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.
Thesis Co-Chair
Education Department
______________________________
Sharon Livingston, Ph. D.
Thesis Co-Chair
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.
Math Journals iv
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
Math Journals v
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
Math Journals 4
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.
Math Journals 6
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.
Math Journals 7
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 twentytwo 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 can math
journals be
successfully
implemented
in a third
grade
classroom?
Moore
(1991)
Type of Method:
Instructional Plan
Rubric and Interview
Can the use of
math journals
positively
affect test
scores?
Lauritzen
(1992)
Burns
(1998)
Type of Data:
Qualitative
Fletcher et
al. (2008)
Type of Validity:
Content
Type of Method:
Teacher made Test
Jitendra &
Xin (1997)
Type of Data:
Interval
Hart &
Thompson
(2009)
Type of Validity:
Content
How are
data
analyzed
Coded for
themes:
Reoccurring
Dominant
Emergent
Rationale
Looking for
categorical and
repeating data
that form
patterns of
behavior
Independent- To determine if
T
there are
significant
differences
between the
means of two
separate
groups
To determine if
there are
significant
Dependent-T differences
between means
of one group
tested twice.
Effect Size
How will
writing during
math class
affect the
attitudes of
teachers and
students about
math?
Dusterhoff
(1995)
Koirala
(2002)
Type of Method:
Reflective Journal
and Surveys
Type of Data:
Qualitative
Ordinal
Countryman
(2002)
Type of Validity:
Construct
To measure the
magnitude of
the treatment
effect.
Coded for
themes:
Reoccurring
Dominant
Emergent
Looking for
categorical and
repeating data
that form
patterns of
behavior
Chi Square
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
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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 prepost 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 chisquare 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
Mean
Variance
Observations
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
t(22) = 0.47, p > .05
Treatment Pre
60.25
569.2954545
12
0
22
0.477240999
0.318948702
1.717144335
0.637897404
2.073873058
Control Pre
55.41666667
661.5378788
12
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
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
T(11) = 4.17, p < .05
Pre-Test
60.25
569.2954545
12
0.577645362
0
11
-4.177558981
0.000771449
1.795884814
0.001542897
2.200985159
Post-Test
83.75
173.1136364
12
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 posttest. 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
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
T(11) = 6.00, p < .05
Pre-Test
55.41666667
661.5378788
12
0.82292182
0
11
-5.999909844
4.46364E-05
1.795884814
8.92728E-05
2.200985159
Post-test
82.91666667
223.719697
12
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
Mean
Variance
Observations
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
T(22) = 0.14, p > .05
Treatment Post
83.75
173.1136364
12
0
22
0.144912318
0.443049756
1.717144335
0.886099513
2.073873058
Control Post
82.91666667
223.719697
12
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 postsurvey (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
1. Journal writing in math
class increases my
understanding of
mathematical concepts.
2. Journal writing helps me
organize my thoughts
3. Journal entries in which
I explain solutions to
mathematical problems
increase my
understanding.
4. I feel comfortable
communicating my
thoughts to my teacher
through journal writing.
5. I enjoy journal writing.
2 – Pre-Survey
n = 12
6
2 – Post-Survey
n = 12
8.67 *
6.67
11.3 *
0.67
5.3
3.3
12 **
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
1. I believe that using journal writing in my
math class could beneficial to my students
understanding of mathematical concepts.
2 – Teach Survey
n = 12
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.
*p < .05, **p < .01, ***p < .001
6
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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 pretest 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
Math Journals 40
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
Math Journals 42
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
References
Bruce, S. (2010). Action research in special education : an inquiry approach for effective
teaching and learning. New York: Teachers College Press.
Burns, M. (1998). Math in action. link classroom projects to math practice. Instructor,
107(8), 69.
Burns, M. & Silbey, R. (2001). Math journals boost real learning. Instructor, 110(7),
18-20.
Carter, S. (2009). Connecting mathematics and writing workshop: it's kinda like ice
skating. Reading Teacher, 62(7), 606-610.
Corley, E. (2000). A Qualitative study of student perceptions regarding electronic
journaling. Paper presented at the annual meeting of the Mid-Western
Educational Research Association. Chicago, IL. Retrieved from
http://www.eric.ed.gov/PDFS/ED447791.pdf
Countryman, J. (1992). Writing to learn mathematics. Portsmouth, NH: Heinemann.
Deatline-Buchman, A., Jitendra, A., & Xin, Y. (2005). Effects of mathematical word
problem-solving instruction on middle school students with learning problems.
Journal of Special Education, 39(3), 181-192.
Dusterhoff, M. (1995). Why write in math?. Teaching PreK-8, 25(4), 48-49.
Eisner, E. (1991). The enlightened eye. New York: Mac Millan.
Fletcher, J., Fuchs, D., Fuchs, L., Hamlett, C., Powell, S., & Seethaler, P. (2008). Effects
of preventative tutoring on the mathematical problem solving of third-grade
students with math and reading difficulties. Council for Exceptional Children,
74(2), 155-173.
Math Journals 49
Garside, C. (1994, November). Building bridges to critical thinking: utilizing student
journals in the college classroom. Paper presented at the Annual Meeting of the
Speech Communication Association. New Orleans, LA. Retrieved from
http://www.eric.ed.gov/PDFS/ED378575.pdf
Greig, A., Taylor, J., & MacKay, T. (2007). Doing research with children. (2nd ed.) Los
Angeles, CA: Sage Publications.
