Differentiated Mathematics Instruction: An Action Research Study

University of South Carolina University of South Carolina

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Theses and Dissertations

2017

Differentiated Mathematics Instruction: An Action Research Study Differentiated Mathematics Instruction: An Action Research Study

Melinda A. Cannon

University of South Carolina

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Differentiated Mathematics Instruction: An Action Research Study.

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DIFFERENTIATED MATHEMATICS INSTUCTION:

AN ACTION RESEARCH STUDY

Melinda A Cannon

Bachelor of Arts

Coastal Carolina University, 1999

Master of Arts

Columbia College, 2004

__________________________________________________________

Submitted in Partial Fulfillment of the Requirements

For the Degree of Doctor of Education in

Curriculum and Instruction

College of Education

University of South Carolina

2017

Accepted by:

Ken Vogler, Major Professor

Susan Schamm-Pate, Committee Member

Richard Lassier, Committee Member

Vic Oglan, Committee Member

Cheryl L. Addy, Vice Provost and Dean of the Graduate School

iii

ABSTRACT

The purpose of this action research study was to evaluate the relationship between two

third grade mathematics classroom; one with differentiated pedagogy and other with

traditional pedagogy. To fulfill these purposes, the study tested the hypothesis utilizing an

independent t-test. The t-test was used to identify statistical differences among variables.

The participant-researcher utilized a differentiated mathematics instructional strategy of

small group instruction, collaborative group instruction, and online instruction with one

classroom and traditional lecture style pedagogy with the other classroom over a five

week period in preparation for a Post-Assessment. Quantitative data included

Mathematics Pre- and Post-Test scores which were given to students to gage their

mathematical problem solving abilities before and after the comparison study.

TABLE OF CONTENTS

BSTRACT

.......................................................................................................................... iii

IST OF

ABLES

................................................................................................................. vii

HAPTER

NTRODUCTION

....................................................................................................1

ACKGROUND

OMMUNITY AND

ISTRICT

..............................................................6

TATEMENT

ROBLEM

....................................................................................8

ESEARCH

UESTION

..................................................................................................9

URPOSE OF THE STUDY

..............................................................................................9

VERVIEW OF DESIGN OF STUDY

...............................................................................10

HEORETICAL

ASE

..................................................................................................12

EFINITION OF KEY TERMS

........................................................................................12

LIMITATIONS

..............................................................................................................14

IGNIFICANCE OF THE

TUDY

....................................................................................14

UMMARY OF THE

HAPTER

......................................................................................15

HAPTER

EVIEW

ITERATURE

..................................................................................16

INTRODUCTION

..........................................................................................................16

ELATION OF

ITERATURE TO

ESEARCH

ROBLEM

.................................................16

ESEARCH QUESTION

................................................................................................18

ESEARCH

URPOSE

..................................................................................................18

ESEARCH

ROBLEM

.................................................................................................19

DUCATION

EFORM

FFORTS

..................................................................................20

ATHEMATICS

NSTRUCTION

....................................................................................21

IFFERENTIATED

NSTRUCTION

.................................................................................23

RADITIONAL

ECTURE

TYLE

NSTRUCTION

HOLE

LASS

) ................................29

MALL

ROUP

NSTRUCTION

ITH

EACHER

...........................................................30

OLLABORATIVE

EARNING

.....................................................................................32

ECHNOLOGY

ATHEMATICS

...............................................................................35

UMMARY

.................................................................................................................39

HAPTER

ESEARCH

ESIGN AND

ETHODOLOGY

.........................................................41

NTRODUCTION

..........................................................................................................41

ESEARCH

ESIGN AND

PPROACH

..........................................................................43

ETTING AND

ARTICIPANTS

.....................................................................................47

ATA

OLLECTION

...................................................................................................50

ATA

NALYSIS AND

EFLECTION

...........................................................................51

UMMARY

.................................................................................................................51

HAPTER

INDINGS AND

NTERPRETATIONS OF

ESULTS

................................................53

NTRODUCTION

..........................................................................................................53

ESEARCH

OPIC

......................................................................................................55

ROBLEM OF

RACTICE

.............................................................................................55

URPOSE OF

CTION

ESEARCH

...............................................................................56

ESEARCH

UESTION

................................................................................................56

CTION

ESEARCH

ATA

OLLECTION

LAN

...........................................................56

UANTITATIVE

ATA

................................................................................................57

VERVIEW OF

ATA

OLLECTION

............................................................................58

THICAL

ESEARCH

CTION

LAN

...........................................................................59

INDINGS OF THE

TUDY

...........................................................................................60

NTERPRETATIONS OF

ESULTS OF THE

TUDY

.........................................................62

ONCLUSIONS

...........................................................................................................62

HAPTER

UMMARY AND

ISCUSSION

............................................................................64

NTRODUCTION

..........................................................................................................64

OCUS OF THE

TUDY

................................................................................................64

VERVIEW OF THE STUDY

.........................................................................................65

UMMARY OF THE

TUDY

.........................................................................................66

MPLICATIONS

INDINGS

..............................................................................67

CTION

LAN

EVELOPMENT

...................................................................................67

CTION

LAN

IMELINE

............................................................................................69

UGGESTIONS FOR

UTURE

ESEARCH

.....................................................................72

ONCLUSIONS

...........................................................................................................72

EFERENCES

.......................................................................................................................74

PPENDIX

NFORMED

ONSENT

......................................................................................90

PPENDIX

SSENT TO

E A

ESEARCH SUBJECT

.............................................................92

PPENDIX

EST

ESULTS

................................................................................................93

vii

LIST OF TABLES

Table 4.1 Math Chapter 1 Assessment Results ................................................................. 62

Table 4.2 Levene’s Test for Equality of Variances .......................................................... 62

Table 5.1 Action Plan Implementation Timeline .............................................................. 71

CHAPTER

Introduction

Globalization of the economy, diverse populations, and rapid changes in

technology are posing many challenges for educational systems. Throughout time,

education has been an area that has seen numerous reform efforts trying to meet the needs

of an ever changing society. The massive reform efforts in the United States have

intended to close the achievement gap among the different subgroups in America and

between the United States and other countries (Zhao, 2009). Despite the numerous reform

efforts to improve educational standards, schools systems are struggling to meet the

needs of 21

Century learners and employers. As we try to meet the needs of these

diverse learners, schools are in need of intensive restructuring. The term “21

Century”

has educators and administrators searching for ways to prepare students for the future and

the educational system is evolving faster than ever (Nichols, 2015). The identified

problem of practice for my Dissertation in Practice (DiP) focuses on the deficit that exists

in public school students in demonstrating high levels of mathematics reasoning as

measured by state assessments.

“To have an equal opportunity to pursue success, particularly financial success,

citizens need equal access to the skills necessary to that pursuit, and schools are charged

with providing everyone with these skills” (Weber, 2010, p 152). Educators today not

only have to enable students with basic skills but critical thinking and process skills to

utilize not only in school but in their daily lives. Some 21

Century skills that have been

identified as important for all learners are critical thinking, communication, collaboration,

and creativity (NEA, 2016). These skills are not new to education but tend to be the basis

of great teaching. Educators and administrators need to incorporate these skills in

classrooms and learning communities around the country. “Students do not learn alone,

but rather in, diverse communities, interacting with their teachers, in the company of their

peers, and bringing with them the values and teachings of their families” (Katz & Porath,

2011, p. 32). Educators and administrators cannot change the environment that students

are born into, but we can change a student’s life by providing the best education possible.

It is important that as educators and administrators, we emphasize instructional strategies

that will produce learners who are productive citizens. “It is clear that when teachers and

administrators focus on things they can control, such as instructional strategies, opposed

to things outside of their control, such as socioeconomic status and demographic factors,

students perform better” (Clayton, 2011, p. 682). Katz and Porath (2011) argue that for

all students to learn, students must be recognized as having diverse needs, and a

classroom that allows all students to learn and develop a sense of belonging. The heart of

instruction has to focus on meeting the diverse needs of the students not teaching the

standards and teaching to the test.

Research reveals how even well-intentioned reforms fail to address the most

urgent issues precisely because such reforms are undertaken as a pre-made

package without the knowledge of local issues, and their relation to the broader

political, cultural, and economic context of society. (Valdiviezo, 2014, p 75)

Instruction today is challenging because it does not begin on the first page of the

curriculum guide, but rather where students are in regards to their ability (Tomlinson,

2001). Educators must understand the diverse ability levels of the students in their class

to make quality instructional decisions. This understanding allows educators to

implement instructional strategies conducive to their students’ strengths and weaknesses.

Marzano, Pickering, & Pollack (2001) stated that the individual instructional strategies

that a teacher uses have a powerful effect on student learning.

