Math Journals i

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-ChairEducation Department Education Department

Math Journals ii

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

Math Journals iii

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.

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Table of ContentsAbstract……………………………………………………………………………..…….iii

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

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

Chapter1: Introduction…………………………………………………………………….1Statement of the Problem………………………………………………………….1Significance of the Problem……………………………………………………….2Theoretical and Conceptual Framework…………………………………………..3Focus Questions…………………………………………………………………...5Overview of Methodology………………………………………………………...5Human as a Researcher……………………………………………………………6

Chapter 2: Review of the Literature………………………………………………………7Use of Math Journals in the Classroom…………………………………………...7Positive Effects of Journal Writing for Teachers………………………………….8Positive Effects of Math Journaling with Students……………….……………….9Math Journals Effect on Test Scores…………………………………………….10Positive Student Attitudes Towards Math Journals……………...………………12Opposing Views on Math Journals……………………………………………....13Negative Student Attitudes About Journal Writing……………………………...14Journal Writing and Research……………………………………………………14

Chapter 3: Methodology……………………………...………………………………….16Research Design………………………………………………………………….16Setting…...……………………………………………………………………….16Subjects and Participants…………………………………………………...……17Procedures and Data Collection Methods……………………………………….17Validity, Reliability, Dependability, and Bias…………………………….……..20Analysis of Data……………………………………………………….…………22

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

Chapter 5: Analysis and Discussion of Results………………………………………….36Analysis……………………………………………………….………………….36Discussion………………………………………………………………………..43Implications………………………………………………………………………44Impact on Student Learning ……………………………………………………..46Recommendations for Future Research………………………………………….46

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

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

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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

Math Journals 1

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

Math Journals 2

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

Math Journals 3

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

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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

Math Journals 5

(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.

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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.

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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

Math Journals 8

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

Math Journals 9

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

Math Journals 10

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

Math Journals 11

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.

Math Journals 12

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

Math Journals 13

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

Math Journals 14

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

Math Journals 15

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.

Math Journals 16

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

Math Journals 17

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).

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Table 3.1 Data Shell

Focus Questions

Literature Sources

Type: Method, Data, Validity;

How are data analyzed

Rationale

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

Moore (1991)

Lauritzen(1992)

Burns (1998)

Type of Method: Instructional Plan Rubric and Interview

Type of Data: Qualitative

Type of Validity:Content

Coded for themes:ReoccurringDominantEmergent

Looking for categorical and repeating data that form patterns of behavior

Can the use of math journals positively affect test scores?

Fletcher et al. (2008)

Jitendra & Xin (1997)

Hart & Thompson(2009)

Type of Method:Teacher made Test

Type of Data:Interval

Type of Validity:Content

Independent-T

Dependent-T

Effect Size

To determine if there are significant differences between the means of two separate groups

To determine if there are significant differences between means of one group tested twice.

To measure the magnitude of the treatment effect.

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

Dusterhoff (1995)

Koirala (2002)

Countryman (2002)

Type of Method:Reflective Journal and Surveys

Type of Data:QualitativeOrdinal

Type of Validity:Construct

Coded for themes:ReoccurringDominantEmergent

Chi Square

Looking for categorical and repeating data that form patterns of behavior

Desire to find which questions are significant.

Math Journals 19

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

Math Journals 20

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

Math Journals 21

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.

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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

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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<.05, p<.01, and

p<.001. The rationale for this is to find statistical significance between the gains in the

pre-post test.

The study was also analyzed holistically. This analysis moves away from

individual focus questions and focuses on the study as a whole. The holistic analysis of

the data focused on the concepts of validation, credibility, transferability, and

transformational.

Validation is closely related to accuracy and consistency. There are two types of

validation that were used for this study. The first was consensual validation. This was

gained through the IRB of Lagrange College and through the Education Department

faculty review. The second form of validation was epistemological validation. This

validation was gained through the literature review found in chapter two of this thesis.

Credibility is a concept defined as triangulation. Eisner (1991) calls this

‘structural corroboration,’ where a confluence of evidence comes together to form a

compelling whole. Credibility was obtained through the structural corroboration by using

multiple sources of data from mixed methods. Fairness is evident in the literature review

where opposing points of view to math journaling are presented, and rightness-of-fit is

presented in Chapter Five of this thesis where all the data are discussed holistically.

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Transferability is the process in which others may apply a study to different

situations. This can only occur after a claim of credibility has been established.

Referential adequacy refers to the research being able to be replicated easily by others.

This was obtained through the detailed methodology section of the thesis.

Transformational or ‘catalytic validity’ (Larther as cited by Khinchloe &

McLaren, 1998) is the degree to which a researcher anticipates his or her study to shape

and transform the participants. With the use of math journaling, the students in this study

were anticipated to have a greater understanding of the subject taught and also an

increase in higher order thinking skills.

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CHAPTER FOUR: RESULTS

The results from this research study are presented, in order, by focus question.

