journaling can help to increase this ability. Garside (1994) believes that students need to foster critical thinking by making connections between concrete and abstract ideas, and journal writing is the way to bridge these two ideas. Writing solidifies knowledge by making abstract concepts and ideas more concrete. This is supported by Wells and Reinertsen’s (1993) study that showed, “writers often do not know what they know until they have written it, reread it, and clarified it further for themselves” (p. 182). Math journals are not limited to only improving critical thinking skills.

Understanding of mathematical concepts is an ability not every person can gain full understanding by listening to a lecture. Journaling allows a student to gain understanding through self reflection and dialogue. Using journals for expressive writing increases the understanding of concepts because it makes the learning experience more active and personal (Wason-Ellam, 1987. Students who have strong writing abilities but are limited in math are able to benefit greatly from the use of math journals. According to Carter (2009), these type students are able to “sneak their literary talents into writing during math class (p.610). Journaling not only increases understanding, but then aids the students in their problem solving abilities.

Problem solving skills are an essential component in being successful in mathematics. Journaling helps to aid problem solving skills through allowing the students to see and review their thought process. When students reflect on their problem solving methods it causes the students to think at a deep level (Koirala, 2002). The student examples from Koirala’s study show the impact that journal writing can have on a student’s problem solving abilities. Journal writing not only helps with problem solving abilities, but also with the development of vocabulary.

Vocabulary development is a crucial component to a student’s ability to attain new concepts, because without vocabulary the student will not be able to be precise with their mathematical language or examine other strategies (Carter, 2009). Vocabulary sets the foundation for learning, and when this step in the process is not fully mastered it will lead to frustration and confusion. Journaling provides an answer to this problem because it forces students use mathematical language in order to express their thoughts and ideas (Garside, 1994, p. 3).

Math Journals Effect on Test Scores

In today’s society, all decisions regarding curriculum must be supported by data to positively affect test scores. According to Fletcher et al. (2008) daily practice of writing in math will lead to being able to decode word problems on a more consistent basis. Being able to decode word problems on a constant basis will increase higher order thinking skills and, in turn, the students will achieve higher test scores. The study focuses on mathematical cognitive skills. This differs from mathematical computational skills due to the addition of linguistic information. The study does incorporate the tier system as seen in the Troup County School System. The schema based approach to math journaling can lead to higher standardized test scores (Fletcher et al., 2008).

Math journals also increase math test scores by making the learning process more personal. Jitendra, Xin, and Deatline-Buchman proved this in their 2005 study of twenty-two middle school children. The study compared schema-based instruction to general instruction. The journaling prompts for the schema-based group related the information to the student’s daily life and showed how the skills could be used outside the classroom. The general group’s prompts related to the topic but were abstract in nature and were not personalized for the intended audience. The results showed the “SBI group performed significantly better than students in the GSI group on all measures of acquisition, maintenance, and generalization” (Jitendra, Xin, & Deatline-Buchman, p.189).

The study conducted by Hart and Thompson in 2009 demonstrated that math scores are related to reading skills. According to the study few interventions have proven to be successful when the student has an absence of phonological decoding, processing speed, and fluency (Hart & Thompson, 2009). The study also showed that problems in reading and math are not situational but are genetic. A genetic covariation between math and reading abilities has been traced to a correlation of .8 in parents and off spring. This shows scientific research linking the deficiencies in reading and math on the genetic level.

Positive Students Attitudes towards Math Journals

Math journals are an effective way for teachers to gauge student attitudes about the subject matter being covered. According to Kiorala (2002), “Math journals not only help instructors in understanding students’ feelings, likes, and dislikes about classes but also helps students to demonstrate their mathematical thinking processes and understanding” (p. 1). Students that possess literary skills will be more responsive to math journaling than a student that does not possess adequate vocabulary and writing skills.

Dusterhoff (1995) also discusses student attitudes toward math journaling. According to the study student’s attitudes towards writing in math increased in a positive way. This occurs because writing in math helps to spark curiosity about the applications of mathematical concepts outside of the classroom. The study also discusses how students appreciate the personalized feedback that is provided by the teacher. Taking the spot light off the student’s asking a question helps to create a better risk taking environment.