To meet the needs of all students and utilize instructional strategies responsive to

each student’s strengths and interests, we must explore alternatives to traditional

instruction. Mathematics is the key to opportunity, for students it opens doors, enables

informed decisions, and provides knowledge to compete in a technological economy

(National Research Council, 1989). For people to function in this global society,

mathematics play an integral role in basic knowledge. People need to have a complex

understanding of numbers and procedures that are used in daily activities. “All students

must have a solid grounding in mathematics to function effectively in today’s world”

(Ball et al., 2005, p. 1056).

The students at Sunshine Elementary showed greater achievement in reading and

writing, however a gradual decline in mathematics achievement was shown on the

Palmetto Assessment of State Standards (PASS) and Measures of Academic Progress

(MAP). When differences in students’ abilities are significant, educators must make

accommodations and differentiate instruction to make teaching and learning more

successful (Tomlinson, 2000). When children do not learn the way we teach then we

must teach the way they learn (Kellough, 1999). Differentiated instruction was used in

this research study as an instructional strategy to improve mathematics achievement in

third grade students compared to traditional lecture style instruction.

The teacher in a differentiated classroom understands that she does not show

respect for students by ignoring their learning differences. She continually tries to

understand what individual students need to learn most effectively, and she

attempts to provide learning options that are a good fit for each learner whenever

she can. She shows respect for learners by honoring both their commonalities and

differences, not by treating them alike. (Tomlinson, 1999, p. 12)

This instructional strategy will allow the researcher a significant opportunity to address

the diverse needs of the learners. Traditional lecture style instruction negates to engage

my students in content and knowledge of mathematics. Standing in front of the classroom

spraying students with information does not meet the individual needs of all of students.

Slavin, Madden, & Stevens work (as cited in Kuntz & McLaughlin, 2001) noted that the

best possible mathematics program for mainstreamed classrooms would be one that

combined cooperative learning with individualized instruction. Good mathematics

instruction engages all students as active learners (NAEYC & NCTM, 2002). Using a

more diverse technique for delivering mathematics instruction allows students the

opportunity to build their knowledge by engaging in multiple mathematic activities.

“Basic skills with numbers continue to be vitally important for everyday uses. They also

provide a crucial foundation for the higher-level mathematics essential for success in the

workplace which must now also be part of a basic education” (Ball et.al, 2005, p. 1056).

Often students have a negative attitude toward mathematics because they are used to

sitting in their desk and having to do work on their own. Making mathematics instruction

more student centered allows students to really take ownership of their own learning.

Effective math instruction allows children to develop positive attitudes toward math

instead of negative ones (Clements, Sarama, & Dibiase, 2004). The major focus on

mathematics instruction in elementary schools is the development of proficiency in

computation and of skills in applying computational ability to solving problems

(Fleischner, 1985).

Dr. Carol Ann Tomlinson (1999) provides the following example of differentiated

classrooms:

In differentiated classrooms, teachers begin where students are, not the front of a

curriculum guide. They accept and build upon the premise that learners differ in

important ways. Thus, they also accept and act on the premise that teachers must

be ready to engage students in instruction through different learning modalities,

by appealing to differing interests, and by using varied rates of instruction along

with varied degrees of complexity. (p. 2)

Students who are taught through differentiated methods not only learn

mathematics effectively, but they also become motivated students who view themselves

as successful mathematicians (Lawrence-Brown, 2004). Making the most of the little

time that can be used on a daily basis for mathematics is crucial for students. Having

students engaged in learning which meet their individual needs is of upmost importance.

Differentiated math instruction based on student readiness meets the needs of students

who are below grade level, as well as those who exceed benchmarks. When applied

correctly, differentiation in mathematics ensures student success (Grimes & Stevens,

2009). Students who are instructed using differentiated instruction can work

independently or collaboratively on activities that allow practice and review of

mathematic concepts. Teachers are able to work closely with children individually or in

small groups providing a more differentiated style of instruction consistently each day.

This individualized instruction allows our students to receive tailored instruction to best

meet their needs (Boushey & Moser, 2014). Utilizing small group instruction,

collaborative learning, and online activities allows the educator to cater the learning goals

to the individual students’ strengths and weaknesses. Grouping has to be flexible and

continually changing based on the content and the individual students’ needs.

Differentiated mathematics groups are no longer rigid groups that follow the whole year

but should be ever constantly changing based on informal and formal assessments of

student progress.

Background- Community and District

Daisy School District, located in Clover, serves a diverse range of students. There

are approximately 9,620 students in the district. The District has 20 schools: nine

elementary schools, one intermediate school, one charter school, four middle schools,

four high schools and one adult education center. Based on Clover’s Department of

Education Website, Daisy School District received an Absolute Rating of Excellent on

the Annual Yearly Progress (AYP) Report Card and a C based on the Federal

Accountability Rating System. Based on the South Carolina Palmetto Achievement Test

of State Standards (SCPASS), 71% of our students received Met or Exemplary on the

ELA portion of the test. Sunshine Elementary received an overall AYP Report Card

Absolute Rating of Average and a C based on the Federal Accountability Rating System.

Based on the SCPASS, 55% of our students received Met or Exemplary on the

Mathematics portion of this test. These statistics are below Elementary Schools with

Student’s Like Ours (61%), meaning Poverty indexes are not 5% below or above. This

also places us below Elementary Schools in the State (76.9%) in Mathematics (Clover

Annual Report Card Summary, 2014).

Based on Measures of Academic Progress (MAP) for Mathematics, students in

Sunshine Elementary also show a deficit. In fall of 2014, 45.3% of third grade students,

62.8 % of Fourth grade students, and 39.7% of fifth grade students were Proficient in

Mathematics (South Carolina Department of Education, 2014). Based on test scores from

these assessments, educators need to evaluate instructional strategies which are most

effective in meeting individual students’ needs. Diverse student populations make finding

effective instructional strategies a challenge faced by many administrators and educators.

Sunshine Elementary is a rural school in Clover. Sunshine Elementary is a Title I

school. Title I provides federal funding to schools that have low poverty levels. The

funding is meant to help students who are at risk of falling behind academically (Meador,

2015). Poverty rates for rural families are higher across all categories and more enduring

than their urban counterparts. Rural African American families and their children are not

empowered by the educational system or provided educational services in a culturally

sensitive context (Kea, 2009). Sunshine Elementary has an 89% Free/Reduced Lunch

Status. Farrigan and Parker (2012) stated in the United States, people living in poverty

tend to be clustered in certain regions, counties and neighborhoods rather than being

spread equally around the Nation. “Rural children are less likely than non-rural children

to be in center-based care other than Head Start during the pre-kindergarten year” (Kea,

2009, p. 12). Students at Sunshine come to school exhibiting deficits because of the

poverty level and lack of pre-kindergarten experience.

Statement of the Problem

The overarching goal of action research is to improve practice immediately within

one or a few classrooms or school. The mathematics needs of our general population in

being left behind in the goal of making all learners literate. The purpose of my action

research study is to examine the effects of differentiated mathematics instruction and

traditional lecture style instruction on the achievement of third grade mathematics

students. The specific purpose of this study was to examine the utilization of small group

instruction, collaborative groups, and the use of online games/activities as a framework to

differentiate learning of mathematics in third grade students.

The challenge for classrooms and schools is finding the best instructional

strategies that meet the needs of the diverse student population. The Daisy School

District implemented High Progress Literacy Classrooms in response to Read to Succeed.

Teachers rework their daily English Language Arts (ELA) schedule and have arranged

use of time so that all students can be highly engaged with text reading and writing at

least 75% of classroom instructional time (HPLC Implementation, 2015). Educators’

daily schedules reflect the large chunk of instructional time dedicated to reading, writing

and research, leaving a small section of time for mathematics instruction.

McMillan (2004) describes action research as being focused on solving a specific

classroom or school problem, improving practice, or helping make a decision at a single

local site. Kea (2009) states the systematic lower achievement of particular groups of

students is an alarming sign for politicians about the crisis of the educational systems,

and it is an important justification behind investments in reforms and research in

mathematics education. Clover and the Daisy School District are creating independent

readers and writers but failing to inspire the mathematicians. Teachers must apply

instructional methods that make math accessible and understandable to all students

(Grimes & Stevens, 2009). We as educators must step back and make hard choices based

on the needs of the students that make their educational journey in our rooms daily.

Mathematics no longer is memorizing facts but actually having a deep understanding of

what the numbers, signs, and answers mean. Educators must improve mathematics

knowledge by focusing on alternative instructional strategies which hold effective

mathematics instruction at its core.