The focus questions of this research study were (1) How can math journals be

successfully implemented in a third grade classroom, (2) Can the use of math journals

positively affect test scores, and (3) How will writing during math class affect the

attitudes of teachers and students about math?

Focus question one was answered through education department faculty review,

through the use of a rubric (see Appendix B), and an interview with the colleague that

evaluated the instructional plan. The qualitative data that were collected were then coded

for the three themes mentioned above in order to be analyzed.

The recurring themes that emerged from all responses of the rubric, interview, and

faculty review were (1) student motivation was not addressed, (2) how will mathematical

vocabulary be taught, (3) preparation for journal writing, and (4) vagueness of the rubric.

The most common theme of the raw data for focus question one was that student

motivation was not addressed. This was mentioned eight times on the scored rubric and

six times during the interview. Mr. Smith, a pseudonym, stated, “It doesn’t matter how

great the instructional plan is put together; if you do not address the issue of how you’re

going to keep your students motivated you’re going to struggle with the math journals.”

The second most common theme from the raw data was the manner in which

mathematical vocabulary was to be taught. During the interview, it was mentioned on

four occasions that the way in which the vocabulary was taught should be chosen very

carefully. This was also mention in the rubric twice that the scorer wanted to know the

strategy that was used during the study. According to Mr. Smith, “The strategy you

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decide to use for helping the student to master the vocabulary associated with your topic

will be very crucial to the success of your study.”

The second least common theme was how the students were to be prepared to

write in journals. This was mentioned twice in the interview and once on the scored

rubric. Mr. Smith stated, “Journaling is a year long process, and if you do not prepare

your student to write in their journals you entire study will be spent teaching students

how to write in a math journal.”

The least common theme noticed was the vagueness of the rubric. The LaGrange

College professor who looked over my rubric provided the feedback “re-word the

questions on the rubric to elicit a narrative response.” The scored rubric mentioned this

once and this was discussed during the interview as well. Mr. Smith said, “I would have

like to have seen the lesson plans or at least a more detailed overview of the procedures.

The procedures listed in your instructional plan are very general and vague.”

Focus question two was answered through pre-post tests. The pre-post tests were

analyzed using both dependent and independent t-tests. The quantitative data were

analyzed using statistics in order to determine if there were statistical differences between

the treatment and control group, and to determine if there were any statistically

significant gains from the treatment group over the control group. The effect size of both

groups was also calculated to measure the magnitude of the change.

Quantitative data were used to answer focus question two. Inferential statistics

were used to analyze pre- and post-tests for both the control and treatment groups. The

reliability between the pre-post tests as determined using the Pearson Correlation. The

results of the statistical tests were analyzed to determine if the groups were significantly

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different and to determine if there were statistical differences between the control and

treatment groups. The calculations for both the independent and dependent t-tests are

provided in the tables below. The effect size was also calculated using Effect Size r for

dependent t- tests and Cohen’s d for independent t-tests. The effect size measures the

magnitude of the treatment, but does not take sample size into account (Salkind, 2010).

Table 4.1- Independent T-Test Comparing Pre-Tests

t-Test: Two-Sample Assuming Unequal Variances

  Treatment Pre Control PreMean 60.25 55.41666667Variance 569.2954545 661.5378788Observations 12 12Hypothesized Mean Difference 0df 22t Stat 0.477240999P(T<=t) one-tail 0.318948702t Critical one-tail 1.717144335P(T<=t) two-tail 0.637897404t Critical two-tail 2.073873058  

t(22) = 0.47, p > .05

An independent t-test was run to find if there was no significant difference in the

test score between the two groups (Salkind, 2010). In Table 4.1, the results from the

independent t-test comparing the control and treatment groups pre-tests show that t(22) =

0.47, p > .05. This means the obtained value 0.47 is less than the critical value of 0.63.

The results from the independent t-test indicate that the null hypothesis be accepted. The

null hypothesis was that there is no significant difference between the scores occurred

between the two groups than what would occur by chance. Therefore, the groups cannot

be considered to significantly different.

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Table 4.2- Dependent T-Test for the Treatment Group

t-Test: Paired Two Sample for Means

  Pre-Test Post-TestMean 60.25 83.75Variance 569.2954545 173.1136364Observations 12 12Pearson Correlation 0.577645362Hypothesized Mean Difference 0df 11t Stat -4.177558981P(T<=t) one-tail 0.000771449t Critical one-tail 1.795884814P(T<=t) two-tail 0.001542897t Critical two-tail 2.200985159  

T(11) = 4.17, p < .05

In Table 4.2, the data from the dependent t-test for the treatment group were

analyzed using a dependent t-test. The dependent t-test was used in order to determine

significant gains that could not occur by chance from the pre-test to the post-test

(Salkind, 2010). The effect size was then calculated using effect size r. The results from

the dependent t-test for the treatment group show that t(11) = 4.17, p < .05. This means the

obtained value 4.17 is greater than the critical value of 0.0008. The results from the

dependent t-test indicate the null hypothesis is rejected. The null hypothesis that there is

no statistical difference in the gains that occurred between the pre- and post-test than

what would occur by chance. Statistical significance is found between the pre- and post-

test. The effect size is r = 0.51, which is a large effect, meaning it has a large magnitude.

