VOCABULARY IN MATH CLASS:
INCREASING PROFICIENCY IN MATHEMATICS
Except where reference is made to the work of others, the work described in this thesis is my
own or was done in collaboration with my Advisor. This project does not include proprietary of
classified information.
Charles Everett Tatom
Certificate of Approval:
____________________________
__________________________
Donald R. Livingston, Ed.D.
Associate Professor and Project Advisor
Education Department
Sharon Livingston, Ph.D.
Assistant Professor and Project Advisor
Education Department
VOCABULARY IN MATH CLASS:
INCREASING PROFICIENCY IN MATHEMATICS
A project submitted
by
Chuck Tatom
to
LaGrange College
in partial fulfillment of
the requirements for the degree of
EDUCATION SPECIALIST
in
Curriculum and Instruction
LaGrange College
July 19, 2011
Vocabulary in Math Class iii
Abstract
Vocabulary in math class: Increasing proficiency of low socio-economic
students in mathematics
The purpose of this research was to introduce the strategies of literacy practices of Jamaica,
or looping cards, into the math curriculum to increase vocabulary proficiency in mathematics and
improving student learning and test scores. The study consisted of comparing test scores of four
tenth grade Mathematics II classes, two as the control group and two as the treatment group. The
students were given a pre- and post-test and a state mandated End of Course Test. The differences
in mathematical proficiency between the classes were measured and analyzed using dependent-t
and independent-t tests. Students showed significant improvement by class and by socio-economic
status where the Jamaican practices were introduced and practiced. The treatment group of students
participated in a survey concerning the use of the looping card strategies, and had favorable
opinions of these strategies. Furthermore, an administrator was interviewed regarding the use of
looping cards, and he believed it to be a great teaching tool for vocabulary and student learning.
Looping cards should be varied with other standards-based practices and should be used across the
curriculum to raise student achievement.
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TABLE OF CONTENTS
Abstract.................................................................................................................................iii
Table of Contents .............................................................................................................. iv
List of Tables ........................................................................................................................v
Chapter I: INTRODUCTION .........................................................................................1
Statement of the Problem ...........................................................................................1
Significance of the Problem ........................................................................................2
Theoretical and Conceptual Frameworks ................................................................3
Focus Questions ...........................................................................................................6
Overview of Methodology ..........................................................................................6
Human as Researcher ..................................................................................................7
Chapter II: REVIEW OF THE LITERATURE ..........................................................9
The use of mathematics...............................................................................................9
How do we talk math? .............................................................................................. 10
What is math vocabulary? ........................................................................................ 12
School structure in Jamaica...................................................................................... 13
Attitudes and skills of math in Jamaica.................................................................. 14
Strategies of the Jamaican Curriculum ................................................................... 17
Applying the Strategies ............................................................................................. 18
School Change ............................................................................................................ 21
Chapter III: METHODOLOGY.................................................................................. 25
Research Design......................................................................................................... 25
Setting .......................................................................................................................... 26
Subjects and Participants .......................................................................................... 26
Procedures and Data Collection ............................................................................. 27
Validity, Reliability, Dependability, and Bias ........................................................ 30
Analysis of Data ......................................................................................................... 33
Chapter IV: RESULTS .................................................................................................... 36
Chapter V: ANALYSIS and DISCUSSION OF RESULTS ................................... 49
Analysis ........................................................................................................................ 49
Discussion ................................................................................................................... 56
Implications ................................................................................................................ 58
Impact on School Improvement ............................................................................ 61
Recommendations for Future Research................................................................ 62
References .......................................................................................................................... 64
Appendixes ........................................................................................................................ 68
Vocabulary in Math Class v
LIST OF TABLES
Tables
Table 3.1 Mathematics II 2009/2010…………...……………………26
Table 3.2 Mathematics II 2010/2011…………...……………………27
Table 3.3 Data Shell………………..…………...……………………28
Table 4.1 Dependent-t Test for Treatment Group – all students.……36
Table 4.2 Dependent-t Test for Control Group – all students……….37
Table 4.3 Independent-t Test Treatment and Control Pre-Test……....38
Table 4.4 Independent-t Test Treatment and Control Post-Test .……38
Table 4.5 Independent-t Test of Treatment Pre-Test
based on Socioeconomics .…………...……………………39
Table 4.6 Independent-t Test of Control Pre-Test
based on Socioeconomics ………..……..…………………40
Table 4.7 Independent-t Test of Treatment Post-Test
based on Socioeconomics ………...………………………40
Table 4.8 Independent-t Test of Control Post-Test
based on Socioeconomics ………...………………………41
Table 4.9 Independent-t Test of Treatment and Control
Math II EOCT ………………..…………...………………42
Table 4.10 Independent-t Test of Treatment and Control
Math II EOCT Low SES…………………………………42
Table 4.11 Independent-t Test of Treatment and Control
Math II EOCT no SES ………..........…………………….43
Table 4.12 Student Survey Results …………...……………..….…......44
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CHAPTER I: INTRODUCTION
Statement of the Problem
Effective mathematics problem solving often depends on understanding of key
mathematical terms. The National Council of Teachers of Mathematics (2008), in the Principles
and Standards for School Mathematics states that students who have opportunities,
encouragement, and support for speaking, writing, reading, and listening in mathematics classes
reap dual benefits: they communicate to learn mathematics, and they learn to communicate
mathematically. As stated by the National Mathematics Advisory Panel (2008), a large
achievement gap of importunate disparities in mathematics as related to race and income must be
acknowledged. If this gap continues unaddressed, it will not only be more devastating for
individuals and families, but also project poorly for the nation’s future, given the high growth rates
of the largest minority populations (National Mathematics Advisory Panel, 2008, p.xi).
Georgia Performance Standards, the state’s math curriculum, expect student learning to
incorporate comprehension of mathematics and integrate their linguistic, cognitive, and
metacognitive skills in developing proficiency (Donovan & Bradsford, 2004). Proficiency defines
the state or quality of being proficient, competent or with expertness (American Heritage
Dictionary, 2010). This aptitude develops in a setting of a community of learners where students
are encouraged and engaged to share knowledge and understanding.
With a curriculum that fosters students to reason mathematically, they must learn to
evaluate problems and mathematical arguments, and explicitly use the language of mathematics to
communicate information and ideas precisely. These types of problems create anxiety in a math
class. Garbe (1985) states, "perhaps we do not spend enough time teaching the vocabulary
necessary for students to read and understand mathematics" (p. 39). Reading and understanding
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word problems is truly different from reading out of a textbook. Reading and comprehension of
word problems involve recognizing mathematical concepts that may or may not be obvious (Flood
& Lapp, 1990). By improving mathematical literacy of language and vocabulary, as well as
increasing deductive skills, teachers can prepare students to be actively engaged in learning and
exceed the expectations of the goals of the state curriculum.
Significance of the Problem
Acknowledging the “Race to the Top” application submitted by the Georgia Governor’s
Office (2010), it states there is an achievement gap between subgroups in reading and
mathematics. According to the Georgia Department of Education (2005) and the implemented
Georgia Performance Standards, the education system and educators will enhance students’
reading across the curriculum. With this new performance curriculum in place and standardized
testing having a greater impact on the meaning of success and proficiency of students, educators
must search for effective means for the achievement of all students, particularly at-risk students.
Amid governmental policies, such as “No Child Left Behind” and the A+ Education Reform Act
of 2000 mandating student performance on standardized testing in the content areas of reading,
language arts, and mathematics, it is apparent that teachers must prepare students to be proficient in
all subject areas and seek to increase the performance of at-risk students.
One of the cornerstones of NCLB, Adequate Yearly Progress [AYP], serves as “an annual
measure of student participation and achievement of statewide assessments and other academic
indicators” (Georgia Department of Education [GADOE], 2008). NCLB mandates that every state
set high academic standards and implement a testing program which is aligned to those standards
in order to measure students’ achievements; each individual school district is held accountable for
the academic success of their students.
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Rural schools are an important focus, especially in the state of Georgia, since, as of 2003,
one-third of Georgia’s schools are located in a rural area and due to the continued consolidation of
rural schools, and Georgia has the largest rural schools in the nation (Georgia Humanities Council
[GHC], 2010). Many of the rural schools in Georgia serve students who live in poverty, and these
schools face a variety of issues regarding student performance since correlations are shown to exist
between that of students attending large schools and the performance of poverty-stricken students.
Because of the AYP requirements, these rural school districts are more concerned than ever about
raising test scores and student performance while continuing to fight against the implications of
large schools with overwhelming numbers of students from poverty-stricken families (GHC,
2010).
Many mathematic teachers view literacy instruction as merely helping students read their
textbooks. Some educators of math curricula tend to emphasize disproportionately computational
skills at the expense of problems-solving skills (Jones & Southern, 2003). Mathematics educators
should help students learn how to read, write, listen, speak, and think in math (Draper, 2002).
Questions and discussions elicit students’ thinking and build solution strategies that lead to greater
clarity and precision. A significant amount of class time is spent developing mathematical ideas,
not just practicing skills (Donovan & Bransford, 2004). Too often students learn and practice
procedures without understanding why they work (Flood & Lapp, 1990).
Theoretical and Conceptual Frameworks
Intending to integrate comparative international education reading and literacy skills in my
mathematics classes, focused on vocabulary to develop problem solving and comprehension
proficiency. My focus engaged students in meaningful, real-life activities to encourage and expand
mathematical knowledge of functions and vocabulary. This was accomplished by building on
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prior knowledge, and integrating the richness of language, specifically vocabulary, to enable the
students to articulate the mathematic processes of problem solving.
Constructivists recognize that experience and environment play a large role in how well the
learner learns, and that language plays a key role in the acquisition of knowledge (Dewey,
1938/1997; Larochelle, Bednarz, & Garrison, 1998). Constructivism advocates a shift in the
behavior of the mathematics classroom toward mathematical communities of learning, and away
from a simple collection of individuals. In addition, the learning environment should stress
mathematical reasoning, conjecturing, inventing, and problem solving, and away from merely
memorizing procedures and answer finding in order for proficiency to take place (National Council
of Teachers of Mathematics, 2008).
Social constructivism extends constructivism by incorporating the role of other
stakeholders and culture in development by stressing interaction over observation. This involves
teachers who teach as if they value what their students think and create learners. Discussion and
interactive discourse promote learning because they afford students the opportunity to use language
as a demonstration of their independent thoughts (Nystrand, 1996). Active reflection and
discussion elicits sustained responses from students that encourage meaning making through
negotiating with the ideas of others. Nystrand (1996) states social constructivism is a type of
learning that “promotes retention and in-depth processing associated with the cognitive
manipulation of information” (p. 28).
In alliance with Tenet 1: Enthusiastic Engagement in Learning of LaGrange College
Education Department’s [LCED] (2010) Conceptual Framework, this research aligns closely to the
Competency Cluster 1.3, Knowledge of Learners. The strategies used will provide for learning
opportunities that support students where they are and of the influences of socio-economics,
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expecting that students can learn at high levels and be proficient in the mathematics classroom.
Further, the study will seek to build on students’ existing knowledge of mathematics vocabulary
and close the recognized socio-economic achievement gap.
There are six domains of the Georgia Framework for Teaching [GFT] (LCED, 2010).
Domain 2 is closely aligned with this research, by relating, developing, and supporting student
learning and achievement. Students acquire the most meaningful understandings and appreciations
of their learning environment and problem solving experiences if they are engaged in learning
activities that allow them to discover relationships and solutions for themselves (Jones & Southern,
2003).
The National Board for Professional Teaching Standards [NBPTS] has five core
propositions that frame the foundations for experienced teachers (LCED, 2010). Proposition
Number One aligned most clearly with this study, stating that educators must treat all students
equitably and with a commitment to provide an environment contributing to learning.
Additionally, this study allowed for professional growth, reflecting on input from others, in
conjunction with the instructional design to increase opportunities of achievement for diverse
learners with high expectations for all students. This growth and action related with Tenet 3:
Caring and Supportive Classrooms and Learning Communities, specifically imploring
Competency Cluster 3.3 (LCED, 2010). Blending with Domains Five and Six of the GFT, Element
1G of NCATE Standard One, INTASC Principle Nine, and Core Proposition Four of the NBPTS,
a tremendous call to action involving teachers in their development of professional character of
instructional strategies and learning environments as they reflect and evaluate the outcomes of their
actions (LCED, 2010).