Research Question

What is the difference in mathematics achievement in third grade students who

have received differentiated mathematics instruction when compared to third grade

students who received traditional mathematics instruction?

Purpose of the Study

The purpose of my action research study was to examine the effects of

differentiated mathematics instruction and traditional lecture style instruction on

mathematics achievement of third grade students. The specific purpose of this study was

to examine the utilization of small group instruction, collaborative groups, and the use of

online games/activities as a framework to differentiate the learning of third grade

students. Effective instructional strategies enable diverse learners to construct their own

knowledge and cultivate talents in an effective manner (Darling-Hammond, 1993).

Schools are faced with the challenge of implementing state standards with a single

requirement for all learners. The problem facing educators is all learners need to have the

same outcome but instructional strategies need to meet the diverse needs of their learners.

This study will examine two of the most predominant instructional strategies for teaching

mathematics: Traditional lecture style and differentiated instruction.

To date, there is very little research conducted on differentiated instruction in the

elementary levels. Hayes and Deyle (2001) claim that it is difficult to determine the

possible effects of differentiated instruction on the achievement of students because the

effects of differentiation may differ in each school. Smit and Humpert (2012) argue that

students who receive differentiated instruction do not experience poorer achievement,

however, clear positive results from differentiated instruction still have to be found.

Overview of Design of Study

Action research is defined as any systematic inquiry conducted by teachers, or

others with a vested interest in the teaching and learning process or environment for the

purpose of gathering information about how their particular schools operate, how they

teach, and how their student’s learn (Mills, 2011). Action research is the appropriate

format for my study to allow a deeper understanding of the diverse learning needs of

students and strategies that would make instruction more effective. This research will

provide insight to my school and district to facilitate mathematics teaching and learning

that will meet the diverse needs of the student population. Action research allows

teachers to study their own classrooms, in order to better understand them and to be able

to improve their instructional quality or effectiveness. It focuses on the unique

characteristics of the population with whom the action must be taken. This in turn

increases the effectiveness for the practitioner (Parsons & Brown, 2002). Educators must

be willing to step up and find the best practices that work for their classrooms. Making

sure that each classroom is different and that the differences reflect the individual needs

of the students within. “True school improvement must begin within the four walls of the

classroom. Teachers must be able and willing to critically examine their own practice as

well as how their students learn best” (Mertler, 2014, p. 12).

The purpose of this quantitative study is to compare instructional strategies and

their effectiveness in mathematics achievement of third grade students. The study is

designed to determine the impact that varied pedagogical methods have on mathematic

abilities of third grade students in a rural school setting. The researcher will investigate

and compare how a math class of third grade students performs when receiving

differentiated instruction. The comparison group is from another class in Sunshine

Elementary that will receive traditional lecture style instruction.

The researcher will utilize small group instruction, collaborative groups, and the

use of online games/activities as instructional tools to facilitate differentiated instruction.

Sunshine Elementary School shows a deficit in the students’ mathematics test scores

when compared to other students in the State of Clover. The action research study

attempted to determine if a differentiated instructional model compared to the traditional

lecture-style instructional model strengthens student achievement in third grade students

during the fall semester by utilizing a pre- and post-test for mathematics.

Many of the students at Sunshine Elementary come with an early learning deficit

versus other children who may live in other areas of the county. The classes will be

comprised of students who are similar in makeup and dynamics. The students will receive

a mathematics pre-test so that the teacher/researcher can compare the scores prior to the

instructional unit and students will also receive a mathematics post-test so that scores can

be analyzed after the instructional unit.

Theoretical Base

The theoretical base for this study is rooted in the works of Gardner (2004),

Vygotsky (1993), and Tomlinson (2001). Gardner (2004) is known for his theory of

multiple intelligences. Gardner believed that when teachers know how students learn and

at what intellectual level, teachers can better instruct students’ individual needs. Utilizing

small group instruction, online activities, and collaborative activities to facilitate

differentiated instruction allows the researcher to accommodate each child’s intelligence.

The social aspects of collaborative learning are tied to Vygotsky’s (1993)

sociocultural theory. According to Vygotsky, children learn by working together as well

as developing concepts by using concrete objects to construct meaning. One of

Vygotsky’s theories that is highly recognized by teachers is the zone of proximal

development (1993). The zone of proximal development is the gap between what a

learner has already mastered and what he or she can achieve when provided with

educational support (Vygotsky, 1993). Utilizing collaborative groups in differentiated

instruction allows students to work together to share ideas and explain their ideas.

Tomlinson (2001) discussed the importance of differentiated instruction and

accommodating the instructional needs of all children. In classrooms without

differentiated instruction, students do not have opportunities to share and express ideas

beyond the traditional realm of study. Tomlinson’s (2001) theories create the foundation

for differentiated instruction, allowing online activities, collaborative learning, and small

group instruction to deliver instruction to meet the diverse needs of learners.

Definition of Key Terms

The key terms and definitions, essential for this study, are provided:

Action Research is any systematic inquiry conducted by educators for the purpose

of gathering information about how their particular schools operate, how they teach, and

how their students learn (Mertler, 2014).

Small Group Instruction typically refers to a teacher working with a small group

of students on a specific learning objective. These groups consists of 2-4 students and

provide these students with a reduced student-teacher ratio. It allows teachers to work

more closely with each student, reinforce skills learned in the whole group instruction,

and check for student understanding. (Meador, n.d.).

Collaborative/Cooperative Learning is the instructional use of small groups so

that students work together to maximize their own and each other’s learning. Class

members are organized into small groups after receiving instruction from the teacher.

Then they work through the assignment until all group members successfully understand

and complete it (DeJesus, 2012).

Differentiated Instruction is a clear and solid method to modify instruction. A

teaching philosophy that allows students to have multiple options for taking in

information, making sense of ideas, and expressing what they learn (Mann & Willis,

2000).

Math achievement is using research-based teaching methods to ensure all students

can show mastery of grade level skills being taught (Byrnes, 2001).

Whole Class Instruction is typically teacher led. The teacher teaches the entire

class the same lesson regardless of the specific needs of the students in the class (Meador,

n.d.).

Limitations

This study was limited to third grade mathematics classes in an elementary

school, which could possible yield different results in a middle school or high school

setting. The study was conducted in a single geographical area. The sample consisted of a

high percentage of minority students from low-income families. These factors limited the

generalizations of the study to third grade students, to school districts in other regions

with other populations. The assessment is multiple choice, open ended questions would

allow students a change to elaborate or explain their answers.

Significance of the Study

The curriculum in schools have become standards based, which means all

students are expected to achieve equally and meet high standards despite their varied

abilities. Educators are therefore challenged to meet the diverse needs of the student

populations. The only way to meet the objective of the standards based curriculum is to

personalize or differentiate the instruction (Lawrence-Brown, 2004). Educators must face

the challenges of changing from traditional lecture style instruction to instructional

methods that meet the diverse needs of their students.

Differentiated instruction is believed to be an effective instructional strategy

because it advocates beginning where individuals are rather than with a prescribed plan

of action, that disregards student readiness, interest, and learning profile (Tomlinson,

2005). This study is significant and contributes to the existing research because it

provides educational leaders with a comparative study of differentiated instruction and

traditional instruction. Society has become more diverse and complex, which is also

represented in our classrooms. Schools need to adopt learning strategies that enable all

students to meet high standards.

Summary of the Chapter

The purpose of this action research study is to examine the effects of

differentiated mathematics instruction and traditional lecture style instruction on two

third grade mathematics classes. The participant-researcher will utilize a differentiated

mathematics instructional strategy of small group instruction, collaborative group

instruction, and online instruction with one classroom and traditional lecture style

pedagogy with the other classroom over a five-week period in preparation for a Post-

Assessment. Quantitative data will include Mathematics Pre- and Post-Tests which will

be given to students to gage their mathematical problem solving abilities before and after

the comparison study. The pre- and post-test data will help the participant-researcher to

gain a more in depth understanding of the student's mathematical problem solving

abilities. Chapter 2 contains a literature review that compares and contrasts different

points of view, research outcomes, and establishes the relationship of the study. Chapter 3

provides a description of the participants, methodology, and instrumentation. Chapter 4

includes a detailed statistical analysis of the data and an interpretation of the findings.

Chapter 5 contains of summary of and interpretations of the findings, implications for

social change, and recommendations for action and future plans.

CHAPTER 2

Review of Literature

Introduction

This review of literature presents reforms that have led to the massive changes in

the public school system. The literature presents a view of differentiated instruction,

traditional lecture style instruction (whole class) and mathematics instruction. The

discussion will analyze the elements of small group instruction, collaborative/cooperative

groups, and online games. Significant works of theorists will be evaluated in detail on the

topics of differentiated instruction and lecture style instruction (whole class).