The Pearson Correlation for the pre-post tests was 0.58, which is a fairly strong reliability

between the two tests.

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Table 4.3 - Dependent T-Test for Control Group

t-Test: Paired Two Sample for Means

  Pre-Test Post-testMean 55.41666667 82.91666667Variance 661.5378788 223.719697Observations 12 12Pearson Correlation 0.82292182Hypothesized Mean Difference 0df 11t Stat -5.999909844P(T<=t) one-tail 4.46364E-05t Critical one-tail 1.795884814P(T<=t) two-tail 8.92728E-05t Critical two-tail 2.200985159  

T(11) = 6.00, p < .05

The data from the pre-post test for the control group were analyzed using a

dependent t-test. In Table 4.3, the results from the dependent t-test for the control group

show that t(11) = 6.00, p < .05. This means the obtained value of 6.00 is greater than the

critical value of 1.79. The results from the dependent t-test mean the null hypothesis that

there is no statistical difference in the gains that occurred between the pre- and post-test

than what would occur by chance is rejected. Significance is found between the pre- and

post-test. The effect size was then calculated using effect size r. The effect size is r =

0.55, which is a large effect size, meaning it has a large magnitude. The Pearson

Correlation for the pre-post test was 0.82, which is a very strong reliability between the

tests.

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Table 4.4 – Independent T-Test for Post-Tests

t-Test: Two-Sample Assuming Unequal Variances

  Treatment Post Control PostMean 83.75 82.91666667Variance 173.1136364 223.719697Observations 12 12Hypothesized Mean Difference 0df 22t Stat 0.144912318P(T<=t) one-tail 0.443049756t Critical one-tail 1.717144335P(T<=t) two-tail 0.886099513t Critical two-tail 2.073873058  

T(22) = 0.14, p > .05

The data from the post tests of the control and treatment group were analyzed

using an independent t-test. In Table 4.4, the results from the independent t-test for the

control group show that t(22) =0.14, p > .05. This means the obtained value of 0.14 is less

than the critical value of 0.89. The results from the independent t-test mean the null

hypothesis that there is no significant difference in the gains that occurred between the

control and treatment group than what would occur by chance is accepted. Significance is

not found between the two groups. The effect size was measured using Cohn’s d. The

effect size is d = .06, which is a small effect size, meaning it has small magnitude.

Focus question three was answered through both quantitative data and qualitative

data. The quantitative data were created through using a chi square for the pre- and post-

survey (Table 4.5) to test for statistically significant questions with-in the survey that was

given to the students. The survey that was given to the teachers was also analyzed using a

chi square (Table 4.6). The surveys were also analyzed quantitatively in order to

determine Cronbach’s Alpha using the responses from each of the three different surveys.

Testing for Cronbach’s Alpha shows the correlation between each test item with total

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score for each participant to make sure the test items measure their intended purpose

(Salkind, 2010). The qualitative data came from a reflective journal that was kept daily to

record events from during the research. The reflective journal was coded for themes in

order to be analyzed effectively.

The first survey given was the pre-survey to the twelve students participating in

the research study. Their answers were analyzed with a chi square to test for statistical

significance. The results are shown in the Table 4.5 listed below.

Table 4.5 Chi Square for Pre-Post Student Surveys

Items 2 – Pre-Surveyn = 12

2 – Post-Surveyn = 12

1. Journal writing in math class increases my understanding of mathematical concepts.

6 8.67 *

2. Journal writing helps me organize my thoughts

6.67 11.3 *

3. Journal entries in which I explain solutions to mathematical problems increase my understanding.

0.67 5.3

4. I feel comfortable communicating my thoughts to my teacher through journal writing.

3.3 12 **

5. I enjoy journal writing. 1.3 7.3

*p < .05, **p < .01, ***p < .001

The results from the chi square for the pre- and post student surveys did not reveal

many statistically significant questions. The pre-survey did not contain any questions that

were significant on any of the three levels. The post-survey found significance in three of

the five questions. Questions one and two were found to be significant at the p < .05

level. Question four however, was found to be significant at the p < .01 level. The items

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were significant due to the trend of response, because the students answered in a similar

enough way that could not have occurred by chance. The level of significance for each of

the questions mean that the majority of the students answered in a similar enough way

that the results could not be the result of chance.

Cronbach’s Alpha was used to test the internal consistency reliability for both the

pre- and the post-survey based on the answers given by each student. The test showed a

Cronbach’s Alpha of α = 0.64 for the pre-survey and a Cronbach’s Alpha of α = 0.84.