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Implementing effective strategies and actively engaging learners in a well-rounded learning
environment should be the goal of every educator. Based on this and the above stated premises,
social constructivism should be used in teaching mathematics in the classroom to assist students in
achieving proficiency in mathematics.
Focus Questions
Students of low socio-economic status tend to perform below the state standards on
mandated tests at our high school. Increasing test score requirements have forced school systems to
explore new strategies in order to continually raise scores because as every educator knows, it is
very difficult, if not impossible, to get 100 percent of students to pass a required test. The avenue
of exploration of this research was to implement an international pedagogical approach to teaching
for mathematics proficiency.
The following questions were of interest in my research and helped drive this focus:
1. How did the integration of vocabulary strategies into the mathematics curriculum increase
low socio-economic students’ proficiency in mathematics?
2. What were the attitudes and opinions of the adopted curriculum strategies among learners?
3. What was the level of success of change in the process strategies as viewed by an
administrator to encourage the use of looping cards in classrooms for achievement equity?
Overview of Methodology
Applying action research in my study, mixed methods of quantitative and qualitative
measures were used to assess the results. These outcomes were measured by incorporating the use
of literacy skills and pedagogy practices from Jamaica. The testing of these effects showed how
these instructional strategies based on vocabulary proficiency affected mathematical knowledge in
student learning.
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Using test scores, to compare previous classes, my control group, taught without
incorporating these comparative educational strategies, to those taught with the integrated literacy
practices of Jamaica, my treatment group. Implementing these strategies and expecting to show
significant gains in the low socio-economic students’ academic performance in mathematics was
the quantitative part of the research. This research statistically compared student test scores from
pre-post tests and the End of Course Tests for Mathematics II from this year 2010-2011 and the
previous school year 2009-2010. The achievement difference of the treatment group was compared
to the control group of the previous year using independent t-tests to determine if there was
significant difference in applying the vocabulary practices.
Qualitative and quantitative data were collected from an interview with an administrator
and surveys of all students who participated in the use of these instructional literacy strategies. The
interview was conducted using a specific set of questions and coded for themes that align with
student success in improvement and perceived learning. The surveys utilized a Likert scale
utilizing chi square analyses.
Human as Researcher
Having a strong background in mathematics and being a Chemical Engineer, I understand
the hands on approach to learning, and the necessity of a logical progression in solving math
problems. It is extremely important to use the knowledge of the student as you begin to teach new
concepts. As a traditional style educator, I struggled to engage some of my students in
mathematical thinking and problem solving. To become a more effective teacher leader and
improve pedagogical practices through continued education, a reflective practitioner must ensure
that mathematics in the classroom must be engaging and create a learning environment that is not
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resistant to combining literacy instruction with regular academic teaching of mathematics (Draper,
2002).
Teaching in the same Class 2A high school for eight years, I have developed a good
working rapport with the central office, school administrators, teachers, and students at all levels of
mathematic ability. Wanting to better engage my students and assure mathematical comprehension
and understanding, I believe there is a need to develop a more student-centered classroom
promoting student mathematical conversation in the use of vocabulary, such as asking them to
discuss and justify strategies they use to solve problems. Lending to proficiency, I addressed
changes in my approach to teaching math by utilizing comparative education literacy strategies,
and taking advantage of the teaching moments to foster insight and student learning.
This research was conducted with the intent of providing secondary math teachers and
administrators with useful information, ideas, and methods concerning vocabulary strategies in
math class to increase proficiency. Lessons needed to be designed with specific mathematical
learning goals in mind in order to utilize vocabulary effectively and provide the avenue for a rich
learning environment for all students no matter the socio-economic status.
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CHAPTER II: REVIEW OF THE LITERATURE
The Use of Mathematics
The U.S. system for teaching children mathematics is large and complex with numerous
components. The curriculum contains learning goals, spelling out the mathematics to be studied. It
also includes instructional programs and materials that organize the mathematical content, together
with assessments for determining what has been learned. In addition, and of primary importance, it
is through teaching that students encounter the mathematical content afforded by the curriculum
(United States Department of Education, 2005). Success in mathematics is not just a matter of
national concern, but should also be for the individual learner, because it lends itself to college and
career options, as well as it increases prospects for future income. This academic achievement in
high school mathematics correlates powerfully with access to college, graduation from college, and
earning income in the top quartile from employment in the workforce (National Mathematics
Advisory Panel, 2008).
In today’s fast paced society, no one can live without the use of mathematics. Whether at
school, in the workforce, or at home, while reading, relaxing, shopping, interacting with others,
and making practical decisions, people are compelled to make use of mathematics, and often must
employ its language and methods (National Mathematics Advisory Panel, 2008). One must have a
goal in mathematics education to prepare students for these tasks, as well as provide for the further
development of new knowledge.
According to Draper (2002), mathematics permeates every aspect of our daily life, such as
grocery shopping, paying for fuel, travel, telephone calls, interpreting newspaper or internet
graphic information, and using calculators. Agreeing that mathematics has application in daily
living, Borsuk (2003) clearly states that “competence in mathematics can open the door to high-
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paid jobs; technology of our times increasingly means that people are working in settings where
the foundation is built on mathematics; our daily lives lead us to call on mathematics for
everything from understanding a tax bill to following the news, to figuring out what 30% off on a
pair of shoes means” (p. 346).
How do we talk math?
The key to increasing vocabulary development is ensuring that students with poor
vocabularies not only learn the meaning of words but also have the opportunity to use them
frequently. Definitions alone do not provide enough support for readers to be able to transfer those
definitions to reading contexts (Allen, 1999). Schools should teach students to be literate in the
most general sense, by being capable of reading, writing, speaking, computing, reasoning, and
manipulating verbal and visual symbols and concepts (Donovan & Bransford, 2004). This lends
itself to the question: is mathematics a language?
Language is defined as communication of thoughts and feelings through a system of
arbitrary signals, such as voice sounds, gestures, or written symbols. Further, it is a system of
signs, symbols, gestures, or rules used in communicating (American Heritage Dictionary, 2010).
Mathematics is a complex language that is used for communicating, problem solving, reasoning,
creating works of art, and designing mechanical tools. The language of mathematics involves the
use of numerals, words, and symbols that are at times interrelated and interdependent and at other
times disjointed and autonomous (Adams, 2003). In fact, Wakefield (2000) stated the following
characteristics of mathematics do indeed qualify it as a language: verbal or written symbols
representing ideas or images are used to communicate; the processes are uniform and consistent;
expressions are linear and serial; understanding increases with practice; success requires
memorization of symbols and rules; translations and interpretations are required for novice
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learners; meaning is influenced by symbol order using PEMDAS; communication requires
encoding and decoding, intuition, insightfulness, and "speaking without thinking" to accompany
fluency. Experiences from childhood supply the foundation for future development, and the
possibilities for expressions are infinite.
Effective mathematics problem solving often depends on the understanding of key
mathematical terms. This is especially true in solving word problems and performance-based tasks,
which can be difficult even for students who are very proficient with mathematical procedures.
Vocabulary is a concept that is fluent throughout the entire Georgia Performance Standards of
school curriculum. Vocabulary refers to the “knowledge of words and word meanings” (Honig,
Diamond, Cole, & Gutlohn, 2008, p. 407). Although interest in vocabulary has repeatedly waxed
and waned with the research community and elementary schools, vocabulary instruction has
always been an interest of middle and secondary school teachers, probably because they recognize
its importance and are familiar with procedures for teaching vocabulary (Jetton & Dole, 2004). For
the most part, direct vocabulary instruction in mathematics has been less comprehensive and more
systematic. Students need and deserve a comprehensive and well-planned program of vocabulary
instruction for proficiency of math terminology (Jetton & Dole, 2004).
What is math vocabulary?
Mathematics has its own system of communication, particularly the meticulous
terminology that is used to communicate ideas within the discipline. These terms have meanings
specific to mathematical topics and may or may not make sense outside of the math environment.
The words, terminology, and vocabulary used in mathematics are important factors in obtaining
proficiency in the communication process of mathematics (Adams, 2003). In mathematics, it is
acceptable for students to use informal definitions as an introduction to formal definitions. These
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informal definitions help students to construct their own understandings, and these are the
definitions students might use when reading word problems or instructions. A student's ability to
recognize and employ the formal definition of terms is the key to understanding and applying
concepts when reading mathematical text (Adams, 2003). An informal definition is a good starting
point and should be encouraged in order to lead a student to construct his or her own understanding
of the term. These informal interpretations will begin to allow the student, when reading
mathematical text, to develop the critical part of comprehension and lend itself to proficiency.
As students build their mathematical proficiency and extend vocabulary, they become more
confident of their ability to learn mathematics and to use it. The more mathematical concepts they
understand, the more sensible the whole subject becomes. In contrast, when they think
mathematics needs to be learned by memorizing rather than by making sense of it, they begin to
lose confidence in themselves as learners. Students who are proficient in mathematics believe that
they can solve problems, develop understanding, and learn procedures through hard work, and that
becoming mathematically proficient is worthwhile for them (Donovan & Bransford, 2004).
School Structure in Jamaica
Education in Jamaica is administered under the Ministry of Education, Youth, and Culture
[MOEY&C] with a headquarters office and six regional field offices (MOEY&C, 2004). These
regional offices are structured similar to the hierarchy of a state’s board of education with the
respective local boards of education being responsible for school’s personnel, supervision, and
maintenance. The education system in the Caribbean, particularly the island country of Jamaica,
models itself after the British system. The public education system is divided into four categories:
early childhood, primary, secondary, and tertiary.
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In Jamaica, early childhood, or Pre-K program, focuses on psychomotor and cognitive
behavior for ages four to five years old. The primary level, or elementary school, utilizes an
integrated approach of subjects for Grades 1-3 and discreet subjects for Grades 4 and 5. After
successful mastery on the Grade Six Achievement Test, the student may then move on to the
secondary level, it being divided into two levels, low grades 7-9 and high grades 10-11. Once
completing the five year requirements at the secondary level, a student may “sit” the Caribbean
Examination Council’s exit exam, or CXC (MOEY&C, 2004). This is equivalent to taking the
graduation tests and qualifying to receive a diploma.
The Jamaican Ministry of Education, Youth and Culture [MOEY&C] is the government
agency responsible for providing a system of universal, almost free, public schooling for young
people through Grade 12. Education is considered a national priority and essential for the Jamaican
country to be successful. Educational reform in Jamaica, under the motto of “Education for All,” is
aimed at improving literacy and numeracy, producing a globally competitive workforce (Davis,
2004). The MOEY&C (2004) stated in their national report on education there are seven strategic
objectives set forth in this reformation: devise and support initiatives striving toward literacy;
secure teaching and learning opportunities to optimize access, equity, and relevance throughout the
education system; support student achievement and core standards to insure national goals are met;
promote cultural development, awareness, and self-esteem for all; establish a system of
accountability and performance management to improve student performance and win public
confidence and trust; provide effective professional development for staff in all aspects of service
to increase student learning; provide and use technology as preparation for life in the national and
global communities.
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Attitudes and Skills of Math in Jamaica
Poor attitudes toward mathematics are evident among many students, and some view the
subject as being of little use to them outside of school (MOEY&C, 2003). Unsatisfactory student
performance in mathematics and the low levels of numeracy impacted the MOEY&C to develop
an initiative aimed at improving mathematic and numeracy proficiency at all levels of education,
but specifically in the primary and secondary schools. This led to cooperation and development
of standards and policies to be taught by educators nationwide. The Jamaican government,
through the MOEY&C, pledged to support the policies by providing human, material, and
institutional resources. Further, the policy stated teacher training and professional development
had to be restructured in order to ensure mathematics learning and the high levels of numeracy
expected in order to be competitive on the global marketplace of the 21st century in both males
and females, and across all levels of socioeconomics (MOEY&C, 2003). Teachers had
previously been asking for supplementary resources and a lower teacher-to-student ratio (Ganser,
2001). Less experienced or beginning teachers stated that their pre-service did not prepare them
for the reality of teaching, and preparation was needed for the “work world” upon completion
and employment (Ganser, 2001). Principals went even further in interviews with Ganser (2001)
to say that classroom management skills and pedagogical content was lacking, but stopped short
of stating that although these are desirable traits, this may be difficult to implement training and
get practicum experience at the teacher colleges.
