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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 Assistant Professor and Project AdvisorEducation Department 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.

Vocabulary in Math Class iv

TABLE OF CONTENTS

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

Statement of the Problem..................................................1Significance of the Problem...............................................2Theoretical and Conceptual Frameworks..........................3Focus Questions.................................................................6Overview of Methodology..................................................6Human as Researcher........................................................7

Chapter II: REVIEW OF THE LITERATURE...........................9The use of mathematics.....................................................9How do we talk math?.....................................................10What is math vocabulary?................................................12School structure in Jamaica.............................................13Attitudes and skills of math in Jamaica............................14

Strategies of the Jamaican Curriculum...........................17Applying the Strategies...................................................18

School Change................................................................21

Chapter III: METHODOLOGY...............................................25Research Design..............................................................25Setting.............................................................................26Subjects and Participants................................................26Procedures and Data Collection.......................................27Validity, Reliability, Dependability, and Bias...................30Analysis of Data...............................................................33

Chapter IV: RESULTS..........................................................36

Chapter V: ANALYSIS and DISCUSSION OF RESULTS.......49Analysis............................................................................49Discussion........................................................................56Implications.....................................................................58Impact on School Improvement.......................................61Recommendations for Future Research...........................62

References............................................................................64

Appendixes...........................................................................68

Vocabulary in Math Class v

LIST OF TABLES Tables

Table 3.1 Mathematics II 2009/2010…………...……………………26Table 3.2 Mathematics II 2010/2011…………...……………………27Table 3.3 Data Shell………………..…………...……………………28Table 4.1 Dependent-t Test for Treatment Group – all students.……36Table 4.2 Dependent-t Test for Control Group – all students……….37Table 4.3 Independent-t Test Treatment and Control Pre-Test……....38Table 4.4 Independent-t Test Treatment and Control Post-Test .……38Table 4.5 Independent-t Test of Treatment Pre-Test

based on Socioeconomics .…………...……………………39Table 4.6 Independent-t Test of Control Pre-Test

based on Socioeconomics ………..……..…………………40Table 4.7 Independent-t Test of Treatment Post-Test

based on Socioeconomics ………...………………………40Table 4.8 Independent-t Test of Control Post-Test

based on Socioeconomics ………...………………………41Table 4.9 Independent-t Test of Treatment and Control

Math II EOCT ………………..…………...………………42Table 4.10 Independent-t Test of Treatment and Control

Math II EOCT Low SES…………………………………42Table 4.11 Independent-t Test of Treatment and Control

Math II EOCT no SES ………..........…………………….43Table 4.12 Student Survey Results …………...……………..….…......44

Vocabulary in Math Class 1

C H A P T E R I : 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. 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


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.


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


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,


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).


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.


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


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.


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

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-


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


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


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.


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.


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


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, 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).

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, 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.


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,


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


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


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, 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.


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,


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 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 I I I : M E T H O D O L O G Y

Research DesignMy 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 self-

reflective 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.


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 twenty-

six 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

Total Female Male African American

Caucasian

Group A 25 12 13 3 22Group B 26 13 13 7 19


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

Total Female Male African American

Caucasian

Group C 24 10 14 3 21Group D 28 16 12 2 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.


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).

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

National Math Advisory Panel. (2008).

Skrla, L. (2009).

Method:Pre / Post Benchmark

Standardized Math 2 EOCT

Type of Data: IntervalType of Validity:Content

Quantitative:Dependent t-testEffect size r Pearson’s corr

Independent t-testsCohen’s d

Quantitative:determine if there are significant differences

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

Evans, H. (1999). Ganser, T. (2001).

Adams, T. (2003) Mvududu, N. (2005).

Method:Survey

Type of Data: Nominal, Qualitative

Type of Validity:Construct

Quantitative:Chi Square test

Cronbach alpha

Quantitative:determine if there are significant differences

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?

Draper, R. (2002).

Friere, P. (2005).

National Council of Teachers of Math (2006).

Skrla, L. (2009).

Method:Interview

Type of Data: Nominal, Qualitative

Type of Validity:Construct

Qualitative:Coded for themes

Qualitative:look for categorical and repeating data

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 pre-


post 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. §20-2-

281. 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.

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

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

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

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

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

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.


