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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. Sharon Livingston, Ph.D.

Associate Professor and Project Advisor Associate Professor and Project Advisor

Education Department Education Department

Windows User, 12/12/10,

Top margins for preliminary pages are 2”

VOCABULARY IN MATH CLASS:

INCREASING PROFICIENCY IN MATHEMATICS

A thesis 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 , 2011


Chuck, since this is a work in progress, put the date for each submission.

Vocabulary in Math Class iii

ABSTRACT

Vocabulary in math class: Increasing proficiency of low socio-economic students in mathematics

The advent of No Child Left Behind in 2001 ushered in an era of increased accountability

for schools across the nation. As a result, , and school personnel felt and continue to feel the

increasing pressure of test score requirements as the law requires that all students should be

reading and completing math on grade level by the year 2014 (U.S. Dept of Education, 2007). The

purpose of this research was to introduce the strategies of literacy practices in the math curriculum

to increase vocabulary proficiency in mathematics in order to improve student learning and test

scores.


ANY MENTION OF JAMAICA?

Vocabulary in Math Class iv

TABLE OF CONTENTS

Abstract.................................................................................iiiTable of Contents...................................................................ivList of Tables and Figures......................................................vChapter I: INTRODUCTION...................................................1

Statement of the Problem..................................................1Significance of the Problem...............................................2Theoretical and Conceptual Frameworks..........................4Focus Questions.................................................................5Overview of Methodology..................................................5Human as Researcher........................................................6

Chapter II: REVIEW OF THE LITERATURE...........................8Chapter III: METHODOLOGY...............................................13

Research Design..............................................................13Setting.............................................................................14Sample / Subjects / Participants......................................14Procedures / Data Collection...........................................15Validity and Reliability Measures....................................15Analysis of Data...............................................................15

Chapter IV: RESULTS..........................................................17Chapter V: ANALYSIS and DISCUSSION OF RESULTS.......18

Analysis............................................................................18Discussion........................................................................18Implications.....................................................................19Impact on Student Learning............................................19Recommendations for Future Research...........................21

Vocabulary in Math Class v

References............................................................................23Appendixes...........................................................................25

MISSING LIST OF TABLES AND FIGURES PAGE

Vocabulary in Math Class 6

C H A P T E R O N E : I N T R O D U C T I O N

Statement of the Problem

Effective mathematics problem solving often depends on understanding of key

mathematical terms. Students of low socio-economic status tend to perform below the state

standards on mandated tests at our high school. The National Council of Teachers of Mathematics

(2006), in the Principles and Standards for School Mathematics (2006), 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, 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


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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

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

(p. 43). 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.

Rural schools are an important focus, especially in the state of Georgia, since, as of 2003,

one-third of Georgia’s school’s 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], 2004. 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,

2004).

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, pp.215-256). 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, we will focus on vocabulary to develop problem solving and comprehension

proficiency. My focus will engage students in meaningful, real-life activities to encourage and

expand mathematical knowledge of functions and vocabulary. This can be accomplished by

building on 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, 2000).

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,

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 aligns 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 will allow 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 relates 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).

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

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 is 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 does the integration of vocabulary strategies into the mathematics curriculum increase

low socio-economic students’ proficiency in mathematics?

2. What are the attitudes and opinions of the adopted curriculum strategies among teacher

leaders and learners?


3. What was the level of success of change in the process strategies among administrators,

students, and teacher leaders?

Overview of Methodology

Applying action research in my study, mixed methods of quantitative and qualitative

measures will be used to assess the results. These outcomes will be measured by incorporating the

use of literacy skills and pedagogy practices from Jamaica. The testing of these effects show how

these instructional strategies based on vocabulary proficiency affects mathematical knowledge in

student learning.

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 will

be the quantitative part of the research. This research will statistically compare 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 will be

compared to the control group of the previous year using independent t-tests to determine if there is

significant difference in applying the vocabulary practices.

Qualitative data will be collected from interviews and surveys of all teachers,

administrators, and students who participated in the use of these instructional literacy strategies.

The interviews will be conducted using a specific set of questions. The surveys will implore coding

for themes that align with student success in improvement and perceived learning.


This is the first mention of Jamaica


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

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 will address

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 will be 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 need 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.


C H A P T E R T W O : R E V I E W O F T H E L I T E R A T U R E

Why integrate vocabulary?

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

(Department of Education, 2002). 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 (Encyclopedia of Education and Human Development, 2005).