The Joint Board of Teacher Education [JBTE] is the centralized quality control agency
for Teacher College’s curriculum, the certification agency for teachers, and prepares final
examinations and provisions for external assessments of students’ work (JBTE, 2008). This
agency stated that a new way of teaching needed to be established. One of student-centered
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learning, teaching under a constructivist attuned environment with such strategies as: cooperative
learning, grouping, project work, sharing of ideas and questioning for understanding. These
teachers must be able to think alongside their students, giving informal and formal assessments
with re-teaching as necessary to provide mastery of misunderstandings in order to bridge the
gaps and develop critical thinking and problem solving skills (JBTE, 2008). As Clarke (2005)
states, the emergent teacher engages in reflective practices and uses their repertoire to understand
and stimulate a constructivist learning environment, while encouraging the same level of
reflection among their students.
The Taskforce on Educational Reform (2004) concluded that every learner will maximize
their potential in a learner-centered education environment with maximum use of learning
technologies supported by committed, qualified, competent, effective and professional educators.
They went further to state that the education system will be equitable and accessible to all
students through Grade 11. In contrast to many countries where 12 or 13 years of formal
schooling is provided, Jamaica provides 11 years from Grades 1-11. Accountability,
transparency and performance are to be the hallmarks of a system that is excellent, selfsustaining and resourced and welcomes full stakeholder participation. The system produces full
literacy and numeracy, a globally competitive, quality workforce and a disciplined, culturally
aware and ethical Jamaican citizenry (Taskforce on Educational Reform, 2004).
Jamaican males have consistently performed poorly or underachieved on standardized
examinations and have been steadily marginalized at all levels of the education system
(MOEY&C, 2010). The ministry commissioned a study of gender differences in academic
achievement in order to determine why boys were achieving less than girls, and to discover what
part, if any, the school plays in this disparity. The research was designed to emphasize school-
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related factors, although recognizing that socialization within the home and community may
contribute a great deal to students’ motivation to achieve (Evans, 1999). Socialization and
culture have impacted the significance of school performance among male and female students
in regards to participation and engagement of learning (Clarke, 2005). The interactive process
through which we construct our meanings, values, and behavioral norms is what is called
socialization (American Heritage Dictionary, 2010). Teachers are prepared to cope with this
social issue and the instructional challenges that confront them daily in their classrooms,
enabling the effectiveness of their teaching strategies to contribute to the successfulness of their
students’ achievements (Clarke, 2005).
While visiting classrooms in Jamaica, Evans (1999) observed that there were clear gender
differences in the way boys and girls responded to the curriculum and to the teaching methods .
Topics taught also elicited different responses from boys and girls. While there were a few
instances in which there was equal participation from boys and girls, in most cases the girls
showed more interest, were more eager to answer questions, to spell words, to read and, in
general, to carry out academic tasks (Evans, 1999). Additionally, lessons in which the boys were
involved and interested can be characterized as requiring action or active participation on the part
of the students, or as activities which drew on students’ experiences, knowledge, or skill, or the
subject matter was of intrinsic appeal to boys. When the teaching method required students to
take notes or to copy from the chalkboard, the boys were less likely to become engaged. It was
hypothesized that school practices can influence students’ motivation to learn and to stay in
school which, in turn, influence students’ academic performance (Evans, 1999). Based on
research findings in Jamaica and elsewhere, it was also expected that these factors would affect
boys and girls differently.
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Strategies of the Jamaican Curriculum
Utilizing international pedagogical practices in numeracy and literacy, the policy of the
Jamaican MOEY&C (2003) highlights the value of helping students appreciate the value of
mathematics in everyday living, as well as critical thinking, developing reasoning, and problem
solving skills. The Policy further states that mathematics is useful for developing and learning
spatial and visual skills, for learning science subjects, as well as economics and other disciplines of
the business world. Many students in the United States and Jamaica encounter problems coping
with mathematics. The National Mathematics Advisory Panel (2008), states in many cases these
students are capable of managing mechanical or straight-forward problems, but struggle in solving
real world worded mathematical problems. In most instances, the issue is comprehension of
vocabulary and students incorrectly interpret the terminology and perform the wrong operation.
Further, if students are requested to reflect and articulate the different steps to apply vocabulary to
solve mathematical problems, they will internalize the mathematical procedures. Reflecting on
learning and verbalizing mathematical ideas can allow students to clarify thinking, demonstrate
understanding and prompt new thoughts. Knowing a word involves more than knowing a word’s
definition (Stahl & Bravo, 2010). Over time, the acquired vocabulary and language being used will
become more readily understood as students assimilate the terms being modeled (Approaches to
teaching and learning mathematics, 2007).
In order to fully engage students in mathematic content and concepts, educators and
school administrators have reflected on the performance data of the Caribbean Examinations
Council, General Certificate of Education, and Secondary School Certificate examinations to
continually re-teach, remediate, and revise for proficient learning (Lee, 2001). The Department
of Education and Skills [DES] (2004) set forth programs to reach the most difficult students,
Vocabulary in Math Class
18
males and low socio-economic pupils. Motivation and effective teaching strategies are what they
determined is needed to reach these students.
In order to increase student learning and achievement, this department surveyed a group
of students and found that lower attaining pupils gave different responses from higher-attaining
pupils (DES, 2004). In the findings, lower attaining and low socio-economic students were less
confident and wanted more opportunities to be shown how to do something, through either
demonstration or modeling. Gifted or bright students, on the other hand, preferred to be given
assignments or tasks, and then be given opportunities to discuss their discoveries (DES, 2004).
Mvududu (2005) also believes that involving your own students in exploring the factors
that help them learn can provide you with useful information that will enable you to tailor and
target your teaching. In the findings, the DES (2004) identified techniques and strategies for a
more student-focused learning classroom: having key words for the lesson on their desks or on
the wall; saying new words out loud then having the opportunity to reason out informal
definitions; analyzing text together with the teacher; repeating a newly learned skill until they
have mastered it; having a small part of the lesson that reviews work; being shown how what
they are learning links explicitly with other work; being shown the big picture; having
opportunities to visualize abstract ideas using model and analogy; getting immediate feedback on
their work and praise for success; having the chance and time to improve their work and correct
mistakes; working with a partner in peer to peer tutoring; making sure that much of the learning
is related to real life; using writing frames to structure writing; using games and competitions to
inject a ‘fun’ element.
Applying the strategies
In engaging students with formal vocabulary, it is extremely necessary to allow students to
Vocabulary in Math Class
19
use informal vocabulary and the knowledge and language at which they brought initially to the
classroom in defining terminology (Mvududu, 2005). This allows students to build on prior
knowledge, formulate procedure, and logically explain mathematical concepts. In light of a
constructivist classroom, an environment of problem-solving creates an atmosphere where students
feel safe to explore, conjecture, hypothesize, and brainstorm (Morrow, Gambrell, & Pressley,
2003). When discussing problems in groups as a community of learners or working on the board,
students are continually encouraged to move towards a proficient math vocabulary. These
opportunities for cooperative learning and interaction between students encourage and allow
students to develop meanings of multiple words and arriving at proficiency in mathematical
terminology (Ganser, 2001).
Many classrooms across the United States have implemented standards-based instruction
and use word walls to display the keywords for student mastery and proficiency (Georgia
Department of Education, 2005). While this may make for colorful decoration, it seems to cause
confusion for lower ability students. The problem is that they do not know which words relate to
their particular topic or unit (DES, 2004). One particular literacy strategy to promote a more active
use of these mathematical words is known as looping cards. In utilizing looping cards, the DES
(2004) states educators should use them frequently throughout a topic as a quick timed informal
assessment of student proficiency. This strategy allows students to write the vocabulary and
collaboratively create a definition on a blank note card, or develop the steps to solving a
mathematical process.
Webbing, or brainstorming, effectively activates students’ prior content knowledge
(Barton, Heidema, & Jordan, 2002). This allows students to generate quickly what they know
about a topic or key concept. Brainstorming involves two basic steps: identifying a key concept
Vocabulary in Math Class
20
while reflecting on the main topic of study, and students working in small groups to generate a list
of words related to the concept in a given number of seconds. This process captivates the students’
interests much more than the traditional rote of memory review (Vacca & Vacca, 2002). One such
example of webbing that will improve students’ understanding of mathematical terminology and
the ability to recognize symbols is a word wall. In Jamaica the students have their own word wall
right on their desk. This simple graphic organizer can be effective in increasing mathematical
proficiency.
In a constructivist classroom, questions and discussions that elicit students’ thinking build
solution strategies that lead to greater clarity and precision. A significant amount of class time
should be spent developing mathematical ideas, not just practicing skills (Donovan & Bransford,
2004). This concept lends itself to group work. The usual form of group work tends to allow
students to develop bad habits of gravitating to their comfort zone and do more talking than
working. Behavioral and instructional guidelines and goals are clearly established and
communicated to each peer tutoring group (DES, 2004). A flexible grouping strategy will
accommodate student interests, learning styles, and social needs, such as friendship, in addition to
meeting instructional needs and goals of mastery or proficiency.
Most teachers are not comfortable utilizing graphic organizers due to the learning curve
for the teacher and the student (Graves, 1985). What does a teacher spend their class time on to
improve student learning and increase student achievement? For teachers, time is a precious
commodity, and the ever sense of urgency to teach the material for the “test” is upon their
shoulders. Teachers are continually feeling the pressure of more responsibility; “do more with
less”. Time is the strongest negative argument for those who oppose direct vocabulary
instruction (Marzano, 2004). Many teachers do not feel it is their responsibility to teach
Vocabulary in Math Class
21
vocabulary, and students learn key vocabulary through daily interaction with the specific
curriculum (Marzano, 2004). In classrooms already pressed for time, many teachers feel the time
necessary for utilizing graphic organizers and direct vocabulary instruction was not worth the
benefit (Graves, 1985). However, Graves (1985) stated, with reflective practice, some students
are more skillful than others at effectively using graphic organizers warranting less support and
time required of the teacher for direct vocabulary instruction.
School Change
The state of Georgia believes in setting high standards, expecting every child to achieve
them, measuring performance, and providing supports to help all children succeed. Georgia has
established an outcomes-based environment which helps the State seed and then scale innovative
practices, while leveraging the creativity of on-the-ground practitioners (Georgia Governor’s
Office, 2010). With each school district being held accountable for their students’ academic
success, the state of Georgia has begun a process of systemic equity whereby all learners are in a
standards based classroom, know as tier 1 (Georgia Department of Education [GADOE], 2008).
Annual Yearly Progress (AYP) serves as one part of the Single Statewide Accountability
System (SSAS) which “integrates both federal and state requirements dealing with educational
accountability…[and] makes the resulting rewards and consequences virtually identical for all
Georgia Schools” (GADOE, 2008, para. 2). In order to make AYP, each school and district is
required to meet the following three criteria:
1. Each school and all student groups (comprising at least 40 members) must have a
95% or greater participation rate on selected state assessments in Reading/English
Language Arts and Mathematics.
Vocabulary in Math Class
22
2. Each school and all student groups must meet or exceed the state’s Annual
Measurable Objectives (AMO) with regard to the percentage of students who
meet the standard or exceed the standard on state assessments in
Reading/Language Arts and Mathematics.
3. Each school and all student groups must meet the standard or show progress
toward meeting the standard on a second indicator. Second indicators include
graduation rate and attendance rates. (GADOE, 2008)
Each year the Annual Measurable Objectives for the selected assessments increases, and each year,
Georgia school systems feel increased pressure to raise test scores in order to make AYP. By the
2013-2014 school year, the AMOs will reach 100 percent; that means that 100 percent of students
are expected to take and pass either the Reading/Language Arts and Math CRCT or the English
Language Arts and Math Georgia High School Graduation Test [GHSGT]. These increasing test
score requirements have forced school systems to explore new avenues in order to continually raise
scores because as every educator knows, it is very difficult, if not impossible, to get 100 percent of
students to pass a required test.
