Statement of the Problem - LaGrange Collegehome.lagrange.edu/educate/Advanced Programs/M.Ed. Defense... · Web viewCrobach’s Alpha reliably determined that the total score was measured

IMPLEMENTING HANDS ON LEARNING, WHILE MAINTAINING STUDENT FOCUS AND IMPROVING STUDENT ACHIEVEMENT.

Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my Thesis Chair. This thesis does not include

proprietary or classified information.

_____________________________________________________________________Debra Andrenna Dorsey

Certificate of Approval:

____________________________ ___________________________Donald R. Livingston, Ed.D. Sharon M. Livingston, Ph.D.Thesis Co-Chair Thesis Co-ChairEducation Department Education Department

Implementing Hands on Learning ii

IMPLEMENTING HANDS ON LEARNING, WHILE MAINTAINING STUDENT FOCUS AND IMPROVE STUDENT ACHIEVEMENT.

A thesis submitted

by

Debra A. Dorsey

to

LaGrange College

in partial fulfillment of

the requirement for the

degree of

MASTER OF EDUCATION

in

Curriculum and Instruction

LaGrange, Georgia

July 26, 2011

Implementing Hands on Learning iii

Abstract

This study explored the use of motivation techniques and differentiated

instruction strategies in a sixth grade math class. This action research took place over a

period of ten days in a mixed ability sixth grade math class of twenty four students.

Many of today’s classrooms are composed of students performing on multiple academic

levels with a lack of motivation. Therefore, the purpose of this study was to determine if

the applied strategies and motivation techniques would positively affect academic

achievement and improve students’ attitudes and behaviors in the classroom. When the

qualitative and quantitative data were analyzed, the results showed that students did

benefit from the use of motivation techniques and differentiated instruction strategies.

Implementing Hands on Learning iv

TABLE OF CONTENTS

Abstract ………………………………………………………………………………....iii

Table of Contents ………………………………………………………………….……iv

List of Tables …………………………………………………………………………....v

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

Chapter 2: Review of the Literature ………………………………………………….…6Differentiated Instruction …………………………………………………….…6Academic Achievement in Mathematics ………………………………………..9Changes in Student Attitudes and Behaviors ………………………………….12

Chapter 3: Methodology ……………………………………………………….………15Research Design ……………………………………………………….………15Setting ………………………………………………………………………….15Subjects/Participants …………………………………………………...............16Procedures and Data Collection Methods ………………………………….…..17Validity and Reliability Measures ………………………………………….….19Analysis of Data ……………………………………………………………….22Summary…………………………………………………………………….….24

Chapter 4: Results …………………………………………………………………...…24

Chapter 5: Analysis and Discussion of Results ………………………….…………….33Analysis ………………………………………………………………………..33Discussion ……………………………………………………………………...37Implications …………………………………………………………………….39Impact on Student Learning ……………………………………………………39Recommendations for Future Research ………………………………………..40

References ……………………………………………………..………….……………42

Appendixes ……………………………………………………………………………..45

Implementing Hands on Learning v

List of Tables

Tables

Table 3.1. Data Shell………………………………………………………………17

Table 4.1. Pre and Post Test Results………………………………………………28

Table 4.2. Chi Square Student Survey…………………………………………….29

Table 4.3. Cronbach’s Alpha Student Survey……………………………………..30

Implementing Hands on Learning 1

CHAPTER 1: INTRODUCTION

Statement of the Problem

This study explored the use of motivation techniques and differentiated instruction

strategies in a mixed ability sixth grade math class. Too many of today’s classrooms are

composed of students performing on multiple academic levels with a lack of motivation.

Ellis, Ellis, Huemann, and Stolarik, (2007) believe that varied academic ability within one

class is a problem across the country. Educators must attempt to reach each student.

In order to meet the Georgia Performance Standards, teachers feel pressure to cover

content and move quickly to the next standard. Many times students are not fully grasping

the concepts. They tend to memorize the content rather than understand it in a way that they

may apply it or explain it (Marlowe & Page, 2005). When students only memorize content

they cannot apply their mathematical knowledge to multiple situations; which results in

confusion and frustration.

Therefore, the purpose of this study was to discover if the use of motivation

techniques and differentiated instruction strategies would benefit students by fostering a

deeper understanding of sixth grade math concepts.

Significance of the Problem

Math is a subject where students are required to build new concepts onto concepts

already mastered. Therefore, it is important for teachers to apply strategies that will

accommodate each learning style and ability level in their classes. Teachers can no

longer rely on the one-size-fits-all curriculum and teaching approach (Subban, 2006).

When student are not engaged, they tend to become discipline problems when

bored. Discipline issues in the classroom will affect their learning as well as the learning


of the students around them. Teachers who are required to spend more time on discipline

will lose time in instruction. With increasing class sizes due to restricted state budgets,

proper classroom management and student focus is more important than ever.

The goal of this research was to be able to implement assignments that promote

interactive hands-on learning that engage students in ways that motivate them to learn.

When students are engaged, learning occurs. There was an increase in the math scores

and the students’ attitudes and behaviors improved.

Theoretical and Conceptual Frameworks

This thesis relates to the three tenets LaGrange College Education Department’s

(2008) Conceptual Framework. Tenet one is about enthusiastic engagement in learning.

Teacher education programs at LaGrange College are based on teacher education

candidates learning how to be critical educators who create environments where learning

is both enjoyable and rigorous. This type of learning environment requires teachers to

have excellent classroom management skills. Teachers are required to organize, manage,

and create hands on learning environments where students will be actively involved

(LaGrange College Education Department, 2008). It is important that the learners be

active participants in the learning process so that students will be motivated to learn.