Implementing writing in math has been shown to increase the self-efficacy of low achieving students. The study that supports this idea was conducted by Baxtor, Woodward, and Olsen (2005) which claims that writing provided struggling students with a way to make sense of mathematical communication, thus leading to higher self-efficacy and a more productive attitude. Students that are low academically achieving also tend to be passive in small group environments. Journaling allows the students a form of asking a question without being put on the spot or embarrassed because they do not understand a concept from class.

Students also believe that math journals help them to better understand the information being taught. When asked why we do not just use calculators in math, one student in the Baxtor, Woodward, and Olsen (2005) study said “It’s not necessary to use a calculator. It doesn’t help your knowledge” (p.124). The students begin to understand the mathematical process through journaling, and it turn helps them to rationalize the use of mathematical knowledge.

Opposing Views on Math Journals

Math journals have been proven through research to help students in several ways, but math journals do have a major drawback. The time it takes to read every student’s journal and give individualized feedback can be overwhelming for some educators. Koirala’s (2002) study states, “teachers need a large amount of time to examine student journals and provide feedback” (p. 1). If a teacher has a large amount of students, then math journals may not be a manageable strategy.

Another problem associated with math journals is the difficulty the students may initially have with writing journal entries. Students who are weak in writing may believe they are unable to complete the assignment. Carter’s (2009) study elaborates on the idea that the missing link for students who struggle with math journals is their inability to transfer writing skills into the math classroom. The feeling of inadequacy the student has may lead to the student not wanting to participate in the assignment, and becoming further behind in the subject. This is supported by Baxter et al.’s (2005) study, which found that, “Problems arise, however, when students do not or cannot describe their mathematical reasoning in a coherent manner” (p.120).

Negative Student Attitudes about Journal Writing

According to Countryman (1992) some students have negative attitudes toward math journaling and any other form of writing. There are students that enjoy math more due to the lack of writing. Countryman notes one student complaining by saying “Why do we have to write? This is math class; not English” (p.2). There is a sect of math teachers that are reluctant to encompass writing in their math class, because they were probably drawn to math due to the lack of writing. Students fail to see the connection of the two disciplines because they have always been separate in the past.

A study conducted by Corley (2000) evaluated students attitudes about journaling. Corley came to the conclusion that all the negative attitudes stemmed around four main points. The four points were remembrance problems, motivation issues, access issues, and cognitive abilities. The study showed that all the students that reported having a negative attitude about journal writing fell into one of these four categories. When students were asked to give suggestions to for the process to help their attitude the answers were for elimination of the process. Student’s that have a negative attitude about journaling tend to dislike the writing the process in all facets.

Journal Writing and Research

The review of the literature has reviewed many aspects to math journaling. Journal writing has been beneficial to both students and teachers in their own ways. Although beneficial, attitudes about math journaling have greatly differed from student to student and teacher to teacher. All of the research presented will assist in the development of a comprehensive research study to further assess the effectiveness of math journaling. The research study presented will collect surveys, student work samples, and monitor student progress. The raw data will then be analyzed in order to see in math journals have a significant impact on test scores in the mathematics classroom.

CHAPTER THREE: METHODOLOGY

Research Design

The purpose of this research study is to determine if implementing journals in mathematics will significantly affect test scores. The study used an action research approach. Action research, as defined by MacNaghton (2009) is “a cyclical process of ‘think-do-think’ research and create change” (p. 1). The study used a control group and a treatment group in order to assess the statistical significance of math journaling.

Mixed methods were used in order to collect data for the study. Quantitative data is described by Greig, Taylor, and MacKay (2007) as a complex are varied field of inquiry. The quantitative data used in this study were a pre-post test and surveys to both teachers and students. The pre-post assessments were analyzed using a dependent t-test in order to determine statistical significance. The surveys from both teachers and students were analyzed using a chi square test. Qualitative data is described as research that answers questions with reference to number or quantities (Greig et al, 2007). The qualitative data from this study were obtained through a reflective journal. The reflective journal was used daily and recorded observations from the study. The journal is analyzed through coding themes that align with the focus questions.