Teachers and administrators know, based on evidence of the GHSGT, that an achievement
gap or educational inequity does exist based on gender, race and socioeconomic status. Therefore,
as teachers and leaders, we must be willing to face the inequity of this situation and take ownership
of the problem, the success of every student. Change can be a difficult if not painful process, but in
the field of education change is expected. Smith (1999) pursues the idea that “understanding that
which confronts us as new is made possible in the “now” by virtue of the forestructure of
understanding which is already through past experience” (p.129). In order to be a change agent,
teachers and administrators must effectively evaluate and assess student engagement, learning,
Vocabulary in Math Class
23
questioning, discussion, teaching practices, and help to prevent gaps in achievement from
occurring (Skrla, McKenzie, & Scheurich, 2009). If a teacher can quickly assess and evaluate
learning or misunderstanding early, they can avoid a gap and ensure equity.
When schools begin to access data and really utilize the information in benchmarks and
state mandated tests to be accountable to all student learning and performance, then the gaps in
student achievement will begin to close. Administrators and school leaders must be able and
willing to reflect, categorize, and address the strengths and weaknesses within the data, recognizing
that every student counts (Skrla et al., 2009). Keeping the research strategies in mind, the
instructional team must collaboratively reflect on the successes and weaknesses in the theories and
institute a procedure to actively engage students to construct learning. As the nation continues to
move towards high stakes testing and performance based curriculum, teachers must be willing to
become less dominating, and become “problem-posing”, real world application communicators,
that listen to students to become jointly responsible for this process of growth (Friere, 2005). By
constantly reflecting on the problem submitted to the students, the educator must continually
consider and reflect on the knowledge level of himself and of his ever-changing students.
Teaching is influenced by the teachers’ values and personality. To effectively have an
equity attitude and create a school that is successful and equitable for all students, it is necessary to
treat everyone with respect, appreciation, and care (Skrla et al., 2009). When addressing these
attitudes one must have courageous conversations in being a change agent and these interactions
are always characterized by that same respect, appreciation, and care. Thus, if a mistake is made or
a gap has been closed in raising student performance, it is important to remind oneself of the longterm endurance of equity work and to continue with a consistent and persistent focus of change
(Skrla et al., 2009).
Vocabulary in Math Class
24
CHAPTER III: METHODOLOGY
Research Design
My research was a mixed methods action research study of qualitative and quantitative
data. Action research helps educators reflect on their practice, collect data about their practice,
and create alternative ways to improve their practice. This study was simply a form of selfreflective inquiry. It consisted of planned, continuous, and systematic procedures for reflecting
on professional practice and for trying out alternative practices to improve outcomes. Stringer
(2007) states action research works through three basic phases: look, act, and think. When
evaluating, or looking, we define, describe, and investigate the problem and the context in which
it is set. We also describe what all the participants have been doing. After evaluating, we analyze
and interpret the situation. We reflect on what participants have been doing, and we look at areas
of success and any deficiencies, issues or problems. Finally, in evaluation we judge the worth,
effectiveness, appropriateness, and outcomes of those activities (Stringer, 2007). We act to
formulate solutions to any problems.
Data were collected over a period of two years implementing two separate teaching
programs. Achievement data were compared from benchmark pre-post tests and the Mathematics
II state adopted End of Course Test. The differences in scores from my four Mathematics II classes
were analyzed using independent t-tests of the pre-post test data and EOCT data. In the instance of
this research study, action research was effectively used for teaching in two of these 10th grade
Mathematics II classes with the treatment of vocabulary in the application of looping cards, or note
cards, having key words on desk, and a modified group work strategy of literacy and numeracy
practices from Jamaica.
Vocabulary in Math Class
25
Setting
The setting of this research was in a rural county high school, in West Central Georgia.
The school population for 9th through 12th was approximately 600 students. Permission was
sought and secured from the high school principal before any research had taken place. Informed
consent forms were given to students for parental permission and to participating administrators
in the study. These forms acknowledged parental consent and the students’ willingness to be in
the study and participate in a survey once the research was completed. All of the sample
populations information, scores, and responses are held confidential.
Subjects and Participants
The subject population, 10th grade students of four independent Mathematics II classes,
were termed Groups A, B, C, and D. Groups A and B represent my students from last year when I
taught Mathematics II without focusing on literacy skills practices from Jamaica. Groups C and D,
the treatment groups, represent my current Mathematics II students who have received instruction
in math introducing and applying these literacy and numeracy skills. These classes were grouped
heterogeneously. Also, the students from these groups came from an uneven mixture of
socioeconomic status consisting of lower to middle class families.
The students in groups A and B consisted of fifty-one students, and of these twenty-eight
were of low socioeconomic status. Of the fifty-one students, twenty-five were female and twentysix were male. Student ethnic backgrounds consisted of ten African Americans and forty-one
Caucasians (see Table 3.1).
Table 3.1: Mathematics II Study Subjects – 2009 / 2010
Group A
Group B
Total
Female
Male
African
American
Caucasian
25
26
12
13
13
13
3
7
22
19
Vocabulary in Math Class
26
There were fifty-two students, twenty-six females and twenty-six males, in Groups C and
D. The racial make-up of the class consisted of five African Americans and forty-six Caucasians
(see Table 3.2), and forty of these students met the requirement of low socioeconomic status.
Table 3.2: Mathematics II Study Subjects– 2010 / 2011
Group C
Group D
Total
Female
Male
24
28
10
16
14
12
African
American
3
2
Caucasian
21
26
The participant in this study was the assistant principal who is responsible for instruction
and curriculum in our building. He was selected because he is involved in assisting in the
systematic change of instructional methods and professional development of teachers.
Procedures and Data Collection Methods
In conducting this action research study, a combination of qualitative and quantitative
data was gathered to investigate the effectiveness of student achievement and understanding by
applying the Jamaican literacy strategies of looping cards. The researcher first introduced the
learning strategy of looping cards to the treatment group of students. Application of this
international approach to learning involved students in the use, application, and definitions of
vocabulary, as well as problem solving strategies on note cards. These note cards were used and
reviewed daily as a warm-up activity having students paired, and became a part of the students’
routine in the mathematics classroom. A sample of student looping cards can be found in
Appendix A. These cards were referred to during instruction and students utilized these cards as
part of the learning process.
Vocabulary in Math Class
27
Pre and post tests, Mathematics II EOCT, student surveys, and an administrative
interview were examined in the application of this approach to student learning. Table 3.3 shows
the overall alignment of data collection methods with the study’s focus questions.
Table 3.3: Data Shell
Focus Question
Literature Sources
Type: Method,
Data, Validity
How are data
analyzed
Rationale
How does the
integration of
vocabulary
strategies into the
mathematics
curriculum
increase low
socio-economic
students’
proficiency in
mathematics?
Department of
Education and
Skills (2004).
Method:
Pre / Post
Benchmark
Quantitative:
Dependent t-test
Effect size r
Pearson’s corr
Quantitative:
determine if there
are significant
differences
U.S. Dept of Educ.
(2007).
Standardized
Math 2 EOCT
National Math
Advisory Panel.
(2008).
Type of Data:
Interval
Type of
Validity:
Content
Skrla, L. (2009).
What are the
attitudes and
opinions of the
adopted
curriculum
among learners?
What was the
level of success
of change in the
process strategies
as viewed by an
administrator to
encourage the use
of looping cards
in classrooms for
achievement
equity?
Independent ttests
Cohen’s d
Evans, H. (1999).
Method:
Survey
Quantitative:
Chi Square test
Ganser, T. (2001).
Cronbach alpha
Adams, T. (2003)
Type of Data:
Nominal,
Qualitative
Mvududu, N.
(2005).
Type of
Validity:
Construct
Draper, R. (2002).
Method:
Interview
Friere, P. (2005).
National Council
of Teachers of
Math (2006).
Skrla, L. (2009).
Type of Data:
Nominal,
Qualitative
Type of
Validity:
Construct
Qualitative:
Coded for themes
Quantitative:
determine if there
are significant
differences
Qualitative:
look for
categorical and
repeating data
Vocabulary in Math Class
28
In examining the success of this study’s teaching strategies on increasing student
performance from focus question one, the quantitative data for Groups A through D are of a prepost benchmark department generated test and the Mathematics II End of Course Test that is
mandated by the state of Georgia. Teachers in the Heard County school system collaboratively
created the benchmark test to assess student learning of mathematics, and as an indicator of
performance on the states’ high stakes tests. A copy of the pre and post test can be found in the
Appendix B. These tests results were compared for significant differences of the treatment group
and between the control and treatment groups.
The State Board of Education of Georgia adopted end of course assessment in grades
nine through twelve in the core subject areas of English Language Arts, Mathematics, Science,
and Social Studies as mandated by the A+ Educational Reform Act of 2000, O.C.G.A. §20-2281. There are eight content area assessments comprising the End of Course Testing [EOCT]
program. This researcher only analyzed the Mathematics II EOCT results of the treatment and
control group.
The state mandates that the EOCTs count fifteen percent of the student’s grade in the class.
These tests are graded by the state and the results are reported to the school system at the end of
each semester (Georgia Department of Education, 2005).
The attitudes and opinions of the control group were solicited through the completion of an
anonymous survey concerning focus question two after the completion of the post test benchmark
and the Mathematics II EOCT. The survey can be found in the Appendix C. The survey utilized a
Likert Scale of responses ranging from strongly disagree, disagree, neutral, agree, and strongly
agree to various statements. The responses were evaluated to determine the strengths and
weaknesses of looping cards and the student’s perception of these strategies.
Vocabulary in Math Class
29
Finally, an interview was conducted to investigate the perception an administrator
concerning focus question three as to the process of looping cards and to what level of success
these strategies were perceived to be effective. A list of interview questions can be found in the
Appendix D. The assistant principal of curriculum and instruction involved in the study was
interviewed in his office after the EOCT scores were returned from the state. The assistant
principal was asked about his feelings regarding direct vocabulary instruction, looping cards, and
from an administrator’s point of view of all teachers using looping cards in a standards-based
classroom.
Validity, Reliability, Dependability, and Bias
As a researcher, Winter (2000) states that attempting to delimit phenomena into
measurable or common categories can be applied to all subjects and similar situations, the
researcher’s methods involve the use of standardized measures so that varying perspectives and
experiences of people can be fit into a number of predetermined response categories to which
numbers are assigned. The traditional notion of discrimination, or bias, is based on a prohibitive
motive, such as gender, race, or national origin. However, there are large, persistent disparities in
mathematics achievement related to race and income (National Mathematics Advisory Panel,
2008). The disparate impact of low socioeconomic students’ proficiency on these mandated tests,
have been attributed to an unfair curriculum where reading and vocabulary have not been
stressed (National Mathematics Advisory Panel, 2008).
Focus question one endeavors to integrate vocabulary strategies into the mathematics
curriculum to increase proficiency and measure student achievement based on the use of a
collaboratively teacher made pre and post test and the state administered Mathematics II EOCT.