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 Drazin (1995), mathematics permeates every aspect of our daily life, such as

grocery shopping, paying for fuel, travel, telephone calls, interpreting newspaper or internet


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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-

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). Mosvold, Vaananan and Trottenberg (2008) stress the importance of

mathematics to everyday living, such as marketing, interpreting data, computer technologies, and

predicting weather conditions.

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, pp.215-256).

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

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. 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 p.173). For the

most part, vocabulary instructionIN 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, p.173).

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

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, pp.215-

256).

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.

This study will focus on the primary and secondary levels of education. Early childhood,

our 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


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There should be no mention of your study in the lit review, except in the transitional paragraphs at the beginning and end of the chapter.


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.

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 (2003) 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.

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-

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, 2009). 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).

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 be established. One of student-centered 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


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Why are there two extensive paragraphs between the intro of the topic of gender disparity and when you discuss it. Rearrange the paragraphs to improve flow.


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, self-

sustaining 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).

While visitingIn the observations of classrooms in Jamaica, Evans observed that there

were clear gender differences in the way boys and girls responded to the curriculum and to the

teaching methods (1999). 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.

The adopted Jamaican curriculum strategies.

Utilizing international pedagogical practices in numeracy and literacy, the policy of the Jamaican

Ministry of Youth and Culture on Mathematics and Numeracy (2007) and the Mathematics

Curriculum (2003) highlight 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.

Ramsay and Bailey (2008), state 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, 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).

Teachers, educators, and school administrators have reflected on the Caribbean

Examinations Council, General Certificate of Education, and Secondary School Certificate

examinations frequently and believe to fully engage students in mathematics content and

concepts must 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, 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


Awkward sentence


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

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).

In the standards-based classroom in Georgia, many classrooms have displays of key words

around the room, known as a word wall (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


This is an awkward interjection of Georgia’s system. Why not just phrase as the use of word wall in the US.


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

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, p.171).

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, pp.215-256). 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.

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.

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 Georgia High School

Graduation Test, 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”

(1999page #). In order to be a change agent, teachers and administrators must effectively evaluate

and assess student engagement, learning, 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, p.63). 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 long-

term endurance of equity work and to continue with a consistent and persistent focus of change

(Skrla, et al., 2009).


C H A P T E R T H R E E : M E T H O D O L O G Y

Research DesignMy research is 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 is simply a form of self-

reflective inquiry. It consists 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.


SettingThe setting of this research is in a rural county high school, in West Central Georgia. The

school population for 9th through 12th wasis 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 will be are held confidential.

Sample / Subjects and / Participants The subjectample population, 10th and 11th 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 ?? students. Of the ?? students, ?? were

female and ?? were male. Student ethnic backgrounds consisted of ?? African Americans and ??

Caucasians (see Table 3.1).

Table 1: Mathematics II – 2009 / 2010

Total Female Male African American

Caucasian

Group A


This subsection will eventually need to be written in past tense.


Group B

There were ?? students, ?? females and ?? males, in Groups C and D. The racial make-up

of the class consisted of ?? African Americans and ?? Caucasians (see Table 2).

Table3. 2: Mathematics II – 2010 / 2011

Total Female Male African American

Caucasian

Group C

Group D

There are were two administrators that who will be participants in this study. One being the

principal as the leader of our school, and other the assistant principal who is responsible for

instruction and curriculum will be interviewed because they will be involved in assisting in the

systematic change of instruction methods and professional development of teachers.

Procedures and Data Collection MethodsPROCEDURES REFERS TO WHAT IT IS THAT YOU WILL BE DOING IN YOUR

STUDY. YOU NEED TO EXPLAIN THE PROCEDURES YOU WILL BE

IMPLEMENTING TO INTEGRATE THE USE OF VOCABULARY INTO YOUR

CURRICULUM. WHO/WHAT/WHERE/HOW/WHEN/WHY

Table 3.3 shows the overall alignment of data collection methods with the study’s focus

questions. EMBED TABLE 3.3 HERE

The quantitative data for Groups A through D are of a pre-post benchmark department

generated test and the End of Course Test that is mandated by the state of Georgia. Teachers in


the Heard County school system created the benchmark test to assess student learning of

mathematics, and as an indicator of performance on the states’ high stakes tests. 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. §20-2-281. There are eight

content area assessments comprising the End of Course Testing program. I will only be

analyzing the Mathematics II data.