Relation of Literature to Research Problem

Research has provided evidence that the education system is failing at meeting the

growing needs of diverse school populations. Research is provided on education reform

efforts to meet the diverse needs of students. In this literature review, I explore an

instructional approach, differentiated instruction, to effectively meet the needs of third

grade students in mathematics instruction. Research regarding online games,

collaborative groups, and small group instruction, as it pertains to higher achievement in

math, is presented.

Darling-Hammond (1993) believed that the job of instruction is to enable diverse

learners to construct their own knowledge and to cultivate talents in an effective manner.

Kluth & Straut (2001) argued that standards should be flexible, present a wide range of

concepts and skills, and educators need to adapt the curriculum to meet the individual

needs of learners. No Child Left Behind (NCLB) (2001) resulted in massive changes in

our public school systems. “Without teachers who have sophisticated skills for teaching

challenging content to diverse learners, there is no way that children from all racial and

ethnic language and socioeconomic backgrounds will reach the high academic standards

envisioned by the law” (Darling-Hammond, 2007, p.48). This reform increases

accountability for schools, educators, and school districts. Therefore, the instructional

strategies that educators incorporate into their classrooms can have a significant impact

on student achievement.

Mathematics is everywhere: it is experienced and practiced by every culture and

must be incorporated into school mathematics curriculum. Instead of instilling

fear and loathing, math education should foster a great understanding of how

mathematics is applied in our increasingly technologically-driven world.

Mathematics instruction should reflect/embrace the cultural diversity of our

classrooms, and of our increasingly interconnected world. (Brandt & Chernoff,

2015, p. 33)

Derman-Sparks (1990) explained that ultimately, teachers, school leaders, parents, and

students must acknowledge that students from all cultures and backgrounds have the

potential to be high ability learners. Curriculum which does nothing to counteract biases

which dominant-culture children encounter in their daily lives does little to help these

children live effectively and fairly with diversity.

My identified problem of practice for my DiP focuses on the deficit that exists in

many United States public school students in demonstrating high levels of mathematics

reasoning as measured by state assessments. In particular, Sunshine Elementary shows a

deficit in students' mathematics test scores when compared to other students in the State

of Clover. Daisy School District implemented High Progress Literacy Classrooms which

schedules English Language Arts for 75% of the school day. Students are being given

daily instruction across the curriculum in English Language Arts but leaving mathematics

behind.

One goal of this review of literature is to enable teachers to find different

instructional strategies that can be utilized in classrooms for differentiated instruction.

These instructional strategies can help to promote mathematical reasoning and

achievement through collaborative learning, small group instruction, and online

game/activity program. In order to reach this goal, an action research study designed to

analyze alternative instructional techniques in mathematics education is proposed.

My action research study will focus on differentiating mathematics instruction to

promote higher achievement in third grade students.

Research Question

What is the difference in mathematics achievement in third grade students who

have received differentiated mathematics instruction when compared to third grade

students who received traditional mathematics instruction?

Research Purpose

The purpose of my action research study is to examine the effects of differentiated

mathematics instruction and traditional lecture style instruction on the achievement of

third grade mathematics students. The specific purpose of this study is to examine the

utilization of small group instruction, collaborative groups, and the use of online

games/activities as a framework to differentiate the learning of third grade students. The

post-test data will be analyzed to determine if there is a statistically significant difference

in the achievement of third grade students taught by differentiated instruction or

traditional lecture style instruction. Sunshine Elementary School shows a deficit in our

students’ mathematics test scores when compared to other students in the State of Clover.

The action research will attempt to determine if a differentiated instructional model

compared to the traditional lecture-style instructional model strengthened student

achievement in two third grade groups during the fall semester by utilizing a pre- and

post-test for mathematics.

Research Problem

No longer can we allow our students to sit idle in their desks with a worksheet.

We must provide an engaging environment, where students are immersed in their own

learning. Finkelstein argued (as cited in Springs, 2014) that in the nineteenth century

teachers were of two types: the intellectual overseer, who stressed memorization and

punished failure in assignments, and the drillmaster, who had the students repeat material

in unison. As educators, we can no longer afford to be the intellectual overseer or the

drillmaster. We must provide education that is diverse based on our student’s strengths

and weaknesses. We must provide varied opportunities for students to be active in the

learning practice promoting their strengths in each task.

The major impact of the Pestalozzian theory was its emphasis on relating

instruction in the early years to objects in the real world, on learning by doing,

and on the importance of activity, as opposed to sitting at a desk. (Springs, 2014,

p. 147)

Students need to practice learning in multiple ways throughout the day to apply their

knowledge to learning.

Education Reform Efforts

The No Child Left Behind (NCLB) Act of 2002 created a sense of urgency in the

education system to aggressively analyze the classroom instruction and student

achievement. NCLB caused massive changes to begin in public school systems around

the nation. Public schools have been placed under a great deal of pressure to demonstrate

that they are providing students with a thorough and efficient education through

improved test scores (Noddings, 2005). NCLB (2001) brought about testing requirements

for reading and math which caused educational systems to design standards based

curriculum that would emphasize reading and math instruction. With the accountability

and testing requirements put into place by NCLB, school systems had a shift regarding

instructional approaches that were being utilized in classrooms around the country.

President Barack Obama placed more accountability on the states by allowing

them to compete against one another, looking for better curriculum, assessments, better

technology, and a commitment to providing the most efficient education for all students.

Race to the Top held students accountable for more rigorous standards to better prepare

them for college and careers, and teachers are using newer and better classroom

assessments to tailor their instruction to students’ needs (US Department of Education,

2015). Race to the Top also saw college and career ready standards (21

Century Skills)

adopted across states to align expectations for college and workplace.

Mathematics Instruction

Lubienski (2002) explained there is much we do not know about how schools fail

in their support of children of color and those in poverty, particularly in elementary

mathematics classrooms. Given this, scholars are calling for in-depth examinations of the

instructional practices, particular to mathematics, that contribute to less opportunities to

engage quality mathematics for students of color.

Mathematics education researchers seek answers to important questions that will

ultimately result in the enhancement of mathematics teaching, learning,

curriculum, and assessment, working toward ensuring that all students attain

mathematics proficiency and increasing numbers of students from all racial,

ethnic, gender, and socioeconomic groups who attain the highest level of

mathematics achievement. (National Council of Teachers of Mathematics, 2014,

p. 6)

The focus has been on improving mathematics instruction so that all students

meet the high standards as measured by state-administered achievement tests, it is crucial

that students at risk for mathematics difficulties, who vary considerably in ability,

achievement, and motivation, develop the necessary mathematical knowledge to meet

grade-level benchmarks (Jitendra et.el., 2013). Creating mathematically literate citizens is

rarely questioned by educators; however, there are different interpretations of the

meaning of the term. Mathematical literacy can be seen as the ability to solve problems,

reason about and analyze numerical information, and know the meaning of important

mathematical vocabulary (Oxford Learning, 2010). Traditional math instruction results in

the class doing the same assignment and practicing the same problems, usually receiving

no feedback until the next school day (Poncy, Fontenelle, & Skinner, 2013). Many

children who would not be identified as having special educational needs are low-

attaining in mathematics (Butterworth, Varma, & Laurillard, 2011). Difficulties in

mathematics often have a marked impact on their educational prospects (Gross, 2007).

Bynner and Parsons (1997) found that most adults with serious numeracy difficulties had

already shown difficulty with mathematics by the age of seven. The development of

suitable interventions is made more challenging by the fact that there are many reasons

why children may experience mathematical difficulties: environmental factors, broader

cognitive difficulties such as problems with language, spatial awareness or working

memory, and more specific weaknesses in some or all aspects of mathematics (Gifford &

Rockliffe, 2012). The traditional structure in elementary and middle school mathematics

classrooms has consisted of textbook driven lesson, rote memorization, and focus on skill

practice (Project Grad, 2008). The National Council of Teachers of Mathematics (2000)

has greatly influenced mathematics instruction, by promoting more meaningful

instruction or standards based instruction. These standards describe skills that students

will need to perform effectively in the 21

Century. Knapp, Zucker, Aldelman, and

Needles (1995) argued that theorists suggest that instructional strategies that emphasize

conceptual understanding of mathematics ideas and procedures across a wide area of

content present the most promise for mathematics instruction in schools with students

that come from homes in the lower economic ranges.