Both tests will produce interval data. Interval data, as described by Salkind (2010), is based on
Vocabulary in Math Class
30
the underlying continuum that we can discuss how much more a higher performance is than a
lesser one. The pre- and post-tests and the EOCT are assessments of student knowledge and were
analyzed to determine if the post-test scores and the 2011 EOCT score of the treatment group are
significantly higher. These assessments have content validity. Popham (2008) describes content
validity as the adequacy that the assessment represents the standards of the domain about which
inferences are to be made. Validity determines whether the research measures what it was
intended to measure or how truthful the research results are. Further, Popham (2008) says that
reliability is a measure of a test’s consistency to accurately measure data. The consistency with
which assessment items are answered can be determined through the test-retest correlation,
whereby a respondent would be asked to answer the same questions at two different times
(Popham, 2008). This attribute of the instrument is referred to as stability. A high degree of
stability indicates a high degree of reliability. The collaborative teacher assessments have the
potential for bias. Bias as defined by Popham (2008) is the unfair penalization of a student’s
performance on an assessment that is distorted because the content disadvantages the student
based on the student’s group membership. In order to minimize the bias that students may
experience, the collaborative group of teachers agreed to the strategies of teaching students and
to ensure that any student that had testing accommodations were strictly followed. Striving for
achievement equity for all students, this study attempts to close the achievement gap utilizing the
process of systematic equity whereby all learners are in a standards based classroom, know as
tier 1 (Georgia Department of Education [GADOE], 2008). This proves effective that all students
are in a systematic learning environment that supports growth, achievement, flexible grouping,
differentiation, and ensures learners have access to quality instruction. Further, a tier 2
classroom, as described by the GADOE, utilizes benchmark assessments and interventions based
Vocabulary in Math Class
31
on data analysis to determine student weaknesses in learning in order to address student
deficiencies (2008). Utilizing this type of equity audit, the process of making choices about how
to proceed with struggling students, gathering data, processing results, and planning for change
will help to close this achievement gap (Skrla et al., 2009).
Analysis of focus question two has an emphasis on student attitude and opinion of the
adopted curriculum of utilizing looping cards and the strategy’s effectiveness. These perceptions
were measured through an anonymous student survey using a Likert scale. The construct validity
of the ordinal data of the responses is a measure of the student’s feelings or dispositions on the
topic of looping cards and vocabulary strategies (Popham, 2008). A Cronbach’s alpha calculation
was performed to determine the consistency or reliability of the students’ answers on the surveys
and allowed for coding by themes (Popham, 2008). In order to minimize any unfair bias, the
survey was read aloud to all students. The results of the survey should attempt to allow for a
reflective practitioner and improve teacher quality. One of the key factors to influence student
learning and achievement is access to highly qualified teachers, and this is based on the content
knowledge and experience of the teacher (Skrla et al., 2009).
The assistant principal of curriculum and instruction was interviewed in light of focus
question three as to the perception of the use of looping cards in teaching to proficiency of the
curriculum in the mathematics classroom. The qualitative data were collected in the effort to
understand the subjects’ point of view and to reveal the meaning of their experience (Kvale &
Brinkman, 2009). The supporting gathered data is based upon the respondent’s feelings yielding
construct related validity (Popham, 2008). Dependability of the interview was ensured due to
audio taping and allowed for transposing for future reference. In order to increase student
achievement and help to close the achievement gap among different groups of students, lending
Vocabulary in Math Class
32
to educational equity, it is hoped, and the researchers personal bias, that the data gathered in the
interview process leads to endorsed usage of looping cards and professional development of
teachers in this researched strategy.
Administrators and school leaders must be able and willing to reflect, categorize, and
address the strengths and weaknesses within the data, recognizing that everybody counts and
then the gaps in student achievement will begin to close (Skrla et al., 2009). Hoping for
systematic equity in the standards-based classroom as prescribed by the state of Georgia and our
school, the success of looping cards will cause the administration to encourage the use of looping
cards in order to increase achievement of all students, but more specifically to assist in closing
the learning gaps. From the data collected, the reflective practitioner will attempt to improve
teaching quality in order to become an effective change agent in the equity of all students. After
all, closing the achievement gap of low socioeconomic and ethnic minorities was the intent of
this research, and the idea of achievement equity attained.
Analysis of Data
The quantitative data of Groups A through D were collected and analyzed. The comparison
of the central tendency showed significant improvement and gains between the groups and by low
socioeconomic status where Jamaican literacy and numeracy strategies were introduced and
implemented. By combining the four groups into two, the control group of A and B and the
treatment group of C and D, a t-test for independent means calculated with a significance level of p
< 0.05, in order to reject the null hypothesis, was conducted using the scores from the state
mandated Mathematics II EOCT. For comparative purposes, the pre and post tests of the control
and treatment groups of students was analyzed using a dependent-t test and the null hypothesis will
be rejected if p < 0.05. The dependent-t tests showed there were significant differences between
Vocabulary in Math Class
33
means of one group tested twice. The data was examined using independent-t tests to determine if
there were significant differences in the achievement levels of the control group and treatment
group from pre-test to post-test after receiving vocabulary instruction using looping cards. The
effect size was calculated to determine the magnitude of the treatment (Salkind, 2010), which in
this case was the application of vocabulary strategies from Jamaica. The acceptance of the use of
effect size interpretation scales permeates education literature. For the dependent-t test, or paired
means, the most commonly excepted value for interpreting effect size is Pearson’s r value. Further,
Cohen’s d statistic was used to estimate the effect size for the independent-t tests of the
independent groups.
The student perception data was collected from the student surveys in order to analyze the
opinions and attitudes of the employed strategies of looping cards in the mathematics classroom. A
chi square analysis was conducted to determine the significance of the student answers. The
significant levels are reported at the p < 0.05, p < 0.01 and the p < 0.001 levels. Also, for the
structural corroboration of the data of this part of the study a Cronbach’s alpha was used to
measure internal consistency, or reliability, of how closely related a set of items are as a group
(Salkind, 2010).
The final part of the data collected was from an interview of the assistant principal to assess
the level of success in the change of the practices used in the study. In reviewing the interview
transcripts, the themes and categories emerging, recurring, or dominant will be coded to discuss
school change and improvement.
To give additional consensual validity to the research, the study was first proposed to the
supervising faculty for approval (Eisner, 1991). A comparison of the literature of the Jamaican
Vocabulary in Math Class
34
strategies of looping cards gives epistemological validation. These measures of validity help to aid
in the meaningfulness and trustworthiness of the design and methods of the research of the study.
Giving further integrity to the study, great care was taken in the design and analysis of the
research. This was done to ensure detail and accuracy in order to produce strong evidence to assert
the value of looping cards in the mathematics classroom. In the review of the literature, the issues
were raised of how can looping cards be effective and the weaknesses of this strategy exposed in
order to give fairness to the study. In this preparation, rightness of fit credibility as described by
Eisner (1991) can be assured. Any research study must be detailed enough so future researchers
can duplicate the study. Additionally, Eisner (1991) states that this attention to detail provides
referential adequacy allowing for ease of transferability for future research. Further, adding
structural corroboration, comparisons of the collected data in the analyses of the central tendency,
dependent and independent t-tests to indicate that there was statistical significance for the study,
and this brought catalytic validity in teaching mathematics with regard to vocabulary and literacy
strategies.
It was hoped that the data collected and presented through this study provided convincing
evidence to serve as a transformational power enabling educational equity for learning, and thus
through catalytic validity, as discussed by Kinchloe and McLaren (1998), enable educators to
change in hopes of helping students to be engaged and proficient in their use of looping cards in
the math class.
Vocabulary in Math Class
35
CHAPTER IV: RESULTS
The research showed a significant statistical achievement for the treatment group when
literature and vocabulary strategies of looping cards were introduced and applied. The results are
organized by focus question. Quantitative and qualitative data are presented in the findings.
Focus question one wanted to determine if the integration of vocabulary strategies into the
mathematics curriculum would increase the proficiency of low socio-economic students in math.
The quantitative data gathered from the pre- and post-test and Math II EOCT test were analyzed
through the computation of dependent-t and independent-t tests to show significance. Table 4.1 and
Table 4.2 display the treatment and control groups’ results, respectively, of the dependent-t tests
used to evaluate significance of the pre- and post- tests’ scores.
Table 4.1: Dependent-t Test for Treatment Group – all students
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(51) = 60.83, p < 0.01
Pre
29.98
24.92
52
0.59859261
0
51
-60.82975651
1.41052E-49
1.67528495
2.82104E-49
2.00758377
Post
76.5
44.84
52
Vocabulary in Math Class
36
The dependent-t test results of the treatment group pre and post-tests indicated an
extremely significant difference with a large increase in student success, t(51) = 60.83, p < 0.01. A
Pearson’s coefficient of r = 0.60 shows a large test-retest reliability.
Table 4.2: Dependent-t Test for Control Group – all students
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
Pre
28.76
16.90
51
0.599093675
0
50
-46.96943739
2.47792E-43
1.675905025
4.95584E-43
2.008559112
Post
70.96
63.52
51
t(50) = 46.97, p < 0.01
The results of the control groups pre and post-test also indicated an extremely significant
difference of the t-test with a large increase in student success, t(50) = 46.97, p < 0.01. A Pearson’s
coefficient of r = 0.60 shows a large test-retest reliability.
The data was further disaggregated to show the comparison of low socioeconomic
student’s achievement using independent-t tests in and between the treatment and the control
groups. These t-tests were analyzed for significance at the confidence level of 0.05. Table 4.3
displays the outcome of an independent-t test of the scores on the pre-test between the treatment
group and the control group. Table 4.4 exhibits the results of another independent-t test of a
comparison of the post-test scores of the treatment and control groups.
Vocabulary in Math Class
37
Table 4.3: Independent-t Test Comparison Treatment and Control Pre-Test
t-Test: Two-Sample Assuming Unequal Variances
Mean
Variance
Observations
Hypothesized Mean Diff
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Pre Treat
29.63
23.73
40
0
66
1.461768107
0.074274994
1.668270514
0.148549987
1.996564419
Pre Cont
28.11
13.58
28
t(66) = 1.462, p > 0.05
The comparison of the pre-test showed to accept the null hypothesis, and that there was no
significance, t(66) = 1.46, p > 0.05, between the treatment and control groups. This result validated
that both groups are at about the same level of knowledge of mathematics on the pre-test.
Table 4.4: Independent-t Test Comparison Treatment and Control Post-Test
t-Test: Two-Sample Assuming Unequal Variances
Mean
Variance
Observations
Hypothesized Mean Diff
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
t(54) = 5.453, p < 0.05
Post Treat
75.73
42.36
40
0
54
5.452799704
6.32157E-07
1.673564906
1.26431E-06
2.004879288
Post Control
66.43
51.74
28
Vocabulary in Math Class
38
The mean for the post-test control group was lower than for the post-test treatment group.
The results, t(54) = 5.45, p < 0.05, of the t-test indicated to reject the null hypothesis, and accept that
there was significant difference. The Cohen’s d calculation yielded a large effect size of 1.36.
To continue the comparison of student test scores and to show the achievement gaps and
proficiency of the subjects, the treatment and control groups’ pre and post test scores were
compared, respectively in Table 4.5 through Table 4.8, using the selection status of
socioeconomics.
Table 4.5: Independent-t Test of Treatment Pre-Test based on Socioeconomics
t-Test: Two-Sample Assuming Unequal Variances
Pre Non Treat
Mean
33.33
Variance
24.61
Observations
12
Hypothesized Mean Diff
0
Df
18
t Stat
2.280726242
P(T<=t) one-tail
0.017481941
t Critical one-tail
1.734063607
P(T<=t) two-tail
0.034963882
t Critical two-tail
2.10092204
Pre SES Treat
29.63
23.73
40
t(18)= 2.281, p < 0.05
The mean scores of the treatment group pre-test were significantly lower for the low
socioeconomic students. The null hypothesis was rejected based on the results of t(18) = 2.28, p <
0.05. The Cohen’s d calculation yielded a large effect of 0.75.
Vocabulary in Math Class
39
Table 4.6: Independent-t Test of Control Pre-Test based on Socioeconomics
t-Test: Two-Sample Assuming Unequal Variances
Pre Non Control
Mean
31.08
Variance
18.41
Observations
25
Hypothesized Mean Diff
0
Df
48
t Stat
2.689928368
P(T<=t) one-tail
0.004900794
t Critical one-tail
1.677224196
P(T<=t) two-tail
0.009801589
t Critical two-tail
2.010634758
Pre SES Control
28.11
13.58
28
t(48) = 2.690, p < 0.05
The results of the independent-t test for the control group pre-test based on socioeconomics
was t(48) = 2.69, p < 0.05. Therefore, the calculation showed significant difference, and the null
hypothesis was rejected. Cohen’s d yielded a medium effect size of 0.30.