Hart, S., Petrill, S., & Thomson, L. (2009). The ABCs of math: A genetic analysis of
mathematics and its links with reading ability and general cognitive ability.
Journal of Educational Psychology, 101(2), 388-402.
Jitendra, A, & Xin, Y. (1997). Mathematical word-problem-solving instruction for
students with mild disabilities and students at risk for math failure: a research
synthesis. Journal of Special Education, 30(4), 412-438.
Kinchloe, J., & McLaren, P. (1998). Rethinking critical theory and qualitative research.
In N. Denzin & Y. Lincoln (Eds.), The landscapeof qualitative research: theories
and issues (pp. 260-299). Thousand Oaks, CA: Sage Publications.
Koirala, H. (2002, July). Facilitating student learning through math journals. Proceedings
of the Annual Meeting of the International Group for Physiology of Mathematics
Education, Norwich, England. Retrieved from
http://www.eric.ed.gov/PDFS/ED476099.pdf
LaGrange College Education Department. (2008). The LaGrange College Conceptual
Framework. LaGrange, GA: LaGrange College.
Lauritzen, C. (1992, February). When children write math stories. Paper presented at the
West Regional Conference of the International Reading Association, Portland,
Oregon. Retrieved from http://www.eric.ed.gov/PDFS/ED345293.pdf
Math Journals 50
Popham, W. (2008). Classroom assessment: What teachers need to know (5th Ed.).
Boston, MA: Pearson, Allyn, & Bacon.
MacNaughton , G. (2009). Doing action research in early childhood studies: a step by
step guide. New York: Open University Press.
Manning, G. & Manning, M. (1996). Teaching reading and writing. keeping writing
portfolios. Teaching Prek-8. 27(1), 132, 134.
Moore, J. (1991, March). Math journals. Paper presented at The Annual Spring
Conference of the National Conference of Teachers of English, Indianapolis,
Indiana. Retrieved from http://www.eric.ed.gov/PDFS/ED333475.pdf
Reinersten, P., & Wells, C. (1993). Dialogue journals and critical thinking. Teaching
Sociology, 21(2), 182-186.
Salkind, N.J. (2010). Statistics for people who (think they) hate statistics (Excel 2nd Ed.).
Thousand Oaks, CA: Sage.
Singh, D, & Stoloff, D. (2008) Assessment of teacher dispositions. College Student
Journal, 42(4), 1169-1180.
Wason-Ellam, L. (1987, March). Writing as a tool for learning: math journals in grade
one. Paper presented at the Annual Meeting of the National Council of Teachers
of English Spring Conference. Louisville, KY: Retrieved from
http://www.eric.ed.gov/PDFS/ED285194.pdf
Vygotsky, L. (1978). Mind and Society: The Development of Higher Physiological
Processes. Cambridge, MA: Harvard University Press.
Math Journals 51
Zane, T. (2009). Performance assessment design principles gleaned from constructivist
learning theory (part 1). TechTrends: Linking Research and Practice to Improve
Learning, 53(1), 81-88.
Math Journals 52
Appendix A
Instructional Plan
Criteria
Participants
Content Area
Standards Met
Description
Two Third grade classrooms consisting on
thirty two students. The gender break down
is 19 boys and 13 girls.
Math with a focus on measurement.
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
Rationale
Role of Teacher
Materials
Procedures
The students will engaged in instructional
time for 45 minutes a day for ten
consecutive school days.
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.
The teacher will be guiding instruction
through both whole group and small group
instruction. The teacher will also be
guiding journal writing through prompts.
Pre-test-Pencil
Post-Test- Pencil
Journal- Paper, Folder, Pencil
Survey-Pencil
The students will participate in whole
group instruction where the information for
the day will be given. During small group
Math Journals 53
Assessments
Modifications
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.
Pre-Test
Post-Test
Pre-Survey
Post-Survey
Journal Writings
Lessons may need to be modified based on
the IEP’s of students participating in the
survey
Math Journals 54
Appendix B
Instructional Plan Rubric
Criteria
Participants
Content Area
Standards Met
Description
Two Third grade classrooms
consisting on thirty two
students. The gender break
down is 19 boys and 13 girls.
Math with a focus on
measurement.
M3M2. Students will measure
length choosing appropriate
units and tools.
Feedback
How can the sample
size be adjusted to better
fit the study?
Will the content area be
applicable to the study?
Could the standards
better correlate with the
content area and the
study?
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
Rationale
Role of Teacher
The students will engaged in
instructional time for 45
minutes a day for ten
consecutive school days.
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.
The teacher will be guiding
instruction through both
whole group and small group
How could the time
frame be adjusted to be
more adequate for the
study?
What changes could be
made to the rationale in
order to better capture
the study?
How could teachers
effectiveness be
maximized in order to
Math Journals 55
Materials
Procedures
Assessments
instruction. The teacher will
also be guiding journal
writing through prompts.
Pre-test-Pencil
Post-Test- Pencil
Journal- Paper, Folder, Pencil
Survey-Pencil
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.
Pre-Test
Post-Test
Pre-Survey
Post-Survey
Journal Writings
better validate the
study?
What materials need to
be added to the ones
listed?
Are the procedures
listed clear? How could
the procedures be
modified to increase the
effectiveness of the
study?
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
Agree
Strongly Agree
5. I enjoy journal writing.
Strongly Disagree
Disagree
Math Journals 57
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
Math Journals 58
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...