It is important for teacher of mathematics to expose student’s strengths and

scaffold them into higher mathematical thinkers and learners. Instead of traditional

question and answer “ping pong,” the teachers allow time for thinking and not to expect

the pupils to answer correctly immediately. Teachers turned the pupils into real partners

in the discourse, communicating, responding to their peers and exposing their difficulties

(Margolin & Regev, 2011). Instructional strategies, such as differentiated instruction,

allow instructional time to be utilized to better meet the individual needs of students.

Math teachers are able to work closely with children individually and in small groups

consistently each day. This individualized coaching allows students to receive tailored

instruction to best meet their needs (Boushey & Moser, 2014). According to Margolin

and Regev (2011)

A meaningful mathematical discourse in which the teacher can observe each

pupil’s engagement in the task, identify his zone of proximal development as well

as misconceptions and relate to them in order to afford construction of concepts

and ideas, can occur in small groups. In a whole class discussion only few pupils

have the opportunity to articulate their thoughts or to expose their misconceptions

publicly and the teacher can’t really know about the others’ understanding and

relate to their difficulties. (p. 18)

In more differentiated mathematical groups, students can be taught strategies that

can be applied when working independently. Van Luit and Nnaglieri (1999) noted that

explicit strategy instruction occurs when “students are taught to flexibly apply a small

repertoire of strategies that reflect the processes most frequently utilized by skilled math

students” (p.99).

Differentiated Instruction

Students in today’s schools are becoming more academically diverse. There are

more students identified for more exceptionalities in special education, more

students whom English is not their first language, and more students struggling to

read. There is a need to ensure challenge for advanced learners when

accountability pressures focus on basic competencies, and a growing economic

gap exists between segments of the student population. (Tomlinson, Kay, & Lane,

2008, p. 1)

“The lack of early literacy and numeracy skills can have a profound impact on school

readiness and overall academic performance. Children need high quality learning

experiences to succeed in school” (Kea, 2009, p. 11). Which brings about the question

does traditional classrooms meet the growing needs of diverse school populations? “The

differences in students are significant enough to make a major impact on what students

need to learn, the pace at which they need to learn it, and the support they need from the

teachers and others to learn it well” (Tomlinson, 2000, p 6). We no longer can afford the

leisure activity of teaching down the middle, we as educators, have to find our student’s

strengths and build on those strengths.

When teachers believe unequivocally in the capacity of their students to succeed

through hard work and perseverance, it’s natural to provide work that

complements the capacity of each student to think, problem solve and make

meaning of important ideas. ‘Teaching up’ communicates clearly that everyone in

the class is worthy of the best curriculum the teacher knows how to create.

(Tomlinson, 2013, p. 8)

Educators need to effectively meet the needs of their students in the most feasible way

possible. “Students will learn best when supportive adults push them slightly beyond

where they can work without assistance (Tomlinson, 2013, p. 7). The key is to providing

opportunities for students to grow in their learning and practices. As Tomlinson (2013)

stated, “achieving the goal of maximum academic growth is dependent upon effective

instructional practices working in concert with an effective curriculum, as well as

effective assessment, and classroom leadership and management” (p. 9). Educators must

promote the individual strengths and goals of each student to build a stronger learning

community. “When students learn and grow in their own ways, differences are

pronounced. When we decide we want to value differences, we make decisions that

expand diversity rather than seek conformity and inappropriate uniformity” (Guild &

Garger, 1998, p. 7).

Differentiated learning is a predominant instructional strategy that educators

employ to facilitate the diverse needs of students. “Differentiation provides one method

by which teachers can provide appropriate challenge at appropriate levels for all learners

in a heterogeneously grouped mathematics classroom where the range of abilities and

interests can be wide” (Reed, 2004, p.120). In terms of differentiation, creating

understanding focused curriculum asks teachers to realize their students will approach

understanding at varied levels, will need different support systems to increase their

current level, and will need a range of application to connect the understanding with their

own life experiences (Tomlinson, Kay, & Lane, 2008). Student’s diverse needs are being

met inside of one classroom because the teacher is attending to the challenges and

strengths of the students. Students in a differentiated classroom utilize their strengths and

are motivated to persevere even when tasks become more difficult. Lawrence-Brown

(2004) describes differentiated instruction as a strategy that recognizes and supports a

classroom as a learning community populated with peers that must be nourished as

individual learners.

Differentiated learning leads to students being engaged in tasks that are based on

their individual level. Engagement in the classroom results when a student’s attention is

attracted to an idea or a task and is held there because the idea or task seems worthwhile.

Students become engrossed because the task is enjoyable, or because it seems to provide

them with the power of competence of autonomy, or because it links with an experience,

interest or talent that is significant to them, or because it is at the right level to challenge

and stimulate rather than to frustrate or bore them (Tomlinson, 2013). The teacher sets

the foundational goals by guiding students to meet their own independent challenges.

Students begin to build stamina and self-reliance when faced with mathematical

adversity. Teaching to the lower level of a class perpetuates the problem of low

mathematics achievement, along with boredom and disengagement on the part of the

middle and high-end learners. Teaching to the middle level causes the less-prepared

students to struggle and fall farther behind, while the better prepared students, who

remain unchallenged, lose their motivation to learn (Rimm & Lovance, 1992). The key

components of modifications to the mathematics curriculum should attend to four broad

principles: The teacher should:

Provide content with greater depth and higher complexity

Nurture a discovery approach that encourages students to explore concepts

Focus on providing complex open-ended curriculum

Create opportunities for interdisciplinary connections (Stepanek, 1999).

Providing a diverse educational experience that meets the needs of all students is

important to mathematics classrooms. Educators must move forward, rapidly and visibly,

in the successful implementation of classroom-level strategies that provide differentiated

curriculum, instruction, and assessment; strategies that when implemented effectively,

result in challenging and supporting all students within the regular, mixed-ability,

heterogeneous classroom (Tomlinson, 2001). In an effective heterogeneous classroom

(one where curriculum and instruction are properly differentiated), students and teachers,

are more likely to view their differences as assets that strengthen the whole school

(George, 2010). The consensus in recent research in learning seems to support the

position of constructivists who argue that the best learning comes when students build

their own mathematics, language skills, or science knowledge by arguing, challenging,

explaining, solving problems, and having keys to creating learning environments that

effectively accommodate the diversity typical of today’s classroom, especially where the

needs of able learners must be accommodated (Tomlinson, 2000). Teachers in

differentiated classrooms accept, embrace, and plan for the fact that learners bring many

commonalities to school, but that learners also bring the essential differences that make

them individuals. Opportunities for challenge and extended learning must be open to all

students whenever possible (Stepaneck, 1999). Gamoran & Weinstein (1998) found that

heterogeneous classes were most effective when teachers used differentiated instruction.

High quality instruction relied on individualization, varied expectations (but at a high

level for all students), and complex authentic assignments. In order to prepare students

for success in and out of the classroom, teachers must differentiate the mathematics

instruction to meet the needs of all learners and provide students with varied

opportunities to learn and grow (Smith, 2010). Gardner (1997) suggested using “several

entry points,” which means approaching a topic in several different ways to allow

students more exposure to the topic” (p. 202). Hockings (2009) argues that “student-

centered learning has the potential to engage a more academically diverse student body

than the more conventional teacher-centered approaches” (p.83). Todd and Curliss

(2003) argued:

Educators should provide all learners with opportunities to obtain optimal levels

of learning. Many, if not most, classrooms include learners with mixed abilities.

These learner differences particularly in, mathematics classes, may be significant.

In order to attain optimal levels of learning for all students, instructional leaders

must move beyond the one-size-fits-all conception of curricular and instructional

practices. Rather, the curriculum should include a sequence of learning activities

constantly being developed in response to learner readiness, which includes the

point at which a student enters a particular study and the pace at which the student

acquires new knowledge and skills. (p. 53).

Educators use the differentiated instruction to build stronger thinkers and learners.

Differentiating learning environments helps to broaden the education of all learners.

However standardized assessments are not driven to protect these differentiated thinkers

and learners. Educators feel torn about differentiated instruction based on standardized

assessments.

There are opponents of differentiated instruction that state that it is not an

appropriate instructional strategy. Stahl (1999) contends that there is no research that

proves that determining a student’s learning style and matching instruction to it has any

effect on learning. Stahl (1999) further argues that there are no studies that prove the

implementation of Gardner’s multiple intelligence model improves achievement. Martel

(2006) theorizes that studies have shown that instruction is effective when matched with

knowledge, skills, and performance levels only. He states that “there is no evidence that

matching instruction to instructional level or learning style has any effect on learning”

(para. 6).