The results from both the pre-test and the post-test show a fairly strong level of

reliability.

The second survey given was the teacher survey. The survey was given to twelve

teachers in grades three, four, and five. All twelve teachers completed the survey. The

results from the surveys were analyzed using a chi square. The reliability of the test was

also measured using Cronbach’s Alpha. The results from the chi square can be seen in

Table 4.6 shown below.

Table 4.6 Chi Square for Teacher Survey

Items 2 – Teach Surveyn = 12

1. I believe that using journal writing in my math class could beneficial to my students understanding of mathematical concepts.

10 *

2. I am receptive to incorporating journal writing in my math classes.

12 **

3. If research proved that journal writing increased students’ academic achievement in mathematics, I would incorporate it into my lessons on a daily basis.

6

*p < .05, **p < .01, ***p < .001

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The results from the teacher survey showed two items to be statistically

significant. Item one and two both showed significance but at different levels. Item one

showed significance at the p < .05 level, the lowest level of significance. Item two

showed significance at the p < .01 level, which is the second highest level of significance.

The items were significant due to the trend of response, because the teachers answered in

a similar enough way that could not have occurred by chance. The level of significance

shows that the way in which the questions were answered has similarities that could not

have occurred by chance.

The internal consistency reliability was determined by using the Cronbach’s

Alpha test. The test showed the teacher survey had a Cronbach’s Alpha of α = 0.72. This

is a high level of reliability in the survey.

Focus question three was also answered using qualitative data. The qualitative

data were gathered through the use of a reflective journal that was kept during the

administration of the treatment to the treatment group. The journal was kept by me, and

was a way to record events that occurred during the duration of the treatment. The raw

data were coded for themes in order to be further analyzed. The three themes that the raw

data were coded for was dominant, recurring, and emergent themes.

The raw data proved to have six recurring themes. The recurring themes were (1)

the student’s were confused about the assignment, (2) student motivation, (3) the

assignment was seen as too difficult, (4) the students were confused by the vocabulary,

(5) the students were unable to communicate their thoughts accurately, and (6) negative

attitudes about writing.

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The recurring themes did have an impact on how the study was conducted. After

several days of the journaling the students became burnt out and did not want to complete

any more journaling prompts. This resulted in changes being made to the lesson plans

with-in the instructional plan in order to maintain student engagement. The most common

theme was negative student attitudes towards writing. This was noted on 72 occasions in

the two week study. The students, for the most part, did not enjoy the incorporation of

writing into math class.

Motivation was the second most recurring theme from the reflective journal, and

instances of student motivation were noted 52 times during the two week study. The

students found that writing was boring and they had a hard time understanding the

connection between writing and math. This led to their not wanting to complete the

assignment.

The third most common recurrence was that the students were confused or did not

understand the assignment. This was noted on 46 occasions; the students had a real hard

time transitioning into journal writing on a daily basis. They did not always understand

the prompts and this lead to the third most common theme that was noted.

The fourth most common theme was the students thought the assignment was too

difficult. There were 31 instances that student’s complained about the assignment being

to hard. The students had a very hard time trying to communicate their thoughts using the

mathematical vocabulary that was introduced during the study.

The second least common theme was that the students were confused about the

vocabulary of the lesson. During the journaling process, I was asked to define a

previously defined mathematical term 26 times. The students had a hard time

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understanding the mathematical jargon when trying to use the jargon to write a journal

response.

The least common theme was that students were unable to communicate their

thoughts accurately. There were 21 journal responses that were either off topic of

vocabulary was used incorrectly. These caused the prompts to not make sense. The most

common error was trying to write too much resulting in the student getting off topic and

not addressing the prompt. This occurred in 13 of the 21 responses mentioned. The other

eight responses use vocabulary incorrectly.

In this chapter, two types of data were presented, qualitative and quantitative. The

inferential statistics and qualitative analysis may have discrepancies. The information

presented in the results section are further analyzed in Chapter Five and the discrepancies

between the two forms of data are discussed.

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CHAPTER FIVE: ANALYSIS AND DISCUSSION OF RESULTS

Analysis

The data for focus question one were gathered through faculty review, the

instructional plan rubric, and an interview. The type of data used to answer focus

question one is was qualitative data. The data were then analyzed by coding for recurring

themes. The coded results were then examined to determine the changes to occur in order

to make the instructional plan more effective. The recurring themes that caused change to

the instructional plan are (1) student motivation was not addressed, (2) how will

mathematical vocabulary be taught, (3) preparation for journal writing, and (4) vagueness

of the rubric.

Student motivation was not initially addressed in the instructional plan. After the

interview with my colleague, it was decided that student motivation needed to be

prepared more in-depth. According to Countryman (1992), some students have negative

attitudes toward math journaling and any other form of writing. When the instructional

plan was created, I did not take into account that students would be in opposition to the

writing assignments. Once the issue was presented, the procedures section was changed

to incorporate story-based prompts to maintain student motivation and engagement in the

study.