C H A P T E R I V : R E S U L T S

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 Pre PostMean 29.98 76.5Variance 24.92 44.84Observations 52 52Pearson Correlation 0.59859261Hypothesized Mean Difference 0Df 51t Stat -60.82975651P(T<=t) one-tail 1.41052E-49t Critical one-tail 1.67528495P(T<=t) two-tail 2.82104E-49t Critical two-tail 2.00758377

t(51) = 60.83, p < 0.01


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 Pre PostMean 28.76 70.96Variance 16.90 63.52Observations 51 51Pearson Correlation 0.599093675Hypothesized Mean Difference 0Df 50t Stat -46.96943739P(T<=t) one-tail 2.47792E-43t Critical one-tail 1.675905025P(T<=t) two-tail 4.95584E-43t Critical two-tail 2.008559112

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.


Table 4.3: Independent-t Test Comparison Treatment and Control Pre-Test

t-Test: Two-Sample Assuming Unequal Variances Pre Treat Pre Cont

Mean 29.63 28.11Variance 23.73 13.58Observations 40 28Hypothesized Mean Diff 0Df 66t Stat 1.461768107P(T<=t) one-tail 0.074274994t Critical one-tail 1.668270514P(T<=t) two-tail 0.148549987t Critical two-tail 1.996564419

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 Post Treat Post Control

Mean 75.73 66.43Variance 42.36 51.74Observations 40 28Hypothesized Mean Diff 0Df 54t Stat 5.452799704P(T<=t) one-tail 6.32157E-07t Critical one-tail 1.673564906P(T<=t) two-tail 1.26431E-06t Critical two-tail 2.004879288

t(54) = 5.453, p < 0.05


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 Pre SES Treat


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.


Table 4.6: Independent-t Test of Control Pre-Test based on Socioeconomics

t-Test: Two-Sample Assuming Unequal Variances Pre Non Control Pre SES Control


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 Post SES Treat


t(17) = 1.490, p > 0.05


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 Post SES Control


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.


Table 4.9: Independent-t Test of Treatment and Control Math II EOCT

t-Test: Two-Sample Assuming Unequal Variances Treatment Control


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 Control SES


t(54) = 4.75, p < 0.01


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 Control Non

Mean 82.67 78.83Variance 36.42 32.33Observations 12 23Hypothesized Mean Difference 0Df 21t Stat 1.822434096P(T<=t) one-tail 0.041330768t Critical one-tail 1.720742903P(T<=t) two-tail 0.082661535t Critical two-tail 2.079613845

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


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 Itemsn = 15

Survey Questions χ2

Item 1 Vocabulary is important in math class. 51.17***

Item 2 My math teacher believes vocabulary is important in learning mathematics.

96.17***

Item 3 Reading in math class is not important. 23.78***

Item 4 Student discussion of vocabulary is a key component in comprehension. 35.96***Item 5 Sometimes we have to read in math and I don’t understand the words. 17.70**

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.

77.26***

Item 8 Learning new words before I read is helpful. 42.04***

Item 9 It is easier to understand informal definitions used on note cards, than book vocabulary.

73.57***

Item 10 It is helpful when my teacher takes the time to discuss vocabulary. 59.43***

Item 11 Graphic organizers help me to learn information. 17.48**

Item 12 Note cards help me to better understand and learn math vocabulary and procedures.

61.17***

Item 13 The vocabulary of the Georgia Performance standards is easy to understand.

20.30***

Item 14 Note cards are a good method to use to become proficient in math class. 61.61***

Item 15 I like to use note cards when learning new vocabulary or steps in problem solving in math class.

55.96***

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

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


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.


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


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


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.


C H A P T E R V : A N A L Y S I S A N D D I S C U S S I O N O F R E S U L T S

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 pre-

versus 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).


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 socio-

economics, 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 t-

tests 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


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


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.


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


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 standards-

based 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


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.”


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 pre-

test 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.


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.


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.


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


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


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


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.


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.


REFERENCES

Adams, T. (2003). Reading mathematics: More than words can say. Reading Teacher, 56(8),

786-792.

Approaches to teaching and learning in mathematics (2007). Retrieved June 16, 2010 available from

http://www.eduweb.vic.gov.au/curriculumatwork/maths/ma_approaches.htm.