Traditional Lecture Style Instruction (Whole Class)

Traditional lecture style instruction is another predominant instructional strategy

that teachers utilize in classrooms around the United States. Traditional lecture style

instruction places the teacher in the front of the room delivering the information to

students. There are theorists that believe traditional, whole class instruction is the best

instructional strategy for educators to utilize. Whole class instruction is an effective tool

in identifying students’ prior knowledge and experiences that will affect the ability to

learn new concepts (Valentino, 2007). Snow (2003) concludes that teachers rely

primarily on whole class instruction and that other forms of instruction do not result in

significant improvement in student achievement. “Whole class instruction is teacher

centered and supports the notion: one group of students, one set of outcomes, and one

instructional plan” (Craft, 2002, p. 1). Teachers may be more effective using whole class

instruction due to the familiarity of whole class instruction (Lloyd, 2008).

Abrami, Yipping, Chambers, Poulsen, and Pence (2000) stated “whole class

instruction is uniform opposed to differentiated instruction and the whole class is taught

by a single set of instructional goals. Whole class instruction still stands as an important

tradition that has been in place since the one room schoolhouse” (p. 162). Ebeling (2000)

argues that schools in the United States are not designed for one on one instruction and

teachers are assigned a group of students that should be taught in that group. In Japan,

whole class instruction is utilized but the teacher is not a dispenser of knowledge but a

guide for discussion of students (Nagasaki & Becker, 1993).

Small Group Instruction with Teacher

Part of the process of differentiation is to provide a more diverse learning

environment. Small group instruction is one of the instructional approaches that is

utilized in my action research. “A myriad of instructional and management strategies

invite teachers to break classes into smaller learning units. Subdividing the class enables

the teacher to think about variation in student need and to create groups that attend to

student learning differences” (Tomlinson, 1999, p. 6). Kameenui (1993) states “the

identification of children as diverse learners itself suggests that multiple perspectives and

approaches will be necessary to accommodate the needs of children who possess

differences in abilities and learning histories, and who will be schooled in various

instructional contexts” (p. 11). Small group serves as a structure that offers opportunities

to meet with a student or students to support them as they work to acquire new learning

and to support them as they transition to their own independence (Serravallo, 2010).

Small groups provide opportunities for students to watch the teacher demonstrate,

opportunities for the student to practice with teacher support, and opportunities to

practice independently, offering a bridge to independence (Serravallo, 2010). Vygotsky

(1978) asserts that new learning occurs when the child accepts the challenge to take on

new competencies, not repeat old ones. Engaging students in the small-group instruction

makes the small groups more similar to conferences than mini-lessons as each child is

responded to as an individual. The teacher gives one-on-one attention and tailors the

focus of the lesson to the individual’s needs. The teacher also differentiates by changing

how he interacts with each child and the type of output expected (Tomlinson, 2001). In

linking the small group, the teacher reiterates what was taught and encourages the

children to practice independently. This is an important part of the conference because it

is essential that children transfer what they’ve done in the small group to their

independent work (Serravallo, 2010). Small group instruction offers time for the teacher

to assess students continuously instead of just through formal assessments. Goodman

(1985) notes:

Evaluation provides the most significant information if it occurs continuously and

simultaneously with the experiences in which the learning is taking place.

Teachers who observe the development of language and knowledge in children in

different settings become aware of important milestones in children’s

development that tests cannot reveal. (p. 10)

During small group learning, teachers’ verbal behaviors could be categorized as

encouraging student initiatives, helping students with their learning tasks, facilitating

communication among students, giving feedback on task performance, and praising

individual student’s effort (Gillies, 2006). Teacher’s mode of teaching also changes

during small group instruction, it is not the lecturing type of teaching. This small group

setting provides the opportunities for teachers to observe and provide more individual

feedback. “When students work in cooperative classrooms where teachers use more

facilitative learning behaviors, they too engage in more positive helping behaviors with

their peers than do students who work in groups where cooperative learning is not

strongly endorsed” (Gillies, 2006, p. 275). Manouchehri and Enderson (1999) claim that

small group discussions encourage students to develop a more reflective stance as they

take ownership of their contributions and learn to justify them in the face of questions

from others. We must remember that decisions about grouping are preliminary and that

what matters most comes next. Given poor instruction, neither heterogeneous nor

homogeneous grouping can be effective; with excellent instruction, either may succeed

(Gamoran, 1992). Research suggests that small group activities were more effective for

social support and the benefits of discussion, while being more inclusive (Howe and

Mercer, 2007). Small group interactions that encourage and prompt students to think

aloud as they do mathematics, with peers providing feedback on their strategy use, is

known to improve student learning (Van Luit & Naglieri, 1999).

Collaborative Learning

Another differentiated instructional strategy that I encompassed in my action

research study is collaborative learning. Collaborative learning is now accepted as an

important teaching-learning strategy that promotes positive learning outcomes for all

students, including students with a range of diverse learning and adjustment needs

(Johnson & Johnson, 2002). The open discussion that occurs in groups enables

participants to clarify ideas and perspectives in a context that is free of the perpetual

scrutiny of the teacher and the wider class group (Howe, 1990). Collaborative groups also

help students to work with diverse students and begin to maximize their opportunities to

develop positive attitudes toward different racial and cultural groups. According to Banks

(1992), problems related to diversity will intensify rather than diminish as the ethnic

texture of the nation deepens. Educators must make efforts to change the problems

related to racial and ethnic diversity into opportunities and strengths. If schools are to

achieve their goals of maximizing human potential, improving the quality of life for all

students, and promoting the ideals of freedom, justice, and dignity for all, they must meet

the challenge of helping students develop more positive attitudes toward different

cultural, racial, and ethnic groups. When children are part of a group with a common

goal, it makes it more likely that they will reach out to peers when they encounter

difficulty. Small collaborative groups give children the chance to hear other students’

thinking (Serravallo, 2010).

School must be a forum where children can express and negotiate meanings,

where each child is engaged and supported in growing toward an understanding of

his or her power to participate in the community. Then the knowledge gained can

be functional and meaningful. (Berghoff & Egawa, 1991, p.130)

If a differentiated classroom is student-centered, students are the workers. The teacher

coordinates the time, space, materials, and activities. Her effectiveness increases as

students become more skilled at helping one another and themselves achieve group and

individual goals (Tomlinson, 1999).

Pupils attain a better understanding of their classmates’ needs, their points of

view, and a better perception of problems. That is why when children help a

classmate they gain a great understanding of their own perspective on the problem

at hand. (Gillies, 2006, p. 278)

Callaghan et al. (2011) points out that collaborative activities oriented towards a common

goal require children to focus their attention on the task, monitoring each other’s attention

in order to comprehend and anticipate their partner’s action. The National Council of

Teachers of Mathematics (NCTM) suggested a shift away from the traditional emphasis

on individual paper and pencil mathematics toward interactive, discussion-based

mathematics classrooms (2000). Learning is a social endeavor, and a student’s ability to

participate in the society of the classroom determines, in part, his ability to construct

useful concepts. A student’s ability to construct useful concepts determines his ability to

take part in the society of the classroom. Thus, discussions among members of the

classroom are ultimately tied to learning (McCrone, 2009). Wagner (1994) defines

instructional interactions as follows:

An instructional interaction is an event that takes place between the learner and

the learner’s environment. Its purpose it to respond to the learner in a way

intended to change his or her behavior toward an educational goal. An

instructional interaction is effective when the environmental response changes the

learner’s behavior toward the goal. Instructional interactions have two purposes:

to change learners and to move them toward an action state of goal attainment.

(p.8)

Collaborative learning is one differentiated learning strategy than fosters students

to search for deeper understanding. Laird, Shoup, Kuh, and Schwarz (2008) identified

“that students who use deeper learning strategies, combine a variety of resources, discuss

ideas with others, reflect on how individual pieces of information relate to larger

constructs or patterns, and apply knowledge in real world situations” (p. 470). Students

who are only learning on the surface level, is due to instruction provided by teachers,

which resulted in students memorizing, reproducing, and repeating information without

much understanding (Smith, Gordon, Colby, & Wang, 2005). Hill and Woodland (2002)

suggested that deep learning is not a one-sided process, but a two-way exchange between

effective teaching and receptive learning. "When the students are more active in the

learning process, the material becomes more relevant and more significant for them, they

remember it better, understand it, and as a result their achievement improve" (Offir, Yev,

& Bezalel, 2008, p. 1181).