The state mandates that the End of Course Tests 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 qualitative data will be collected from student surveys and the administrator

interviews. This data will be coded for themes while utilizing a chi squared tests.

Table 3.13. Data Shell

Focus Question

Literature Sources

How data were gathered and what type of data

How these data are analyzed

Why these data provide valid data

Rationale Strengths/ Weaknesses


How does the integration of vocabulary strategies into the mathematics curriculum increase low socio-economic students’ proficiency in mathematics?

Department of Education. (2005).

National Math Advisory Panel. (2008).

U.S. Dept of Educ. (2007).

Skrla, L. (2009).

Method:

Assessment

Pre / Post

Math 2 EOCT

Data:

Interval

Quantitative:

Dependent t-test

Independent t-tests

Type of Validity:

Content*

Quantitative:

determine if there are significant differences

Qualitative:

look for categorical and repeating data

Validity

Reliability

Dependability

Bias

What are the attitudes and opinions of the adopted curriculum among teacher leaders and learners?

Bryan, B. (2004).

Lockheed, M., et al

(2006).

Ganser, T. (2001).

Mvududu, N. (2005).

Evans, H. (1999).

Method:

Survey, reflection

Data:

Nominal, Qualitative

Quantitative:

Chi Square test

Cronbach alpha

Qualitative:

Coded for themes.

Type of Validity:

Content

Construct

Predictive

Quantitative:

determine if there are significant differences

Qualitative:


Validity

Reliability

Dependability

Bias

What was the level of success of change in the process

Draper, R. (2002).

Friere, P. (2005).

Method:

Survey, reflection, interview

Quantitative:

Chi Squared test

Cronbach

Type of Validity:

Content

Quantitative:

determine if there are significant

Validity

Reliability

Dependability


strategies among administrators, students, and teacher leaders?

National Council of Teachers of Math (2006).

Data:

Nominal, Qualitative

alpha

Qualitative:

Coded for themes

Construct

Predictive

differences

Qualitative:


Bias

Analysis of DataThe 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, gender, and

by race where reading 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 was

conducted using the scores from the state mandated End of Course Test.

The analysis of the central tendency and the t test show that there is statistical significance

in teaching mathematics with regard to reading and literacy strategies.


Working References

FQ 1:

Department of Education. (2005). No child left behind [NCLB Overview]. Available from

Department of Education, http//:www.ed.gov/nclb

Under No Child Left Behind, states are working to close the achievement gap and make sure all

students, including those who are disadvantaged, achieve academic proficiency.

No Child Left Behind] has forced schools to focus on their minority students like never before,

[State Schools Superintendent Kathy] Cox said.”(Atlanta Journal-Constitution, 6/13/05)

Forty years after the Brown v. Board of Education decision, some schoolchildren were taught

well while others – mostly poor and minority – were left to struggle or drop out.

A growing "achievement gap" between white and African American students was left

unaddressed for far too long. Ed.gov (2005) NCLB

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the


national mathematics advisory panel. Washington, DC: U.S. Department of Education.

The 2007 Programme for International Student Assessment (PISA), U.S. 15-year-olds ranked

25th among 30 developed nations in math literacy and problem solving (Baldi, Jin, Shemer,

Green, Hergert, & Xie, 2007). P.4

“The achievement gap between students of differing ethnic and socioeconomic groups can be

significantly reduced or even eliminated if low-income and minority students increase their success

in high school mathematics and science courses” (as cited by NMAP from Evan et al., 2006, p. 11).

“There are large, persistent disparities in mathematics achievement related to race and income—

disparities that are not only devastating for individuals and families but also project poorly for the

nation’s future, given the youthfulness and high growth rates of the largest minority populations”


FQ 2:

Bryan, B. (2004). Language and literacy in a creole-speaking environment: A study of primary

schools in jamaica. Language, Culture and Curriculum, 17(2), 87-96. Retrieved from

ERIC database.

English as 2nd language - principles of: (1) Immersion; (2) Practice; (3) Scaffolding; and

(4) Contrasts. Teaching as ELL for vocabulary

Lockheed, M., Harris, A., Gammill, P., Barrow, K., Jayasundera, T., & Academy for Educational

Development, W. (2006). New Horizons for Primary Schools in Jamaica: Inputs,

Outcomes and Impact. Revised. Academy for Educational Development, Retrieved from

ERIC database.