Allen, J. (1999). Words, words, words. : Teaching vocabulary in grades 4-12. York, ME: Stenhouse

Publishers.

American Heritage Dictionary (4th ed.). (2010). New York: Houghton Mifflin.

Barton, M.,Heidema, C., & Jordan, D. (2002). Teaching reading in mathematics and science. Educational

Leadership, 60(3), 24-28.

Borsuk, A.J. (2003). Rhetoric aside, math does matter: But as technological demands rise, performance

in US seen as inadequate. Available from

http://www.testsonline.com/story/indexspx?/id=175561

Clarke, C. (2005). Socialization and teacher expectations of Jamaican boys in schools: The need for a

responsive teacher preparation program. International Journal of Education Policy, Research,

and Practice, 5(4), 3-34. Retrieved July 16, 2010 from Eric.

Davis, R. (2004). Jamaica a transformed education system. Kingston, Jamaica: Ministry of Education.

Department of Education and Skills [DES]. (2004) Pedagogy and practice: Teaching and learning in

secondary schools. Norwich: Cambridge University Press.

Dewey, J. (1938/1997). Experience and education. New York: Touchstone.

Donovan, S., & Bransford, J. (Eds). (2004). How students learn: Math in the classroom.

Washington, DC: National Academies Press.

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. Retrieved Sunday, June 16, 2010 from Academic Search Premier database.


http://us.f625.mail.yahoo.com/dc/launch?

action=welcome&YY=2081780978&.rand=7tsocr95b7q5v - bib8up#bib8up

Eisner, E. (1991). The enlightened eye. New York: MacMillan.

Evans, H. (1999). Gender differences in education in Jamaica. Education for All in the Caribbean.

Trinidad: FASTER Publishing Services.

Flood, J., & Lapp, D. (1990). Reading comprehension instruction for at-risk students: Research-

based practices that can make a difference. Journal of Reading, 33, 490-496.

Friere, P. (2005). Pedagogy of the oppressed. New York: Routledge.

Ganser, T. (2001). Beginning teaching in Jamaica: Challenges and assistance. Retrieved June 16, 2010

from ERIC database.

Garbe, D.G. (1985). Mathematics vocabulary and the culturally different student. Arithmetic

Teacher, 33, 39-42.

Georgia Department of Education. [GADOE] (2005). Office of curriculum, and testing. Available from

Georgia Department of Education, http://public.doe.k12.ga.us

Georgia Department of Education. [GADOE] (2008). Answers to frequently asked questions about AYP.

Available from Georgia Department of Education,

http://www.doe.k12.ga.us/aypnclb.aspx?PageReq=FAQS

Georgia Governor’s Office. (2010). Race to the top. Available from georgia.gov,

http://gov.georgia.gov/vgn/images/portal/cit_79369762/155733684RacetotheTopApp.pdf

Georgia Humanities Council. (2004-2010). New Georgia Encyclopedia: Rural education. Athens, GA:

University of Georgia Press. Retrieved June 16, 2010, from

http://www.georgiaencyclopedia.org/nge/Article.jsp?id=h-2616

Graves, M. (1985). A word is a word…Or is it? New York: Scholastic.

Honig, B., Diamond, L., Cole, C.L., & Gutlohn, L. (2008). Teaching reading sourcebook: For all

educators working to improve reading achievement. Novato, CA: Arena; Berkeley, CA:

Consortium on Reading Excellence.


Jetton, T. & Dole, J. (2004). Adolescent literacy: Research and practice. New York: Guilford Press.

Joint Board of Teacher Education [JBTE]. (2008). Authority, structure and functions of the joint board of

teacher education. Retrieved from http://www.jbte.edu.jm/about_jbte.htm

Jones, E., & Southern, W. (2003). Balancing perspectives on mathematics instruction. Focus on

Exceptional Children, 35(9), 1-16. Retrieved June 16, 2010 from the

Academic Search Premier database.

Kinchloe, J., & McLaren, P. (1998) Rethinking critical theory and qualitative research. In N. Denzin & Y.

Lincoln (Eds.), The landscape of qualitative research: Theories and issues (pp. 260 – 299).

Thousand Oaks, CA: Sage Publications.