Mathematical vocabulary was another cause for concern. The instructional plan

stated that mathematical vocabulary would be taught, but it did not state how it would be

taught. The way in which mathematical vocabulary is taught is important, because the

students are often unfamiliar with the words and their meaning. Vocabulary development

is a crucial component to a student’s ability to attain new concepts, because without

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vocabulary the student will not be able to be precise with their mathematical language or

examine other strategies (Carter, 2009). The instructional plan was altered to focus more

on how vocabulary would be taught. Vocabulary was taught through discussion, the use

of flash cards, and through examples of the word used in context.

Preparation for journal writing was also a theme that changed the way the study

was conducted. Preparing the students to write in journals was not a concept that was

originally placed into the instructional plan. After seeing the scored rubric and having the

interview it was determined that this was an important issue that needed to be addressed.

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. If the students did not know how to write in math journals, then the entire

study would be spent teaching them this skill. This problem was addressed by

incorporating math journals a few days a week for two months before the study. This

allowed the students to know the expectations of the quality of work associated with their

math journals before the study began.

The initial rubric was vague in nature. It was designed as an overview of the

instructional plan, but lacked the detail needed for someone to fully understand the study.

The rubric was also lacked questions that elicited a narrative response, according to a

LaGrange college professor. The instructional plan and rubric were both revised in order

to better convey the purpose of the study and a better holistic view of the study.

The second focus question was answered through the use of pre-post tests for both

the treatment and the control groups. The pre-post tests were analyzed using inferential

statistics. The two forms of statistical analysis that were used were dependent t-tests and

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independent t-test. These tests were used in order to determine if there was statistical

difference between the two groups (independent t-test) and if there were statistically

significant gains in each of the two groups (dependent t-test). The effect size was also

calculated. The reliability between the pre-post tests was determined using the Pearson

Correlation.

The first in dependent t-test that was run compared the pre-test of the treatment

group with the pre-test of the control group. The results were t(22) = 0.47, p > .05. this

simply means the obtained value of 0.47 is less than the critical value of 0.63. In this

case, the null hypothesis is accepted, because p > .05. The two groups do not have any

statistically significance difference. Since there was no significant difference in the two

groups they are said to be similar in nature and able to be compared (Salkind, 2010).

The treatment group and control group were both given post test similar to their

pre-tests. The pre-post tests from each of the control and treatment group were analyzed

using a dependent t-test to test for significant gains. The effect size was also calculated in

order to determine the magnitude of the treatment. Since dependent t-tests were used, the

effect size was calculated with the effect size r. The treatment groups results from the

dependent t-test were T(11) = 4.17, p < .05. This means the obtained value of 4.17 is

greater than the critical value of .0008. There was a significant difference from the pre-

test to the post-test. The effect size also helps to validate these data, Effect Size r = 0.51.

The effect size calculation shows that was a large magnitude associated with the

treatment. The Pearson Correlation for the pre-post tests was 0.58, which is a fairly

strong reliability between the two tests.

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The data from the control group were also analyzed using a dependent t-test and

the effect size was calculated using Effect Size r. The results from the control group were

t(11) = 6.00, p < .05. This means the obtained value of 6.00 is greater than the critical value

of 1.79. In this case the null hypothesis that there was no significant difference in the

gains of the test scores is rejected. Significance was found between the pre-test and the

post-test. This means that a math lesson can be successful without the use of math

journals. Effect size r = 0.55, this is large magnitude for the control group. The Pearson

Correlation for the pre-post test was 0.82, which is a very strong reliability between the

tests.

The final statistical test that was conducted to answer focus question two was the

independent t-test comparing the post-test of the control and treatment group. The results

from the test were T(22) =0.14, p > .05. The obtained value of .014 is less than the critical

value of 0.89, which means the null hypothesis that there were no significant gains

between the treatment group and control group was accepted. The magnitude can be

defined as Cohen’s d = 0.06, which is a small effect size. The results suggest that the use

of math journals did not have a significant impact of the test scores when the students

who used math journals as opposed to when they did not. I believe the results may have

been different if the math journaling process was established at the beginning of the

school year, and used on a daily basis. The two week study was too short for the desired

outcome to be reached. Koirala’s (2002) study supports this idea by discussing how the

math journaling is a time-consuming process.

Focus question three was answered using both qualitative and quantitative data.

The qualitative data for focus question three was created through the use of a reflective

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journal. I recorded daily entries in the reflective journal to record events I considered

important or interesting in terms of the study. The journal entries were analyzed by

coding for recurring themes. This six recurring themes were listed in Chapter Four of this

thesis.

Negative student attitudes about writing were noted on 72 occasions during the

two weeks study. The students do not enjoy the writing process in any facet. According

to Countryman (1992) some students have negative attitudes toward math journaling and

any other form of writing. This was evident in my classroom.