1. innovative mathematics and literacy programs NHP more advantaged 2. in-service teacher training NHP more advantaged 3. governance and leadership training NHP more advantaged 4. parent education and training No difference (both low) 5. selective nutrition and health programs No difference 6. supplementary reading and math materials NHP more advantaged (both high) 7. establishing computer use in school and training teachers

NHP more advantaged

8. training resource teachers NHP more advantaged 9. integrating databases (JSAS) NHP more advantaged 10. linking project schools with EMIS NHP more advantaged (both low)

Drop Everything and Read program, the presence of Competence Shelter (most schools did

not have one) or being a Summer Literacy Camp venue (most schools reported being one)

supplemental reading and math materials, and NHP schools reported receiving a greater

variety of materials, including books and computer software, all in support of the RPC (figure

3.1). Ninety-three percent of NHP and 79 percent of matched non-NHP schools received

supplementary reading materials (p < .05), and 85 percent of NHP and 54 percent of matched

non-NHP schools received supplementary math materials (p < .001)

The survey describes support teachers, as follows: “In some primary schools, experienced

teachers have been identified as persons who can provide support to other teachers. These

support teachers are called Resource Teachers or Literacy/Numeracy/Assessment


Coordinators. Some larger schools have Support Teachers that help other teachers on a

grade by grade basis, called Grade Coordinators. …We call all of these types of teachers

Support Teachers.”

emphasis on computers

Since USAID interventions are typically targeted at raising the math and literacy achievement

of lower performing students, USAID monitoring indicators need to be sensitive to small

changes in the performance of low scorers as well as in changes overall.

Ganser, T. (2001). Beginning Teaching in Jamaica: Challenges and Assistance. Retrieved from

ERIC database.

perceptions of school teachers, principals, and college lecturers regarding the challenges, obstacles, and needs faced by beginning teachers in Jamaica. the knowledge the teacher has of each student

the act of parenting and that a good teacher exhibits very strong affective and caring characteristics in his or her elations with children within the classroom context. He defines the term pedagogy as ‘… “excellence of teaching or parenting”

High/Scope early childhood education philosophy - This curriculum model emphasizesadult–child interaction, a learning environment carefully designed to promote active learning from key experiences and a plan-do-review process for all learning activities stimulating,with many attractive and colorful charts and pictures mounted on the walls, a wide range of manipulative table top materials

build trusting and comfortable relationships with the children four main strategies: (1) building and maintaining positive, caring and respectful relationships

with the children; (2) creating an orderly classroom environment with acknowledged rules; (3) proactively motivating and recognizing good behavior among the children; and (4) using specific and consistent approaches for punishing inappropriate and unacceptable behavior.

opportunities for small group cooperative learning, encouraged hands on-learning and interaction with the wide range of games and manipulative materials she provided. Story telling.

Mvududu, N. (2005). Constructivism in the Statistics Classroom: From Theory to

Practice. Teaching Statistics, 27(2), 49-54.

In engaging students with formal vocabulary, it was extremely necessary to allow students to

use informal vocabulary and the knowledge and language at which they brought initially to

the classroom. When discussing problems in groups as a community of learners or working

on the board, students were continually encouraged to move towards a proficient math

vocabulary. This allowed students to build on prior knowledge, formulate procedure, and


logically explain mathematical concepts. In light of a constructivist classroom, an

environment of problem-solving was created to build an atmosphere where students felt safe

to explore, conjecture, hypothesize, and brainstorm.

FQ 3:

Draper, R. (2002). School mathematics reform, constructivism, and literacy: A case for literacy

instruction in the reform-oriented math classroom. Journal of Adolescent & Adult Literacy, 45(6),

520.

Locate the common language and goals among educators and administrators.

As long as mathematics teachers pose problems, solve problems, and the analyses

appear as text, educators have an obligation to help their students negotiate and

make meaning of the text in order to keep mathematics within the reach of all

student. When math teachers attend to literacy needs of their students and the

need to construct meaning because of the interaction with mathematical text, then

they will be truly engaging and educating their students for mathematical

proficiency.

As professional educators, and more importantly mathematics teachers, we should

be less resistant to combining literacy instruction with the regular academic

teaching of mathematics.

Friere, P. (2005). From pedagogy of the oppressed. The Critical Middle School Reader.

Brown, E. and Saltman, K. (Eds). New York: Routledge.

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. 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.

National Council of Teachers of Mathematics. (2006). Overview: Principle for school

mathematics [The Learning Principle]. Available from NCTM, http://standards.nctm.org

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.


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Bryan, B. (2004). Language and literacy in a creole-speaking environment: A study of primary

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