Kvale, S. & Brinkman, S. (2009). Interviews: Learning the craft of qualitative research interviewing

(2nd ed.). Thousand Oaks, CA: Sage Publications.

Larochelle, M., Bednarz, N., & Garrison, J. (Eds.) (1998). Constructivism and education. New

York: Cambridge University Press.

LaGrange College Education Department [LCED] (2010). Conceptual framework. LaGrange, GA:

LaGrange College.

Lee, N. (2001, April/September). Challenges in teaching mathematics. Caribbean Journal of Education,

21, 181-191.

Marzano, R.J. (2004). Building background knowledge for academic achievement: Research on what

works in schools. Alexandria, VA: Association for Supervision and Curriculum Development.

Ministry of Education, Youth, and Culture. (2003). Mathematics and numeracy policy. Kingston,

Jamaica: Ministry of Education Policy.

Ministry of Education, Youth, and Culture. (2004). The development of education. Kingston, Jamaica:

National Report of Jamaica.

Ministry of Education, Youth, and Culture [MOEY&C]. (2010) Education statistics 2009-2010.

Available from MOEY&C, http://www.moeyc.gov.jm/EDUCATIONSTATISTICS2009-

2010.pdf


Morrow, L., Gambrell, L., & Pressley, M. (Eds). (2003). Best practices in literacy instruction.

New York: Guilford Press.

Mvududu, N. (2005). Constructivism in the statistics classroom: From theory to practice. Teaching

Statistics, 27(2), 49-54. Retrieved June 16, 2010 Academic Search Premier database.

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

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

National Council of Teachers of Mathematics [NCTM]. (2008). Overview: Principle for school

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

Nystrand, M. (1996). Opening dialogue: Understanding the dynamics of language and learning in

the English classroom. New York: Teachers College Press.

Popham, W. (2008). Classroom assessment: What teachers need to know (5th ed.). Boston: Pearson,

Allyn, & Bacon.

Salkind, N. J. (2010). Statistics for people who (think they) hate statistics (Excel 2nd ed.). Thousand Oaks,

CA: Sage.

Skrla, L., McKenzie, K., & Scheurich, J. (2009). Using equity audits to create equitable and excellent

schools. Thousand Oaks, California: Corwin.

Smith, D. (1999). Pedagon: Interdisciplinary essays in the human sciences, pedagogy, and culture.

New York: Peter Lang Publishing, Inc.

Stahl, K., & Bravo, M. (2010). Contemporary Classroom Vocabulary Assessment for Content Areas.

Reading Teacher, 63(7), 566-578. Retrieved from Academic Search Complete database.

Stringer, E. (2007). Action research in education. Columbus, OH: Prentice Hall.

Taskforce on Educational Reform. (2004). Jamaica: A transformed education system. Kingston, Jamaica:

Ministry of Education, Youth, and Culture.

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

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


Vacca, R. & Vacca, J. (2002). Content area reading: Literacy and learning across the curriculum (6th

ed.). Menlo Park, CA: Longman.

Wakefield, D.V. (2000). Math as a second language. The Educational Forum, 64, 272-279.

Winter, G. (2000). A comparative discussion of the notion of validity in qualitative and quantitative

research. The Qualitative Report, 4(3&4).


Appendix A

Samples of Looping Cards


Appendix B

Student Pre-Post Test


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.


3. Reading in math class is not important.


4. Student discussion of vocabulary is a key component in comprehension.


5. Sometimes we have to read in math and I don’t understand the words.


6. The vocabulary words we use in math class are easy to remember.


7. Note cards help me to understand the math concepts of word problems and equations.



8. Learning new words before I read is helpful.


9. It is easier to understand informal definitions used on note cards, than book vocabulary.


10. It is helpful when my teacher takes the time to discuss vocabulary.


11. Graphic organizers help me to learn information.


12. Note cards help me to better understand and learn math vocabulary and procedures.


13. The vocabulary of the Georgia Performance standards is easy to understand.


14. Note cards are a good method to use to become proficient in math class.


15. I like to use note cards when learning new vocabulary or steps in problem solving in math class.



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?

vocabulary in math class: - lagrange collegehome.lagrange.edu/educate/advanced programs/ed.s....

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