The students confusion about the assignment was a cause for concern. If the

student’s did not fully understand what was expected of them, then the assignment loses

credibility. This resulted in me spending several hours a day reading all of the journals to

provide quick feedback for students. Koirala’s (2002) study states, “teachers need a large

amount of time to examine student journals and provide feedback” (p. 1). Even though I

spent most of free time reading and responding to journals in order to clarify expectations

and directives, there were still some students that did not fully understand all of the

assignments.

Student motivation was the third most common theme noted in the reflective

journal. There were 52 noted incidents of student motivational issues documented during

the research study. The students did not like the journaling process to say the least. Every

time I would ask the students to get out their math journals the grumbling began. The

main reason behind the motivation is that they could not make the connection between

writing and math. Countryman (1992) notes one student complaining by saying “Why do

we have to write? This is math class; not English” (p.2).

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Students found the assignments to be difficult on several occasions. The students

found it to be very difficult to convey their thoughts unto the paper having to use

mathematical vocabulary. Situations of this nature were noted 46 times in the two week

study. Baxter, Woodward, and Olsen’s (2005) study states, “Problems arise, however,

when students do not or cannot describe their mathematical reasoning in a coherent

manner” (p.120). This was seen when the students began to hit their frustration level with

their understanding of the concepts taught during the study.

The mathematical vocabulary needed to write detailed responses to the journal

prompts was another issue that arose. Students were unsure of the vocabulary on 26

occasions during the study. This was frustrating from a teaching prospective, because I

had already adjusted my instructional plan to help avoid this problem. Journaling

provides an answer to this [vocabulary] problem because it forces students use

mathematical language in order to express their thoughts and ideas (Garside, 1994, p. 3).

If the students do not understand the vocabulary than it becomes very difficult to

effectively use a math journal. This was seen in a few of my students.

The previous two themes led to the next theme that was recorded. The sixth theme

was the students were unable to communicate their thoughts accurately. This was caused

by being frustrated with the assignment and not being able to master the vocabulary

needed to accurately respond to the journal prompt. Wells and Reinertsen’s (1993) study

states, “Writers often do not know what they know until they have written it, reread it,

and clarified it further for themselves” (p. 182).

Focus question three also used quantitative data to analyze a pre-post survey

given to the students and a survey given to the teachers. The surveys were analyzed using

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a chi square to test for significance, and they were also analyzed using Cronbach’s Alpha

to test for reliability with-in the survey.

The results from the chi square showed that there were no significant items on the

pre-survey at the p < .05, p < .01, or p < .001 levels. The student post test did show

significance in three of the questions. The first item that showed significance was journal

writing in math class increases my understanding of mathematical concepts. This item

received a significance level of one star, meaning p < .05. The significance occurred

between strongly agree and agree. This suggests that students do believe that math

journals help them to understand mathematical concepts. The next item on the post

survey for the students that was found to be significant at the p < .05 level was journal

writing helps me organize my thoughts. The significance for this item was found between

strongly agree and agree. This suggests that students believe that math journals do help

them to organize their thoughts. The last item on the post-survey that had significance at

the p < .01 level stated, “I feel comfortable communicating my thoughts to my teacher

through journal writing.” This was the most significant item on the student survey. In can

be concluded from the results of the student survey that the students believed the math

journals helped them to understand and organize mathematical concepts, but they did not

feel comfortable communicating through the journals.

The teacher survey was also analyzed using a chi square for significance and

Cronbach’s Alpha for reliability. There were two items from the teacher survey that

showed significance. The first item that showed significance at p < .05 states, “I believe

that using journal writing in my math class could beneficial to my students understanding

of mathematical concepts.” The significance was found between agree and disagree. In

Math Journals 43

this case, in can be concluded that teachers either believe math journals will or will not

benefit their students. The second item showed significance at the p < .01 states, “I am

receptive to incorporating journal writing in my math classes.” The significance was

found between agree and disagree. The survey suggests that teachers either are or are not

receptive to math journals. The overall survey suggests that teachers either agree or

disagree over the use of math journals in class.

I believe that the surveys confirmed what I have experienced in my school. The

children disliked journal writing, but they did admit that it helped them. As for teachers,

teachers either like math journals or they do not like them. I have not met an extremist for

either side.

Discussion

The results produced by the research were not what not what I expected, possibly

due to the short period in which the study took place. I believe if the study would have

been conducted over the period of an entire school year, significant gains would have

been recorded between the control and the treatment group. The poor attitudes of the

students about math journaling comes from their disdain for writing. The students

complain about writing in all content areas, not just math. If the students involved in the

study would have had a better pre-disposition about writing, their attitudes may have

been more positive. The students did admit in their survey they believed that math

journals helped them to organize their thoughts and better understand concepts. I believe

this is very meaningful because the students admitted that this was strategy that helped

them, even though they do not enjoy the strategy. This is a rarity and could be very

beneficial if used over the period of an entire school year.