Table 4.7: Independent-t Test of Treatment Post-Test based on Socioeconomics
t-Test: Two-Sample Assuming Unequal Variances
Post Non Treat
Mean
79.08
Variance
48.27
Observations
12
Hypothesized Mean Diff
0
Df
17
t Stat
1.489864878
P(T<=t) one-tail
0.077289531
t Critical one-tail
1.739606726
P(T<=t) two-tail
0.154579062
t Critical two-tail
2.109815578
t(17) = 1.490, p > 0.05
Post SES Treat
75.73
42.34
40
Vocabulary in Math Class
40
The comparison of the post-test t-test showed to accept the null hypothesis, and that there
was no significance at t(17) = 1.49, p > 0.05, between the treatment and control groups. This result
corroborated that both groups are at about the same level of proficiency on the post-test.
Table 4.8: Independent-t Test of Control Post-Test based on Socioeconomics
t-Test: Two-Sample Assuming Unequal Variances
Post Non Control
Mean
76.48
Variance
21.18
Observations
25
Hypothesized Mean Diff
0
Df
46
t Stat
6.12304766
P(T<=t) one-tail
9.46596E-08
t Critical one-tail
1.678660414
P(T<=t) two-tail
1.89319E-07
t Critical two-tail
2.012895599
Post SES Control
66.43
51.74
28
t(46) = 6.123, p < 0.01
The mean scores of the control group post-test were significantly lower for the low
socioeconomic students. The null hypothesis was rejected based on the results of the independent-t
test at t(46) = 6.12, p < 0.01. The Cohen’s d calculation yielded a large effect of 1.67.
To give additional strength to the study of the use of looping cards in the mathematics
classroom, the Georgia Math II EOCT data was disaggregated by treatment and control group and
socioeconomics utilizing independent-t tests. The independent-t tests were analyzed for
significance at the 0.05 level. Table 4.9 displays the results of the independent-t test comparing the
treatment group to the control group.
Vocabulary in Math Class
41
Table 4.9: Independent-t Test of Treatment and Control Math II EOCT
t-Test: Two-Sample Assuming Unequal Variances
Treatment
Mean
75.90
Variance
47.97
Observations
52
Hypothesized Mean Diff
0
Df
94
t Stat
2.425300318
P(T<=t) one-tail
0.008602865
t Critical one-tail
1.661225855
P(T<=t) two-tail
0.01720573
t Critical two-tail
1.985523442
Control
72.06
81.14
51
t(94) = 2.425, p < 0.05
The comparison of the Mathematics II EOCT scores indicated to reject the null hypothesis,
and that there was significance, t(94) = 2.43, p < 0.05, between the treatment and control groups.
The Cohen’s d calculation yielded a medium effect of 0.48.
Table 4.10: Independent-t Test of Treatment and Control Math II EOCT Low SES
t-Test: Two-Sample Assuming Unequal Variances
Treatment SES
Mean
74.63
Variance
41.47
Observations
40
Hypothesized Mean Diff
0
Df
54
t Stat
4.75126296
P(T<=t) one-tail
7.67977E-06
t Critical one-tail
1.673564906
P(T<=t) two-tail
1.53595E-05
t Critical two-tail
2.004879288
t(54) = 4.75, p < 0.01
Control SES
66.5
52.85
28
Vocabulary in Math Class
42
The comparison of the socioeconomic groups of the treatment and control groups revealed
another significant difference, t(54) = 4.75, p < 0.01. This level of confidence acknowledges
rejecting the null hypothesis and the Cohen’s d effect size was large at 1.18.
Table 4.11: Independent-t Test of Treatment and Control Math II EOCT no SES
t-Test: Two-Sample Assuming Unequal Variances
Treatment Non
Mean
82.67
Variance
36.42
Observations
12
Hypothesized Mean
Difference
0
Df
21
t Stat
1.822434096
P(T<=t) one-tail
0.041330768
t Critical one-tail
1.720742903
P(T<=t) two-tail
0.082661535
t Critical two-tail
2.079613845
Control Non
78.83
32.33
23
t(21) = 1.82, p < 0.05
The mean for the scores of the Math II EOCT were higher for the treatment group than for
the control group without low socioeconomic students. Once again, the null hypothesis was
rejected based on the results of the independent-t test, t(21) = 1.82, p < 0.05. Cohen’s d calculation
yielded a large effect size of 0.66.
The data from student surveys were analyzed to reveal the attitudes and opinions of
students as to the use of the adopted curriculum strategy of looping cards. The survey was
administered to the subjects after completion of the course. The survey utilized a Likert response
scale consisting of fifteen questions. Students were questioned as to how they felt about vocabulary
in the math classroom, the use of looping cards, and their overall attitude to vocabulary instruction
Vocabulary in Math Class
43
in the mathematics classroom. A chi square analysis was performed on the student survey
responses. Table 4.12 displays the results of the student survey responses.
Table 4.12: Student Survey Results
Survey
Items
n = 15
Item 1
Survey Questions
χ2
Vocabulary is important in math class.
51.17***
My math teacher believes vocabulary is important in learning
mathematics.
Reading in math class is not important.
96.17***
35.96***
Item 5
Student discussion of vocabulary is a key component in
comprehension.
Sometimes we have to read in math and I don’t understand the words.
Item 6
The vocabulary words we use in math class are easy to remember.
16.17**
Item 7
Note cards help me to understand the math concepts of word problems
and equations.
Learning new words before I read is helpful.
77.26***
73.57***
Item 10
It is easier to understand informal definitions used on note cards, than
book vocabulary.
It is helpful when my teacher takes the time to discuss vocabulary.
Item 11
Graphic organizers help me to learn information.
17.48**
Item 12
Item 14
Note cards help me to better understand and learn math vocabulary and 61.17***
procedures.
The vocabulary of the Georgia Performance standards is easy to
20.30***
understand.
Note cards are a good method to use to become proficient in math class. 61.61***
Item 15
55.96***
Item 2
Item 3
Item 4
Item 8
Item 9
Item 13
I like to use note cards when learning new vocabulary or steps in
problem solving in math class.
* p < .05, ** p < .01, *** p < .001
23.78***
17.70**
42.04***
59.43***
From the chi square analysis of the student survey, the statistical analysis revealed that all
of the answered questions were significant at either the p < 0.05, p < 0.01, or p < 0.001 levels. The
Vocabulary in Math Class
44
questions were answered in a comparable manner by the subjects. Salkind (2010) stated when
using a chi square analysis of survey responses, they are compared by what is observed on a survey
to what would be expected by chance. This gave further meaning to student responses and the
results just did not happen by chance. A Cronbach’s alpha test was implemented to determine the
internal consistency reliability of the student survey. The internal reliability alpha measure was
calculated at α = 0.78. This student survey had a high level of reliability in regard to student
perception of note cards and vocabulary in the math classroom.
The students’ responses indicated that they typically feel as vocabulary discussion and
instruction was important as answered on the survey in items 1, 4, and 6. From the responses on
items 2 and 10, they believed that their teacher believes vocabulary and vocabulary instruction was
extremely important in learning mathematics. Reading is very important in education and the
students felt in reviewing items 3, 5, and 8 that reading in math was necessary and part of the
curriculum. Items 7, 9, and 12 indicated that students feel note cards were useful learning tools in
the math class. Most students responded in items 14 and 15 that note cards helped them learn the
math vocabulary and become more proficient in math class.
The final focus question of this study was to solicit the views and opinions of an
administrator in a leadership position to assist in bringing change and equity to all students,
particularly utilizing looping cards as an instructional method. He was chosen because his opinions
are highly regarded among his administration peers and teachers. Further, he serves in capacity of
being the assistant principal [AP] of curriculum and instructional leader at the school level for the
school system. The interview took place in his office once all the data were collected and evaluated
so the results could be presented.
Vocabulary in Math Class
45
The AP stated, “the Georgia math curriculum is in a state of constant change right now, and
has been for the last four years”. Students have been socially promoted without the necessary
preparation, knowledge and skills to be successful. This constant change and gaps in knowledge
have put a tremendous strain and struggle on our kids and teachers. These changes in the math
curriculum have directed and required teachers to spend valuable time teaching vocabulary. As a
school, the AP stated “we have recognized that vocabulary instruction with the Georgia
Performance Standards [GPS] is key to our student success”. Further, he commented that the new
math curriculum was so inundated with vocabulary that students must be familiar with the verbiage
of the standards in order to be prepared for the EOCT questions. Vocabulary instruction has been
“highly encouraged” by the administration for the last four years with the utilizing of word walls
and standard-based instruction, mostly using graphic organizers, as prescribed by the Georgia
Department of Education (2008).
The AP conveyed that he believed looping cards were a great strategy to learn vocabulary,
as his teaching experience was in foreign language and students must become familiar with
vocabulary in order to be successful. Vocabulary is the basic structure for learning and
remembering. Due to the difficulty some students have in math, direct vocabulary instruction and
step by step processes on looping cards are “a great idea”. In the AP’s opinion to become proficient
in math, students “definitely must have direct vocabulary instruction”. Further stating, “vocabulary
is a valuable teaching tool which kids gain access to the lesson”.
Graphic organizers are definitely encouraged school wide and are research based “best
practices.” Making his rounds and observations, the AP stated he liked how the students knew how
to get into their groups and how to employ the looping cards strategies. Further, he stated that
students seemed to have fun with the practice of the looping cards, and heard students in the
Vocabulary in Math Class
46
hallway talking about how fast they were getting the looping cards with the “math stuff”. He
elaborated, from his observations of the use of looping cards, “by allowing kids to verbalize their
own meaning and understanding (it) was very beneficial. Kids will tend to use terms that are
meaningful to them, which helps activate prior knowledge, and our looping card strategies
produced good results in their attitudes and in achievement.” We discussed that students’ attitudes
toward math have improved due to the success of the applied looping card strategy, and how this
approach was helping to eliminate the vocabulary barrier and allowing for student success in the
math classroom.
While discussing the results of the collaborative pre and post benchmarks and state EOCT
data, the AP commented that from an administration point of view that the looping card strategies
of problem solving and direct vocabulary instruction, as compared with other classes, had shown
improved student achievement and had definitely helped to increase our low socioeconomic
students’ scores. In regard to encouraging other teachers to adopt and utilize looping cards, the AP
believed to become a school initiative we needed to share the results of our student achievement
data, and he would be willing to provide the opportunity to share. Additionally, the AP mentioned
that through our school improvement plan and the master schedule have allowed for collaborative
planning on the four by four block by department. We have professional development
opportunities and time set aside specifically to utilize strategies, research and discuss ideas,
develop benchmarks and assessments all in order to improve and increase student learning.
Recognizing the difficulty that some teachers are hesitant to change, the AP noted that “our
faculty and staff are always willing to adopt practices that will increase student achievement”.
From an administrative point of view, he likes direct vocabulary instruction, but reminds that
“differentiation is a must.” He further commented that the “looping card strategies are great for
Vocabulary in Math Class
student retention, but it should be used along with other methods for incorporating vocabulary
proficiency.”
The results presented from the test data collected indicated that student achievement
increased in all students. Furthermore, student attitude toward math improved and they felt the
looping card strategies were good methods for learning problem solving skills and math
vocabulary. Additionally, from the interview of the administrator, he expressed his support of the
practice and use of looping cards as a great way to incorporate student mastery of the vocabulary
and the standards.
47
Vocabulary in Math Class
48
CHAPTER V: ANALYSIS AND DISCUSSION OF
RESULTS
Analysis of Results
The quantitative data of the of the pre- and post- tests and the Math II EOCT tests of the
control and treatment groups were analyzed for significance to determine the effectiveness of the
Jamaican strategies of looping cards in numeracy and literacy. The success of all students was of
interest, but more particularly the achievement of low socio-economic students. A dependent-t
test was conducted on the pre- and post-test data of both the treatment and control groups. For a
dependent-t test, a Pearson coefficient, or r value, was measured to determine the effect size of
the paired means. Several independent-t tests were performed to compare the treatment and
control groups utilizing the following categories: pre-tests of all students, post-tests of all
students, pre-tests of low socio-economic students, post-tests of low socio-economic students,
Math II EOCTs of all students, Math II EOCTs of low socio-economic students, and Math II
EOCTs with no low socio-economic students. The effect size for the independent-t test was
measured by the calculation of a Cohen’s d value.