Technology in Mathematics

Chisholm (1998) asserted that integrating technology in the classroom is

important for several reasons: the preparation of children for a technological society, the

assurance of equal opportunities and participation in society, the empowerment of human

capabilities within all children, especially those of a minority who are currently

marginalized. “As we move into the 21

century, the growing variety of technologies that

have become available to the general public has changed the way society conceptualizes

technology integration, whether at school or for personal uses” (Allsopp, McHatton, &

Farmer, 2010, p.57). In the United States, billions of dollars have been invested in

purchasing technology-related resources (New Media Consortium, 2014). Computers and

their associated technology can revolutionize the way we teach and learn and offer

tremendous potential learning. People approach technology with different means,

different strengths, and certainly different interests (Guild & Garger, 1998). Technology

has great potential to provide greater access to relevant contexts within which to situate

the big ideas in mathematics (Allsopp, McHatton, & Farmer, 2010). Students enjoy using

technology and it provides an interactive way for students to encounter learning in a fun

and new way. Technology tools allow students to organize data, model mathematical

situations, and support calculation work. These functions decrease cognitive load by

allowing students to focus more on mathematical reasoning, forming and testing

conjectures, and evaluating various mathematical situations (National Council of

Teachers for Mathematics, 2011).

Many educational justifications for the use of computers in schools center on the

need to prepare students for the information age and life with computers. An integral part

of this is that children love to work and play with computers (Yelland, 2002). NCTM

(2008) wrote: “With guidance from effective mathematics teachers, students at different

levels can use these tools to support and extend mathematical reasoning and sense

making, gain access to mathematical content and problem-solving contexts, and enhance

computational fluency” (p. 1). From an analysis of thousands of students in the Early

Childhood Longitudinal Study found that using technology paired with mathematical

reasoning was associated with statistically significant gains in mathematics achievement

compared to reasoning without technology (Polly, 2008).

“Prior investigations indicate that instructional gaming can be an effective tool for

enhancing both motivation and achievement in the learning of mathematics” (Allen,

Jackson, Ross, & White, 1978, p.27). Computer games constitute an important part of

young children’s lives out of school, and within school contexts, games are often used to

consolidate practice or in order to motivate students to engage with conceptual material

or ideas (Yelland, 2002). "To emphasize the equal positions of motivational and

cognitive aspects of learning processes in multimedia learning environments, studies

have proposed a potential relationship between learners' motivational processing and

their mental effort investment" (Mayer, 2001, para. 3). Traditional mathematics curricula

typically use rote procedures that do not improve mathematical understanding and are not

motivating to students (Woodward, 2011). Getting students engaged using real-world

applications and technology is critical to improve their problem-solving skills and

increase their productive dispositions (NRC, 2001). Slow and inaccurate computational

skills has serious implications for later learning of higher level mathematical and

technological skills essential for the vast majority of jobs in the 21st century (Mautone,

DuPaul, & Jitendra, 2005). Academics interventions that alter the classroom

environment, such as peer tutoring, task or instructional modifications, and computer-

assisted instruction (CAI), may provide the conditions necessary for enhancing the

academic performance of children (DuPaul & Eckert, 1998). DuPaul and Eckert (1998)

state that computer-assisted instruction is presumably more cost effective than

consequence-based interventions, and this is especially useful in general education

classrooms where teachers must work with large classes and under difficult time

constraints (p. 310). Mautone, DuPaul, and Jitendra (2015) argue:

Computer Assisted Instruction requires minimal teacher involvement and

preparation time. Teachers can adjust the computer software settings to each

student's instructional level. Furthermore, many software programs allow the

computer to monitor the student's progress and make instructional-level

adjustments accordingly. In addition, while the student receives increased

opportunities to practice the targeted skill and frequent feedback and progress-

monitoring information from the computer, the teacher is free to focus on other

students and/or classroom tasks. (pp. 310-311)

Various interactive web sites and mobile device applications allow students to

model and create representations of mathematical situations (Arzarello, 2012). Since

these representations of mathematical situations are digital, they can easily be

manipulated, allowing learners to view multiple representations to compare and analyze

in a short period of time (Zbiek, Heid, Blume, & Dick, 2007). Studies have demonstrated

that by offering challenges, gameplay can be both enjoyable and motivating, as

challenges are almost inherently motivational (Allen, 2007). Baker, D’Mello, Rodrigo,

and Graesser (2010) summarize engaged concentration as a state of engagement with a

task such that concentration is intense, attention focused, and involvement complete.

Technology can support students’ task exploration, create dynamic mathematical

representations, and model mathematical situations. While concrete manipulatives or

pictorial drawings could be used to explore the mathematical content, using technology

provides learners with the ability to quickly generate and manipulate mathematical

representations (Polly, 2014).

Researchers of interactive learning environments have grown increasingly

interested in designing these systems to become more responsive to differences in

students’ cognitive-affective states. They believe that the detection of and

adaption to student cognition and affect may boost student learning gains and

enhance the quality of students’ overall learning experience. (Rodrigo, 2011,

p.116)

Researchers believe that games that can detect and adapt to changes may become more

effective at boosting student learning gains and the quality of students’ overall learning

experiences (Rodrigo, 2011). We think and understand best when we can imagine a

situation and that prepares us for action. Games present a similar situation through

simulation, providing us the opportunity to think, understand, prepare, and execute

actions (Gee, 2003). Games are built with clear goals and provide immediate feedback

(Dickey, 2005). These games should present players with challenges that are matched to

their skill level in order to maximize engagement (Kiili, 2005). "The key is to set the

level of difficulty at the point where the learner needs to stretch a bit and can accomplish

the task with moderate support" (Jalongo, 2007, p. 401). Gee and Shaffer (2010) state:

Games require the kind of thinking that we need in the 21st Century because they

use actual learning as the basis for assessment. They test not only current

knowledge and skills, but also preparation for future learning. They measure 21st

Century skills like collaboration, innovation, production, and design by tracking

many different kinds of information about a student, over time. (p.3)

Games are frequently cited as important mechanisms for teaching 21st century

skills because they can accommodate a wide variety of learning styles within a complex

decision-making context (Squire, 2006). Dowker (2004) argued that the use of computers

might reduce the impact of emotional communication or motor difficulties: software

programs might therefore enhance children’s confidence, so long as they do not replace

teachers. “Technology is essential in teaching and learning mathematics; it influences the

mathematics that is taught and enhances students’ learning” (National Council of

Teachers of Mathematics, 2000, p. 11).

Summary

As our nation has become more culturally, ethnically, and linguistically diverse,

so has our educational system. Demographers report that by 2020, one in every three

people will be what is now termed a minority (Sobol, 1990). Educators and students are

engrossed in conversations about how our one size fits all delivery system-which

mandates that everyone learn the same thing at the same time, no matter what their

individual needs-has failed them (Sarason, 1990). Through test scores and classroom

observation, students are screaming for help in mathematics instruction. The one size fits

all classroom is no longer an option for learners to be productive in our global society.

Education is facing many changes by having to adapt instructional strategies to better

meet the needs of this society now and for the future. Whole group instruction is still a

predominant teaching strategy for many classrooms. However, differentiated instruction

is causing a shift toward meeting the needs of the individual learners through different

instructional methods. There is an intense body of research and published works on

traditional lecture style instruction (whole class) and differentiated instruction. The

research presented methods utilized in my classroom to facilitate the differentiated

instructional strategy: small group instruction, collaborative learning, and online

activities. Jointly, the research review stressed the significance of the study, the rationale

for the purpose of the study, and provided a theoretical basis for the research question

addressed in this study.

CHAPTER 3

Research Design and Methodology

Introduction

This study investigated instructional strategies and the impact that each strategy

has on student achievement. The purpose of this quantitative study was to compare

instructional strategies with student achievement. The instructional strategies that were

used were traditional lecture style (whole class) instruction and differentiated instruction.

One group of students received traditional lecture style (whole group) instruction. The

other group received differentiated instruction with flexible grouping utilizing, small

group instruction, collaborative learning, and online math activities. Both classes will

receive mathematics instruction from the My Math Textbook Series, adopted by the

Daisy School District. However, the method of differentiated instruction will vary the

presentation of instruction to meet the identified strengths and weaknesses of the group of

students. The purpose of this study is to investigate which instructional strategy was most

effective based on student achievement on a post-test after unit instruction, traditional

lecture style instruction (whole class) or differentiated instruction.

Quantitative research is the best choice for this action research study after

analyzing the question, purpose of the study, and problem of practice. The identified

problem of practice for this Dissertation in Practice (DiP) focuses on the deficit that

exists in many public school students who do not demonstrate high levels of mathematics

reasoning as measured by state assessments. Based on the research question, the

study will compare the achievement of third grade mathematics classes one with

traditional lecture style instruction (whole class) and differentiated instruction. In

comparing the achievement of the two groups, the quantitative data will include the pre-

and post-test scores from a mathematics assessment. The mathematics assessment will be

taken from the My Math Series Assessment Masters, which was adopted by the Daisy

School District.