Setting

The research study took place in an elementary school located in LaGrange, GA. The action research was conducted in the classroom in which I taught. The school was composed of 392 students, of which 86 percent of the students were eligible for free and reduced lunch. The racial composition of the school was 62 percent African American, 31 percent Caucasian, and 3 percent Hispanic. The study specifically focused on one home room classroom. Permission to conduct the study was granted by the Troup County School System, the principal of the school, and through LaGrange College’s IRB protocol.

Subjects and Participants

The students involved with this research study were all third grade students of mixed ability levels. The students came from one home room class and totaled 12. Of the 12, 9 students were male and 3 were female. The racial composition of the class was 10 African American and 2 Caucasian students. All of the students whom participated in the survey were eligible for free and reduced lunch.

The students were chosen for the study because they were all my students. The students from my classroom served as both the control and treatment group. There were also 12 teachers who participated in an anonymous survey. The teachers all taught in grades three through five. The instructional plan was also reviewed by a building level administrator from my school.

Procedures and Data Collection Methods

The action research study used mixed-methods in order to fully answer and collect data to answer the focus questions. The use of the mixed methods is shown in Table 3.1. Mixed-methods refer to the use of both quantitative and qualitative to acquire data in a study (Bruce, 2010).

Table 3.1 Data Shell

|Focus Questions |Literature Sources |Type: Method, Data, Validity; |How are data analyzed|Rationale |

|How can math journals be|Moore (1991) |Type of Method: Instructional |Coded for themes: |Looking for categorical |

|successfully implemented| |Plan Rubric and Interview |Reoccurring |and repeating data that |

|in a third grade |Lauritzen | |Dominant |form patterns of |

|classroom? |(1992) |Type of Data: |Emergent |behavior |

| | |Qualitative | | |

| |Burns (1998) | | | |

| | |Type of Validity: | | |

| | |Content | | |

|Can the use of math |Fletcher et al. |Type of Method: |Independent-T |To determine if there |

|journals positively |(2008) |Teacher made Test | |are significant |

|affect test scores? | | | |differences between the |

| |Jitendra & Xin |Type of Data: | |means of two separate |

| |(1997) |Interval | |groups |

| | | | | |

| |Hart & Thompson |Type of Validity: | |To determine if there |

| |(2009) |Content | |are significant |

| | | | |differences between |

| | | | |means of one group |

| | | | |tested twice. |

| | | |Dependent-T | |

| | | | |To measure the magnitude|

| | | | |of the treatment effect.|

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | |Effect Size | |

| | | | | |

|How will writing during |Dusterhoff (1995) |Type of Method: |Coded for themes: |Looking for categorical |

|math class affect the | |Reflective Journal and Surveys |Reoccurring |and repeating data that |

|attitudes of teachers |Koirala (2002) | |Dominant |form patterns of |

|and students about math?| |Type of Data: |Emergent |behavior |

| |Countryman (2002) |Qualitative | | |

| | |Ordinal | |Desire to find which |

| | | |Chi Square |questions are |

| | |Type of Validity: | |significant. |

| | |Construct | | |

The first focus question was answered through a peer review of the action research study’s instructional plan (see Appendix A). The plan was evaluated using a rubric (see Appendix B) which prompted elicit narrative responses for areas that needed improvement by a colleague. The peer review of the instructional plan was performed in order to ensure the instructional plan contained correct content and was absent of bias.

The action of the research consisted of the daily implementation of math journals. The math journaling process occurred during a small group math session. The journal prompts included the use of open ended questions, acrostics, what I thought you taught, and quad clusters. The prompts were specific to the material covered early that day during whole group math. The students were given a thirty minute block where they were able to read the prompt, reflect, and then write about the prompt. I responded to each students prompt daily to optimize the effectiveness of the treatment. The students were allotted time before class in the morning to read my responses and ask questions. This process occurred over ten school days and consisted of ten total prompts. During these ten days I also recorded instances of importance or difficulties I experiences in my reflective journal. The reflective journal responses were then coded for recurring themes.

Teacher and student surveys were used to answer the third focus question. The surveys were issued to all teachers (see Appendix D) in third grade through fifth grade at my school. As part of the study, the student’s who served as subjects in the study were given a student survey (see Appendix E). The purposes of the surveys were to assess the attitudes of teachers and students about the use of math journals. Surveys can be used in research to help “determine relationships that exist between specific events” (Greig et al, 2007, p.128).