To begin a comparison of the treatment and control groups, the paired means of the
dependent-t tests were examined, and it was found to reject the null hypothesis in both instances.
The means in both administrations, the treatment and the control, showed significant gains and
tremendous increases in each case. The achievement in part can be attributed to the pre-test being
administered prior to instruction, and the post-test after the completion of the teaching of the
Math II curriculum. It is a natural assumption that the increase in the test means on the preversus the post-test can be attributed to the students learning the curriculum. The proficiency of
students’ results can be credited to the performance curriculum, and educators effectively
reaching students in the content areas, and particularly at-risk students (GADOE, 2005).
Vocabulary in Math Class
49
The data of the pre- and post-tests were disaggregated using independent-t tests to
compare the test scores between the treatment and the control group to measure for significance.
The effect size was used to determine the magnitude of the treatment (Salkind, 2010). In the
comparison of the pre-test treatment and control groups, the result of the independent-t test
revealed to accept the null hypothesis. This outcome validated that there was no significance, and
both groups were on about the same level of knowledge on the administered pre-test. To further
compare the treatment and control groups, the independent-t test data of the post-test indicated to
reject the null hypothesis and accept that there was a significant difference in the means of the
groups. The control groups mean score was significantly lower than the treatment groups mean
score. The Cohen’s d calculation yielded a large effect size, and in this case was the use of the
looping card strategies.
To determine if there was significance in the performance of low socio-economic
students [SES] and general education students, comparisons using independent-t tests were used
on the treatment group and the control group pre- and post-tests. Comparing the low SES and
general students’ pre-tests of the control and treatment groups, the t-tests showed to reject the
null hypothesis in both instances. There being significance in the comparison using socioeconomics, and according to the Cohen’s d calculations, there was a large effect in the treatment
group and a medium effect in the control group. This means achievement gaps existed prior to
the introduction of the Math II curriculum. A bigger achievement gap existed in the means of the
treatment than of the control. The comparison of the treatment and control groups’ post-test ttests on the basis of SES revealed exciting results for the treatment using looping card strategies.
The post-test control group corroborated that achievement gaps continue to exist and at a large
effect. The post-test treatment group showed to accept the null hypothesis. This result validated
Vocabulary in Math Class
50
that both low SES students and general education students were at about the same level of
proficiency. This result meant that the gap was no longer significant according to this result.
The Georgia Math II EOCT data was disaggregated to give additional strength to the
study. Independent-t tests were analyzed by treatment and control groups and socio-economic
status for significance. The statistical assessment of the treatment and the control group
indicated to reject the null hypothesis, and that there was significance. The resulting data
indicated there was a difference in favor of the treatment group. The Cohen’s d calculation
yielded a medium effect in the use of the treatment. To further investigate the findings, an
independent-t test between low SES and the general students found to reject the null hypothesis,
and that there was significance. The findings showed there was a difference between the two
groups, and that the treatment SES group’s mean was about twelve percent higher than the
control’s mean. A Cohen’s d value acknowledged a large effect size and this was at the
confidence level of p < 0.01. Additionally, an independent-t was calculated on the general
education students from the treatment and control groups to determine significance. Once again,
the null hypothesis was rejected determining that there was significance, and the Cohen’s d value
yielded a large effect. This result demonstrated that there was an achievement difference between
the groups in favor of the treatment.
Based on the resulting statistical data from the dependent-t tests and the independent-t
tests of the pre- and post-test and the Georgia Math II EOCT, there was a significant difference
between the treatment and control groups. Although both groups pre-test showed them to be at
the same level of knowledge, there originally existed a significant achievement gap by SES.
However, the treatment groups’ scores increased significantly and had a large effect after the use
Vocabulary in Math Class
51
of looping cards between the comparisons of the low SES of both groups and the general
education students.
The results of the pre- and post-tests and he Georgia Math II EOCT were considered
reliable. Popham (2008) stated reliability is a measure of a test’s consistency to accurately
measure data. For the dependent-t test, a Pearson coefficient value was measured to determine
the effect size of the paired means, and it indicated a large test-retest certainty. A Cohen’s d
value was measured to determine the effect size for all independent-t tests. Content validity is the
adequacy that the assessment represents the standards of the domain about which inferences are
to be made (Popham, 2008). Validity determines whether the research measures what it was
intended to measure and in the case of the pre- and post-tests, they were aligned to the Math II
GPS state standards. The Math II EOCT was mandated and provided by the state. This test was
aligned with the Georgia curriculum standards by the state of Georgia, and it assesses specific
content knowledge and skills (GADOE, 2005). The assessments provided diagnostic information
to help identify strengths and areas of need in learning, therefore improving performance in all
high school courses and on other assessments. The EOCT also provided data to evaluate the
effectiveness of classroom instruction at the school and system levels (GADOE, 2005). With this
confidence and assurance from the state, the EOCT was assumed fair, reliable, and valid.
A survey was given to the treatment group of students regarding their attitudes toward
math and the use of the looping card strategies. The responses of the survey were reviewed and a
chi square analysis of the questions was calculated. A Cronbach’s alpha calculation was
performed to determine the consistency with which the questions were answered. An overall
summary of the students’ attitudes were overwhelmingly in favor of the looping card strategies
and felt that these practices increased their proficiency in the math classroom.
Vocabulary in Math Class
52
From the chi square analysis of the questions of the survey, they were found to be
significant at the 0.01 and 0.001 levels. These levels of significance revealed that the attitudes
and responses to the questions were answered in a comparable manner. Questions 7, 12, 14, and
15 were answered favorable concerning the use of the strategies of looping cards, or note cards
as the survey stated. These attitudes of the students were favorable toward the treatment and of
fastidious interest for this study. When asked if looping cards helped them learn the concepts and
vocabulary of the curriculum, question 7 and 12 were very similar in content and found the
majority of the students strongly agreed with the questions. Question 7 responses were thirty-two
students strongly agreed, ten agreed, three neutral, and only one strongly disagreed. In question
12, the student responses were twenty-eight strongly agreed, fourteen agreed, two neutral, one
disagreed, and one strongly disagreed. These two questions were significant at the 0.001 level
finding that most students agreed or strongly agreed with the statements. Question 14 inquired of
the attitude of the learner in respect to becoming proficient in mathematical concepts and
vocabulary using note cards. Overwhelmingly, the assertiveness of the students were in favor of
the use of the treatment strategies and it was found statistically significant to the 0.001 level.
Student reaction on question 14 was similar to questions 7 and 12, finding twenty-seven strongly
agreed, sixteen agreed, two neutral, and one strongly disagreed. Question 15 specifically
addressed if students liked using looping card strategies for vocabulary and problem solving.
Twenty-six strongly agreed, sixteen agreed, two neutral, one disagreed, and one strongly
disagreed that they were fond of applying the note card strategies in math class. Garbe (1985)
stated that spending time on vocabulary was necessary to eliminate anxiety in the math class.
Agreeing with the literature and the findings of these survey questions, students had a favorable
opinion of looping cards and excitement for learning in the math class. Motivation and effective
Vocabulary in Math Class
53
teaching strategies kept students engaged and looping card strategies have involved all students.
The DES (2004) found lower attaining and low SES students need to build confidence through
modeling and demonstration, while gifted and bright students preferred opportunities to discuss
their discoveries. The technique of looping cards allowed students to repeat a newly learned skill
for mastery (DES, 2004).
Informal definitions are a good beginning to proficiency and lead students to construct
meaning in order to develop comprehension of mathematical concepts (Adams, 2003). Students
regarded discussion of vocabulary, definitions, and verbalizing problem solving steps in the math
class as helpful in their achievement. Responses to questions 4, 9, and 10 helped to evidence
students’ favor of communicating in math while utilizing their own definitions. As Draper (2002)
detailed, when teachers allowed students to read, write, listen, speak, and think in math they built
solution strategies that led to greater clarity and proficiency. The discussion and interactive
discourse between students sustained by the teacher promoted learning and retention (Nystrand,
1996). The looping card strategies of the treatment and discussions in the classroom allowed for
improved student achievement, attitude, and understanding
An interview was conducted with the AP of curriculum and instruction about the use of
the Jamaican looping card practices, its perceived level of success, and the willingness to
encourage adoption of these procedures in an effort of achievement equity. The administrator
was presented with the collected and analyzed data and interviewed as to his feelings about
vocabulary instruction and the use of the observed looping card strategies.
An emergent theme throughout the interview was making sure to teach using standardsbased instruction. The AP commented that direct vocabulary instruction was “highly
encouraged”, and the use of a word wall was part of the adopted strategy of the administration
Vocabulary in Math Class
54
and the standards-based initiative of the state of Georgia (GADOE, 2005). He later confirmed the
findings of DES (2004) stating that “looping cards served as individual word walls on each
student’s desk”. He pointed out that vocabulary was a valuable teaching tool which a lot of
teachers tended to ignore, but was very beneficial to students. Clarke (2005) concluded teachers
should reflect to understand and stimulate, not ignore, a learning environment, while
encouraging their students to do the same.
After review of the data and success of looping cards, the AP said our note card strategy
has given every child access to what the notes were telling them and the problem solving
strategies the standards of the curriculum required. He stated from an administration standpoint
the looping card method helped produce an eighty-eight (88) percent pass rate on the Math II
EOCT. Further, he noted that from discussions he had with students they really liked the note
card practice and their overall attitude toward math was positive.
Discussing the pros and cons of looping cards, the only negative he had was it would be
another “change.” Change is a scary thing, and the excuse he would hear from recommending
this strategy is “we (teachers) do not have the time to try something else”. He said “some
teachers had not yet embraced the GPS curriculum and are truly not knowledgeable, in some
instances, when it comes to what the children are expected to know and do”. Interestingly the
JBTE (2008) and the Taskforce on Education Reform (2004) made almost the same statement
concluding that to maximize learning and the learning environment, students must be supported
by committed, qualified, competent, effective, and professional educators. Although he stated,”
in our school we have found that the general attitude of our teachers has always been one to
adopt practices that will increase student achievement.”
Vocabulary in Math Class
55
Construct validity was evidenced in the interview with the AP as it measured his attitude
and temperament regarding the use of the looping card strategies. His willingness to support the
extensive use of note cards revealed the significance of the interview. Would he be willing to
assist in change and assist in achievement equity to our students? “Yes…absolutely! I like this
looping card method. It scaffolds onto itself and allows for student-centered learning and
discussions, and it has increased student achievement, specifically in our low SES students.”
Discussion
Engaged students are much more inclined to be proficient in mathematics than students
who have not had high expectations placed upon them. The study showed that there was
statistical significance between the treatment and the control groups where the Jamaican literacy
practices were introduced and practiced. Student achievement was assessed through a pre- and
post-test given upon entering my Math II class and at the end of the term. In review of the pretest data both incoming groups scored about the same across SES levels. This result validated
that the control and treatment groups were at about the same level of knowledge for the Math II
curriculum. An achievement gap was found to exist on the pre-test between general students and
low SES in both groups. Through normal instruction of the Math II standards student
achievement should have increased regardless of the instructional method. However, in review of
the post-test data, the treatment group confirmed my hypothesis of applying the Jamaican
looping card practices to math vocabulary and problem solving with an overall increase of
student achievement. The general education students and the low SES students of the treatment
had positive significant gains. Utilizing an independent-t test to compare the control and
treatment SES groups’ achievement, the treatment was found to be significant with a large effect
size in the use and practice of looping cards.
Vocabulary in Math Class
56
The process of looping cards engaged the students in activities which were perceived as
fun. The student survey that was administered indicated a favorable attitude and opinion of
application and practice of these strategies among the subjects. Questions 4, 9, and 10 from the
survey all indicated with a 0.001 level that discussion of vocabulary and informal definitions as a
community of learners made learning the required material of the curriculum easier. This
confirmed Adams (2003) belief that the use of informal vocabulary and definitions were key to
understanding and applying math concepts. These discussions were important for students who
were continually encouraged to become proficient with math vocabulary and allowed them a safe
environment to explore, hypothesize, and brainstorm.