“To have an equal opportunity to pursue success, particularly financial success,

citizens need equal access to the skills necessary to that pursuit, and schools are charged

with providing everyone with these skills” (Weber, 2010, p 152). Educators today not

only have to enable students with basic skills but critical thinking and process skills to

utilize not only in school but in their daily lives. Some 21

Century skills that have been

identified as important for all learners are critical thinking, communication, collaboration,

and creativity (NEA, 2016). These skills are not new to education but tend to be the basis

of great teaching. Educators and administrators need to incorporate these skills in

classrooms and learning communities around the country.

Instruction today is challenging because it does not begin on the first page of the

curriculum guide, but rather where students are in regards to their ability (Tomlinson,

2001). Educators must understand the diverse ability levels of the students in their class

to make quality instructional decisions. This understanding allows educators to

implement instructional strategies conducive to their students’ strengths and weaknesses.

Marzano, Pickering, & Pollack (2001) stated that the individual instructional strategies

that a teacher uses have a powerful effect on student learning.

The challenge for classrooms and schools is finding the best instructional

strategies that meet the needs of the diverse student population. The Daisy School District

implemented High Progress Literacy Classrooms in response to Read to Succeed.

Teachers rework their daily English Language Arts (ELA) schedule and have arranged

use of time so that all students can be highly engaged with text reading and writing at

least 75% of classroom instructional time (HPLC Implementation, 2015). Educators’

daily schedules reflect the large chunk of instructional time dedicated to reading, writing

and research, leaving a small section of time for mathematics instruction.

Research Design and Approach

The participant-researcher utilized a differentiated mathematics instructional

program utilizing small group instruction, collaborative group instruction, and

online instruction with one classroom. Traditional lecture style instruction was utilized

with the other classroom. Both groups received a five-week period of study in preparation

for the Post-Assessment. Both groups received instruction from the My Math Series,

adopted by the Daisy School District. However, the differentiated instruction was varied

in the presentation based on the pre-test analysis of the student’s strengths and

weaknesses. Quantitative data included Mathematics Pre- and Post-Test scores which

were given to students to gage their mathematical problem solving abilities before and

after the treatment. The Mathematics test was taken from the My Math Assessment

Masters that was adopted by our district for Mathematics Instruction. The test was used

to gauge students’ skill levels to determine their prior knowledge of the concepts in the

chapter. The test scores were also utilized to determine class groupings for differentiated

instruction.

Action research is defined as any systematic inquiry conducted by teachers or

others with a vested interest in the teaching and learning process or environment for the

purpose of gathering information about how their particular schools operate, how they

teach, and how their students learn (Mills, 2011). Johnson (2008) stated, action research

is characterized as research that is done by teachers for themselves. It is truly a systematic

inquiry into one’s own practice. “Action research is participative, since educators are

integral members- not disinterested outsiders-of the research process” (Mertler, 2014, p.

20). “Action research in not done “to” or “by” other people; it is research done by

particular educators, on their own work, with students and colleagues” (Mertler, 2014, p.

21).

Schmuck (1997) stated that the public, fueled by the mass media, has criticized

schools for low levels of achievement in math, science, reading, writing, and history.

Action Research is an important step for educators to guide the first steps toward school

improvement. Because of the continued imposition of more traditional research findings,

there is a real need for the increased practice of teacher initiated, classroom-based action

research (Mertler, 2014). Action research is a way to examine issues within a school or

district. Educators analyze their teaching and learning environments on a daily basis to

meet the diverse needs of their students. McMillan (2004) describes action research as

being focused on solving a specific classroom or school problem, improving practice, or

helping make a decision at a single local site. Action research offers a process by which

current practice can be changed toward better practice. This research seems like the

appropriate format for my study because of the emphasis that it would eventually have on

my teaching. The researcher is hoping to provide insight to the school and district to

facilitate mathematics teaching and learning models that will meet the diverse needs of

the student population.

Mills (2011) stated that action research consists of four steps: (a) identifying an

area of focus; (b) collecting data; (c) analyzing and interpreting the data; (d) developing a

plan of action (p. 12). Action research usually refers to research intended to bring about

change of some kind, whereas teacher research quite often has the goal only of

examining a teacher’ s classroom practice in order to improve it or to better understand

what works (Dana & Yendol-Hoppey, 2014). To satisfy the daily questioning

educators/researchers bring forth the action research process is used to gather data that

can support their action plans. Educators are active in the role of researchers in the

learning process. McLean (1995) stated the fact that action research is largely about

examining one’s own practice, reflection is an integral part of the action research process.

Parsons & Brown (2002) stated that in order for teachers to be effective, they must

analyze and interpret classroom information-that has been collected in a systematic

manner-and then use that information as a basis for future planning and decision making.

Mill’s work (cited in Mertler, 2014) noted that teachers are encouraged to become

continuous, lifelong learners in the classrooms with respect to their practice. This notion

is central to the very nature of education-action research encourages teachers to examine

the dynamics of their classrooms, critically think about the actions and interactions of

students, confirm and challenge existing ideas or practices, and takes risks in the process.

Action research is a great way for educators to examine various techniques to meet the

needs of their students.

This quantitative action research study will utilize a group comparative design.

The general idea behind group comparison designs is that two or more groups,

which differ on some characteristic or have somehow been exposed to different

conditions, are compared on a single, common measure in order to see if the

differing characteristic or condition may have resulted in different performance.

(Mertler, 2014, p. 98)

The initial step of my study included questioning the techniques and procedures that are

in use in my classroom, school, and district. Answers to questions of a professional

nature often require much more information; however, human nature prompts us to try to

find answers to those questions as quickly as possible (Mertler, 2014).

Action research is also a cyclic process- providing educators/researchers the

opportunity to continue to build on research. here may never be a clear end to the study-

teachers may continue to go through subsequent cycles of planning, acting and observing,

developing a new plan, and reflecting, which seemingly spiral from one year into the next

(Mertler & Charles, 2011). Many action research projects are completed several times in

order to increase findings on a given topic. Most action researchers firmly believe that

once through an action research cycle is simply not enough. It is critical to proceed

through a number of cycles, where the earlier cycles are used to help inform how to

conduct the later cycles (Melrose, 2001). To have a deeper understanding of your topic

and research completing the research several times adds credibility to your action

research. Bachman’s (2001) downward spiral suggests that participants gather

information, plan actions, observe and evaluate those actions, and then reflect and plan

for a new cycle of the spiral, based on the insights that were gained in the previous cycle.

The purpose of this quantitative study was to compare instructional strategies with

student achievement. The instructional strategies that were used were traditional lecture

style (whole class) instruction and differentiated instruction. One group of students

received traditional lecture style (whole group) instruction. The other group received

differentiated instruction with flexible grouping utilizing, small group instruction,

collaborative learning, and online math activities. Both classes will receive mathematics

instruction from the My Math Textbook Series, adopted by the Daisy School District.

However, the method of differentiated instruction will vary the presentation of instruction

to meet the identified strengths and weaknesses of the group of students. The purpose of

this study is to investigate which instructional strategy was most effective based on

student achievement on a post-test after unit instruction, traditional lecture style

instruction (whole class) or differentiated instruction

Setting and Participants

Daisy School District, located in Clover, serves a diverse range of students. There

are approximately 9,620 students in the district. The District has 20 schools: nine

elementary schools, one intermediate school, one charter school, four middle schools,

four high schools and one adult education center. Based on Clover’s Department of

Education Website, Daisy School District received an Absolute Rating of Excellent on

the Annual Yearly Progress (AYP) Report Card and a C based on the Federal

Accountability Rating System. Based on the South Carolina Palmetto Achievement Test

of State Standards (SCPASS) 71% of our students received Met Or Exemplary on the

ELA portion of the test. Sunshine Elementary received an overall AYP Report Card

Absolute Rating of Average and a C based on the Federal Accountability Rating System.

Based on the SCPASS, 55% of our students received Met or Exemplary on the

Mathematics portion of this test. These statistics put us below “Elementary Schools with

Student’s Like Ours (61%)”, meaning Poverty indexes are not 5% below or above. This

also places us below “Elementary Schools in the State (76.9%)” in Clover in

Mathematics (Clover Annual Report Card Summary, 2014).

Based on Measures of Academic Progress (MAP) for Mathematics students in

Sunshine Elementary also show a deficit. In fall of 2014, 45.3% of third grade students,

62.8 % of Fourth grade students, and 39.7% of fifth grade students were Proficient in

Mathematics. Based on test scores from these assessments, educators need to evaluate

instructional strategies which are most effective in meeting individual students’ needs.

Diverse student populations make finding effective instructional strategies a challenge

faced by many administrators and educators.