A reflective journal (see Appendix E) was also used to help answer focus question three. I used the journal to write down my daily reflections about the study. Bruce (2007) describes the use reflections as an integral part of action research. The journal helped me to assess the effectiveness of the lessons and the attitudes of the students.

Validity, Reliability, Dependability, and Bias

Validity is considered by many, including Popham (2008), to be the most significant concept in terms of assessment. Validity, as defined by Popham, is “the degree to which evidence supports the accuracy of test-based inferences (interpretation) about students” (p. 504). Validity for this study was obtained by analyzing the focus question with three types of validity. The types of validity assessed for this study were content validity, construct validity, and criterion validity.

Content validity is defined by Popham (2008) as, “Evidence indicating that an assessment instrument suitably reflects the content domain it is supposed to represent” (p. 501). Content validity was used to validate focus questions one and two. Focus question one was validated by content validity through the use of the instructional plan. The instructional plan outlines the lessons of the study and is strictly related to discipline by way of the Georgia Performance Standards. Focus question two also uses content validity for validation. Focus question two is validated by the use of a pre-post test to demonstrate student attainment of the concepts from instructional plan.

Construct validity is defined by Popham (2008) as, “Empirical evidence that (1) supports the posited existence of a hypothetical construct and (2) indicates an assessment device does, in fact, measure that construct” (p.500). Construct validity was use to validate focus question one and three. Focus question one was validated by allowing a colleague the opportunity to evaluate the instructional plan in order to gain feedback and optimize the effectiveness of the study. Focus question three was validated by the use of a reflective journal and surveys, that provided, an insight into student and teacher dispositions of math journaling.

Criterion validity is defined by Popham (2008) as, “An external variable that serves as to the to-be-produced target for that predictor exam, such as an aptitude test” (p.501). Focus question two was validated by criterion validity through the use of a pre-post test. This allowed for the same test to be given before and after treatment to show the gains of the students.

Reliability is defined by Popham (2008) as, “the consistency of results produces by measurement devices” (p. 503). Reliability is used to make sure that research is consistent and can be repeated. Focus question two achieves reliability in two ways. The first way reliability was obtained was through the Test-Retest Correlation. The pre-post test makes focus question two reliable. The second way reliability was obtained was through using Cronbach’s Alpha to evaluate the surveys issued in the study.

Dependability is term used for the consistency of qualitative data. Dependability was gained in this study through several ways. The thesis contains a detailed methods section that gains the study dependability. Dependability is also gained through maintaining well organized raw data. The length of time for the data collection in this study is persistent and prolonged gaining further dependability for the study.

Bias can be described as being unfair. Popham (2008) states that, “Bias really can be a serious shortcoming of tests” (p. 119). In this study, all instruments were checked for fairness or offensiveness. The study was designed to objective and fair in all possible ways.

Analysis of Data

Data gathered from the study were analyzed according the focus question in which they corresponded. The qualitative data from focus questions one and three were analyzed by coding for themes. The quantitative data from focus question two and three were analyzed statistically. The data were then analyzed holistically in terms of validation, credibility, transferability, and transformational.

Focus question one was collected data through the use of the instructional plan and rubric. The instructional plan was given to colleague with instruction to evaluate the plan using the rubric to provide feedback. The feedback was analyzed to determine if any changes needed to be made in order to increase the effectiveness of the instructional plan.

The results from the pre-post test were analyzed using a dependent-t test. The purpose of the dependent-t test was to test for significant increases after the treatment of the study. An effect size calculation (Effect Size r) was also necessary to analyze the magnitude of the treatment effect on the group. The rationale for this was to find statistical significance between the gains in the pre-post test.

A reflective journal was kept during the duration of the study, which was analyzed by coding for themes. The themes were then analyzed in order to gauge the dispositions of both the students and me during the study. The rational for this is to look for categorical and repeating data that form patterns of behavior. The students in the study were given a survey before and after treatment. The results from the survey were analyzed statistically by using a Chi Square. According to Salkind (2010), “The chi-square test involves a comparison between what is observed and what would be expected by chance” (p.313).The Chi Square was able to determine if the survey questions were statistically significant at one of three levels. The three levels were p ................
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