Math Journals 44

Credibility is a concept defined as triangulation. Eisner (1991) calls this

‘structural corroboration,’ where a confluence of evidence comes together to form a

compelling whole. Credibility was obtained through using multiple sources to gather

data. The data from the sources were then analyzed and arranged in a way to form a

coherent argument.

Opposing viewpoints were introduced in the literature view and cited again in

Chapter Four and Chapter Five of this thesis. The opposing viewpoints were introduced

in order to have fairness within this thesis. The purpose of having fairness was to increase

the tightness and coherence of my argument. The argument was tight, but could have

been sounder if two separate groups could have been tested for a control and treatment

group, instead of having the same group taught one concept with the treatment and

another concept without the treatment. The results were presented accurately and without

bias in order to further strengthen the case presented. Rightness of fit was also present in

this thesis. The results did agree with the literature, in that the use of math journals did

cause significant gains from pre-test to post-test. The results did slightly differ from the

literature because the use of math journals did not have significant gains over traditional

teaching methods. However, this may be linked to the short time period of the study.

Implications

The results from the study cannot be generalized for the entire school population

due to the small sample size. The results showed that the implementation of math

journals did have significant gains from pre-test to post-test. Math journals are an

effective strategy for teaching mathematics. In the case of math journals being more

effective than standard math teaching strategies, the results of this study suggest that

Math Journals 45

journals are not significantly different. In order for a teaching strategy to be successful, in

my opinion, the teacher needs to believe the strategy is effective and will bring results.

Based on the teacher surveys, the findings suggest that the teachers who are not receptive

to the use of math journals, using math journals in the classroom is a big commitment on

the part of the teacher because the time associated with providing individual feedback for

each child. The themes associated with the qualitative results do help confirm that

referential adequacy is present. When making the decision to use math journals an

educator needs to prepare for lack of student motivation, difficulty with understanding

vocabulary, preparation of the writing process, and students not being able to convey

their thoughts into words. I believe these themes will occur in most situations involving

the implementation of math journals.

Even though the students were not very receptive to having to write about

mathematics on a daily basis, they were willing to admit through their surveys that math

journals helped them to better understand mathematical concepts and organize their

thoughts. This proves that the study contained catalytic validity, because even though the

students did not enjoy the strategy used they admitted it help them. Transformational or

‘Catalytic Validity’ (Larther as cited by Kinchloe & McLaren, 1998) is the degree to

which you anticipate your study to shape and transform your participants. The results

from the student survey suggested that a transformation of students did occur.

The students were not the only participants in the survey who were transformed to

some degree. I, as a teacher, was also transformed through this study. When making

lesson plans, I now plan more in-depth and concentrate and the attainment of vocabulary

needed to discuss a mathematical concept in detail. I also have a better understanding of

Math Journals 46

how my students process information. This has helped me to become a better teacher by

being more aware of the individual needs of my students.

Impact on Student Learning

This thesis impacts student learning by showing that math journals can be an

effective strategy in significantly increasing test scores. Math journals can be a great tool

for teachers looking to incorporate writing across their curriculum. The results show that

math journals were no more effective than strategies already implemented into my

classroom through inferential statistics. I suggest that a strategy’s success is going to be

dependent on the amount of time a teacher spends trying to insure the strategy is

successful as possible. Math journals are not a cure all for teachers seeking to raise their

math scores, but if used correctly they can significantly raise the student’s scores over a

period of time, as long as the teacher is willing to read all the journals and provide

individual feedback for their students.

Recommendations for Future Research

If a researcher is interested in doing a study on math journals, I would like

recommend that they start the journaling process at the beginning of the school year. As a

teacher and a research, I would like to see the effects of math journaling over the period

of an entire school year. Student attitudes was an obstacle I faced in my study but if the

journaling process began at the beginning of the year, not in the middle as seen with this

study, then student attitudes may change. The study may be more effective if the same

students are not used for the control and treatment groups with the same concept being

taught. The goal original goal was for this study to have two completely independent

groups, but due to unexpected obstacles than was unable to occur. If a research is able to

Math Journals 47

have two independent groups and complete a year long study, I believe that the research

would have more catalytic validity and referential adequacy.

Math Journals 48

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Appendix A

Instructional PlanCriteria DescriptionParticipants Two Third grade classrooms consisting on

thirty two students. The gender break down is 19 boys and 13 girls.

Content Area Math with a focus on measurement.Standards Met M3M2. Students will measure length

choosing appropriate units and tools.

a. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances.

b. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.

c. Estimate length and represent it using appropriate units.

d. Compare one unit to another within a single system of measurement.

Time Frame The students will engaged in instructional time for 45 minutes a day for ten consecutive school days.

Rationale The study is designed to assess the role math journals play in the comprehension of mathematical concepts. The study will also evaluate student attitudes towards using journals in math class.