The administration had positive comments and was very supportive of the use of the
Jamaican looping card practices to teach vocabulary and problem solving strategies. Further, the
AP noted that students attitudes toward math had improved and the note card approach enabled
student involvement in the learning process. Additionally, he openly encouraged others to try the
new techniques and was willing to assist in the educational process for staff development.
In adding to the body of knowledge for student achievement, there had been very little
research in applying the accepted Jamaican strategy of looping cards. Ganser (2001) stated that
lack of training was typically why teachers were reluctant to try something new or different.
Also, and more importantly for teachers, it was the issue of time. Many teachers feared direct
vocabulary instruction due to the time commitment it required. This study demonstrated the
effectiveness of teaching vocabulary strategies to enrich the curriculum, and helping students to
construct their own understandings in a systematic well-planned program. Stahl and Bravo
(2010) stated students that reflected on learning and articulated the different steps to apply
vocabulary were better enabled to solve mathematical problems.
Vocabulary in Math Class
57
The study confirmed that teaching vocabulary increased student proficiency significantly,
and it was well worth the time required to effectively learn the strategy of looping cards. The
students enjoyed the process of learning vocabulary and math strategies using the structured note
card methods. Further, the administration found the application of looping cards to increase
student achievement and the overall attitude of the students in math had improved. Therefore
they were willing to encourage and employ the use of looping cards for academic equity of all
students.
Multiple sources were used to gather quantitative and qualitative data yielding structural
corroboration. The pre- and post-test and the EOCT results reinforced the Jamaican looping card
strategies of literacy and numeracy. Additionally, students and the AP of curriculum and
instruction had a favorable and supportive attitude in the use of note card practice for meeting the
instructional goals of the math curriculum.
Fairness was addressed in the study by having presented opposing views in the review of
the literature. The arguments against teaching with graphic organizers were cited due to not
having the time for vocabulary instruction, and teachers being unfamiliar, unwilling, or not
responsible to teach vocabulary (Graves, 1985; Marzano, 2004). However, due to the significant
gains in student achievement of the treatment group on the post-test and the EOCT, the results of
this study supported vocabulary instruction. Low attaining or low SES students in the treatment
group benefitted from the discussions and techniques used in the practice of looping cards, and
had significant gains in their scores on both the post-test and EOCT as compared to those of the
control group. These gains in achievement were strong enough evidence to determine that the
Jamaican looping card practices were a skillful tool in meeting the instructional needs of
students.
Vocabulary in Math Class
58
Implications
Do reading and vocabulary strategies in the math classroom work? Absolutely, literacy
skills in the math classroom make a difference. It facilitates student communication and allows
them to examine their thoughts in analyzing problems. Language and reading are the foundations
for all of our children in their education, and we as educators must tap into this base of knowledge
in order to build for proficiency and success.
In order to improve the education of students, we must acknowledge that there is a failure
in the system, and it does not meet the needs of our diverse youth. In the qualitative results of this
study it was found that the treatment was significant and there was a medium to large effect size
calculated for the treatment group. Although this study focused specifically on low SES student
proficiency, the attained data can be generalized to a larger population due to student gains across
the then entire treatment group. Our students’ attitude toward looping cards was one of acceptance
and approval. This acceptance combined with student achievement lends itself to attempt the
learning curve of looping cards.
During the interview of the AP several themes were discovered, such as: vocabulary is a
great teaching tool, change takes time, graphic organizers are acceptable practice and are expected
to be utilized, and the benefits realized due to the looping card strategy. Vocabulary is a valuable
tool and should be addressed in every classroom per the GPS standards and the GADOE (2005) as
a standards-based classroom. The collaborative process of discussing formal and informal
definitions allowed students to verbalize their own meaning of the math vocabulary of the
curriculum (Adams, 2003). This manner activated prior knowledge and with the use of looping
cards helped raise student achievement. The most common heard argument from mathematics
teachers against incorporating literacy strategies is that they are already pressed for time to teach
Vocabulary in Math Class
59
the material required of the standards. Besides this fact, math teachers are worried of trying to
integrate something into our curriculum that puts more stress on our already strained planning
time. In order to embrace change, the “old dogs” must see how the new changes will work.
Additionally, teachers are expected to utilize a word wall and graphic organizers in daily
instruction. The DES (2004) stated strategies for more student-focused learning would be that of
having a word wall on their desk, or looping cards, and informal definitions on the other side. The
looping card strategy allowed the fulfillment of these requirements. Lastly, student achievement
increased significantly, and with this being our overall goal looping cards are an excellent resource.
Math educators must take seriously the National Council of Teachers of Mathematics’
(NCTM) claim that students need to be able to represent and communicate data in a variety of
forms. Students draw on knowledge from a wide variety of topics, sometimes approaching the
same problem from different mathematical perspectives or representing the mathematics in
different ways until they find methods that enable them to make progress (NCTM, 2008). Teachers
help students identify, incorporate, and explore conjectures on a variety of basis of evidence and
use a variety of reasoning and proof techniques to confirm or disprove those statements. Students,
whether alone or in groups, work productively and reflectively, with the skilled guidance of their
teacher. Orally, and in writing, students must communicate their ideas and results effectively
(NCTM, 2008).
How the study can be replicated is referred to as referential adequacy. Much discussion was
had during math departmental meetings, with the AP of curriculum and instruction in attendance,
on the importance of vocabulary instruction and the benefit of all students in the use of looping
cards. Achievement increased for all populations in the treatment group. The study can be easily
Vocabulary in Math Class
60
replicated using basic note card practice and grouping strategies in a peer-to-peer environment
after defining vocabulary and math processes collaboratively.
Catalytic validity is the degree to which the study shaped and transformed those involved
in the study. The subjects in the treatment of the study have found a new method for learning
vocabulary and process concepts. Further, the students realized how learning vocabulary increased
their achievement. Other teachers observed the looping card practice and have considered utilizing
the strategies in the future. The administrator willingly began discussing these vocabulary practices
with other departments, and because of his input I have begun fielding questions on the process
and benefits of teaching with the Jamaican looping card strategies.
Being a teacher leader, this strategy has allowed me to reflectively learn with my students
and become a better instructor. I have previously worked on vocabulary learning strategies, but this
note card style practice has effectively allowed me to reach students that have typically been hard
to educate. I do not believe that looping cards should be a sole method of instruction, but part of
the differentiated structure in teaching. The process of looping cards allowed my students and me
the flexibility of a constructivist learning environment; which allowed for differentiation in each
class. These opportunities of cooperative learning and teacher-student interactions encourage and
allow multiple meanings of multiple words and finally arriving at proficiency in mathematical
terminology (Ganser, 2001).
As our students continue to struggle as they read, we as educators must remember why we
are in this profession, which is to teach. How we teach is a matter of how students are learning.
Students who cannot read or understand vocabulary in today’s math class will ultimately perform
poorly on tests and will continue to be frustrated. This dissatisfaction with education will cause the
student to be retained, socially promoted, or dropout, and the vicious cycle will continue. I believe
Vocabulary in Math Class
61
it to be in our best interest as educators to help students improve their literacy in order to be
proficient learners and contributors in our society.
Impact on School Improvement
The practice of looping cards enabled me to immediately determine who was lacking the
basic knowledge and informally assess those gaps. Through this study much discussion was had
with other teachers in the use of vocabulary instruction, and the merit of teaching vocabulary
directly using graphic organizers. The process of looping cards has been discussed with the other
math teachers and co-lab teachers in our building and will be a math department initiative next
year. Other departments have expressed interest and our AP of curriculum and instruction has been
promoted to the position of Assistant Superintendent. He has expressed interest in developing this
vocabulary strategy further and has asked for the math department to collaboratively plan to
effectively utilize the looping card strategies next year. As the instructional team and being
effective change agents for school improvement and student equity, we must recognize that all
students count, and be willing to reflect, categorize, and address strengths and weaknesses of
looping card procedures and actively engage students to construct learning. By constantly
reflecting on the problem submitted to the students, the educator must continually consider and
reflect on the knowledge level of himself and of his ever-changing students (Freire, 2005).
Recommendations for Future Research
With the coming approach of the new Common Core Georgia Performance Standards,
mathematic teachers should be aware that literacy is part of the complete curriculum. In order for
the standards to be implemented effectively, math teachers must be properly trained.
Communication, language, reading, and writing are now part of the standards across the new
curriculum, making my efforts and research applicable.
Vocabulary in Math Class
62
Contact had been made with actual teachers in Jamaica but no input was given on their
part to the process of looping cards or the strengths and weaknesses of the strategy. It would have
been beneficial to actually see the process in use, or at least been given some opinions or insights
about its usefulness. There was not a lot of literature for review due to Jamaica being a rural
country. Also, most teachers have very limited access to computers and even less have access to
the Internet. Teacher training is also an issue in Jamaica. They have these strategies but have not
had professional development to be properly trained (JBTE, 2008).
Personally literacy practices of teaching vocabulary are extremely useful. Although it does
take time to develop these skills. I like to think that implementing literacy strategies is an effective
means of teaching mathematics to students. I believe that a school-wide initiative is possible and
should be studied. Further research along these lines would greatly increase the value of looping
cards. The study should actively measure significance for all student performance and see if there
is educational equity for all involved. Learning and progressive education is not of a single subject
curriculum, but of interdependence among educators and academia. Workshops and training would
be very important and having time to effectively plan would be a necessity for teachers to
incorporate actively all aspects of the looping card strategies.
I would also suggest a study of the benefits of incorporating a journal into the vocabulary
strategies I performed on the high school level. Most research studies and resources I found dealt
mainly with elementary and middle school grades in Jamaica. I believe that incorporating writing
would allow students another way of expressing ideas to obtain proficiency, and would continue
to promote the active learning of the participants.
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63
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Appendix A
Samples of Looping Cards
68
Vocabulary in Math Class
Appendix B
Student Pre-Post Test
69
Vocabulary in Math Class
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Vocabulary in Math Class
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Vocabulary in Math Class
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Vocabulary in Math Class
Appendix C
Student Survey
Please circle the choice that best describes your feelings about the question or statement.
1. Vocabulary is important in math class.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
2. My math teacher believes vocabulary is important in learning mathematics.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
Neutral
Agree
Strongly Agree
3. Reading in math class is not important.
Strongly Disagree
Disagree
4. Student discussion of vocabulary is a key component in comprehension.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
5. Sometimes we have to read in math and I don’t understand the words.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
6. The vocabulary words we use in math class are easy to remember.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
7. Note cards help me to understand the math concepts of word problems and equations.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
74
Vocabulary in Math Class
75
8. Learning new words before I read is helpful.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
9. It is easier to understand informal definitions used on note cards, than book vocabulary.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
10. It is helpful when my teacher takes the time to discuss vocabulary.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
Agree
Strongly Agree
11. Graphic organizers help me to learn information.
Strongly Disagree
Disagree
Neutral
12. Note cards help me to better understand and learn math vocabulary and procedures.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
13. The vocabulary of the Georgia Performance standards is easy to understand.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
14. Note cards are a good method to use to become proficient in math class.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
15. I like to use note cards when learning new vocabulary or steps in problem solving in math class.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
Vocabulary in Math Class
76
Appendix D
Interview Questions for Administrator
1.
Why do you feel that students struggle with the curriculum in math?
2.
Why do you feel that students tend to struggle more in math now than in previous
years? Why do you feel that way?
3.
Do you feel that the time required to teach direct vocabulary is worth the benefit?
4.
Which vocabulary instruction method do you prefer?
5.
How do you feel about using note cards and literacy strategies such as grouping and
student collaborative informal definitions to increase proficiency?
6.
Do you feel that note cards have the potential to raise student achievement?
7.
In observing the use of note card practice and / or these literacy practices, do you
think student attitudes toward learning math have improved? Do you feel these practices
have contributed to learning the standards and required material of the math standards?
8.
Do you feel that other teachers would be willing to incorporate the use of note cards
and these literacy strategies of this study into their teaching practices? Why?
9.
Why do you think that teachers would be reluctant to use note cards and literacy
practices from this study? Why?
10. From an administrative standpoint do you feel that teaching direct vocabulary using:
note cards; grouping; collaborative student informal definitions are a good practice?