Role of Teacher The teacher will be guiding instruction through both whole group and small group instruction. The teacher will also be guiding journal writing through prompts.

Materials Pre-test-PencilPost-Test- PencilJournal- Paper, Folder, PencilSurvey-Pencil

Procedures The students will participate in whole group instruction where the information for the day will be given. During small group

Math Journals 53

instruction the lesson topic will discussed and the student’s will participate in journal prompts to further assess their knowledge and increase understanding of the topic. The journal prompts will be worded in order to engage students and promote writing. The prompts will be story based so that the students will feel more comfortable writing. Vocabulary was also taught through discussion, flashcards, and examples.

Assessments Pre-TestPost-TestPre-SurveyPost-SurveyJournal Writings

Modifications Lessons may need to be modified based on the IEP’s of students participating in the survey

Math Journals 54

Appendix B

Instructional Plan RubricCriteria Description Feedback Participants Two Third grade classrooms

consisting on thirty two students. The gender break down is 19 boys and 13 girls.

How can the sample size be adjusted to better fit the study?

Content Area Math with a focus on measurement.

Will the content area be applicable to the study?

Standards Met M3M2. Students will measure length choosing appropriate units and tools.

a. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances.

b. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.

c. Estimate length and represent it using appropriate units.

d. Compare one unit to another within a single system of measurement.

Could the standards better correlate with the content area and the study?

Time Frame The students will engaged in instructional time for 45 minutes a day for ten consecutive school days.

How could the time frame be adjusted to be more adequate for the study?

Rationale The study is designed to assess the role math journals play in the comprehension of mathematical concepts. The study will also evaluate student attitudes towards using journals in math class.

What changes could be made to the rationale in order to better capture the study?

Role of Teacher The teacher will be guiding instruction through both whole group and small group

How could teachers effectiveness be maximized in order to

Math Journals 55

instruction. The teacher will also be guiding journal writing through prompts.

better validate the study?

Materials Pre-test-PencilPost-Test- PencilJournal- Paper, Folder, PencilSurvey-Pencil

What materials need to be added to the ones listed?

Procedures The students will participate in whole group instruction where the information for the day will be given. During small group instruction the lesson topic will discussed and the student’s will participate in journal prompts to further assess their knowledge and increase understanding of the topic. The journal prompts will be worded in order to engage students and promote writing. The prompts will be story based so that the students will feel more comfortable writing. Vocabulary was also taught through discussion, flashcards, and examples.

Are the procedures listed clear? How could the procedures be modified to increase the effectiveness of the study?

Assessments Pre-TestPost-TestPre-SurveyPost-SurveyJournal Writings

How do the current assessments provide an effective way to evaluate the study?

What other assessments could be incorporated into the study?

Modifications Lessons may need to be modified based on the IEP’s of students participating in the survey

What other modifications could be made in order to maximize effectiveness and further validate the study?

Math Journals 56

Appendix C

Student Survey: Journal Writing

1. Journal writing in math class increases my understanding of mathematical concepts.

Strongly Disagree Disagree Agree Strongly Agree

2. Journal writing helps me organize my thoughts.

Strongly Disagree Disagree Agree Strongly Agree

3. Journal entries in which I explain solutions to mathematical problems increase my understanding.

Strongly Disagree Disagree Agree Strongly Agree

4. I feel comfortable communicating my thoughts to my teacher through journal writing.

Strongly Disagree Disagree Agree Strongly Agree

5. I enjoy journal writing.

Strongly Disagree Disagree Agree Strongly Agree

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Appendix D

Teacher Survey- Journal Writing

Please read the following question and circle your answer.

1. Do you incorporate journal writing into your math class?

Yes (If “yes” go to question #2) No (If “no” then go to question #3)

2. How often do you incorporate journal writing into your math class?

1-3 times a month 4-6 times a month

7-9 times a month 10 or more times a month

Please answer the following questions on the scale given:

Scale: 1- Strongly Disagree 2-Disagree 3-Agree 4-Strongly Agree

3. I believe that using journal writing in my math class could beneficial to my students understanding of mathematical concepts.

1 2 3 4

4. I am receptive to incorporating journal writing in my math classes.

1 2 3 4

5. If research proved that journal writing increased students’ academic achievement in mathematics, I would incorporate it into my lessons on a daily basis.

1 2 3 4

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Appendix E

Reflective Journal Prompts

Class  

Date  

Strategy  

1. What were three main things I learned from this session?

 

2. What did we not cover that I expected we should?

 

3. What was new or surprising to me?

 

4. What have I changed my mind about, as a result of this session?

 

5. One thing I learned in this session that I may be able to use in the future is...

 

6. I am still unsure about...  

7. Ideas for action, based on this session...

 

8. What I most liked about this session was...

 

9. What I most disliked about this session was...

 

10. Miscellaneous interesting facts I learned in this session...