This study showed that by implementing differentiated instruction strategies in the math

class, students will be actively engaged and can relate their classroom content to outside

activities, and then they will be motivated to learn the concepts taught.

This study also relates to the second tenet of the Conceptual Framework which

concerns exemplary professional teaching practices. It states that “an exemplary

practitioner draws from multiple resources in order to teach in diverse classrooms”


(LaGrange College Education Department, 2008, p. 5). It is important for a teacher to be

prepared for a mixed-ability class as well as a variety of attitudes and behaviors.

Understanding the different qualities the students possess in each class is important for

implementing proper strategies to promote motivation.

Teachers use both extrinsic and intrinsic strategies to motivate their students. Due

to the high focus on standards and test driven data, teachers are finding it more

convenient to apply extrinsic rewards to get students to pay attention. In addition to

extrinsic motivation, one of the focuses of this study was on cooperative and

collaborative learning where students were allowed to interact and learn from each other.

This promoted intrinsic motivation. In either case, teachers must take time to plan and

develop engaging and rigorous activities. I agree with the statement in the Conceptual

Framework of LaGrange College that says “solid preparation by candidates before

instruction not only increases student achievement, but it also reduces inappropriate

classroom behaviors” (LaGrange College Education Department, 2008, p. 7).

The third tenet of the Conceptual Framework focuses on caring and supportive

classrooms and learning communities. It is stated that through action research, positive

classroom practices, and ongoing research in school communities, educators can affect

policies and practices around them. This will be applied as teachers are going through

and completing the research process.

The first subgroup of the Conceptual Framework’s third tenet is focused on

reflection. It is important to write, reflect, and discuss experiences in the classroom.

This will assist in modifying instruction to improve academic achievement. The


reflection process for this research project was done through anecdotal notes taken

throughout the study.

Focus Questions

My research explored the use of motivational techniques and differentiated

instruction strategies in a mixed ability sixth grade math class. This research question is

broken down addressing three very specific questions: 1.) What is the process for

implementing differentiated instruction strategies in the math class so that students will

be motivated to learn? 2.) How do the applied motivation techniques and differentiated

instruction strategies affect academic achievement in the math class room? 3.) How will

students’ attitudes and behaviors change within the classroom when educators apply

motivation techniques and differentiated instruction strategies?

Overview of Methodology

This study was conducted using action research with a class of 24 sixth grade

students at a Title One school in Georgia. The study took place over a 2 week period.

Multiple differentiation and motivation strategies were applied in the class during this

study. There was a pre-test given to students to determine a baseline level of academic

achievement. A survey was given to students to determine their different learning styles.

This helped with the different lesson presentations and helped to determine the group

dynamics when students worked in cooperative groups. There was a post-test given.

Data were then analyzed to determine if there was any significant difference between the

pre and post test. Observations were conducted throughout the study and used to reflect

upon student behavior and attitudes. Reflective notes were made throughout the study

and used to reflect upon the lessons once the study was complete.


Human as Researcher

I believe that I was qualified to complete this study because I am a certified

teacher, highly qualified in teaching the subject of mathematics and social studies, and I

am currently in my sixth year of teaching. I have taught one year of 6th grade math where

50% of the students began the year below their grade level. I have also taught four years

of 7th grade math. During two of those years, I taught collaboratively, where many of the

students were on Individualized Education Programs. I have taught in classes where

there were a mixture of ability levels, and many challenging behaviors. Each year was

successful overall, however, each day ended in exhaustion. I believe that if there are

strategies in place to keep students focused and consistently, engaged, academic

achievement will increase and behavior issues will decrease.


CHAPTER 2: REVIEW OF THE LITERATURE

This study provided students the opportunity to explore mathematics by engaging

in a variety of hands on activities. Wonderful things seem to occur when students get to

explore rather than sitting and listening to lectured material each class period.

It promotes excitement and enhances learning to the educational environment. According

to Erwin (2003), when students are unmotivated, they usually do little or no work.

However, when students are motivated, they usually turn in high quality work and learn

well.

It is important for teachers to apply strategies that will accommodate each

learning style and ability level in their classes. Therefore, my research centered on the

implementation of hands on learning, while maintaining student focus and improving

student achievement. When students apply hands on learning or discovery learning, they

are more likely to retain and use what they have learned.

The review of the literature centers on the concepts of this study’s focus

questions.

Differentiated Instruction

How do you engage students in ways that motivate them to learn and what is the

process for implementing differentiated instruction strategies in the math class? With

differentiated instruction. A differentiated classroom is student centered. The focus is on

the students learning; not on the teacher. Some instructional strategies for the math class

are collaborative grouping, projects, use of manipulative materials, math games, peer

learning, discovery learning and hands on activities. The effective use of these non-

traditional teaching strategies deepens understanding and requires the students to take


more responsibility for their own learning (Sealey, 1966). There should be a shift from

the traditional classroom where the students listen and memorize to the constructive

classroom where students inquire and investigate. In the constructive classroom,

teachers’ roles are to question, listen, and set high expectations (Marlowe & Page, 2005).

However, a challenge that teachers face is to keep students motivated and adapt lessons

to meet the needs of various learners and learning styles. Teachers are to make education

appropriate for each individual student by making accommodations when necessary to

ensure success.

As teachers are planning for their lessons, they should put the focus on students’

abilities, talents, and challenges. Instead of teachers asking how they can teach a concept

to their students, they should seek the best way for their students to learn a particular

concept (Marlowe & Page, 2005). Teachers should be more open to changing from their

traditional roles to a more constructivist role. The traditional stand and deliver method

used in the past where students sit quietly, study in silence, and obey the teachers

unquestionably may not the best method today. Supporters of a student centered

classroom believe that the classes should be enjoyable places where students develop

naturally, and in curriculum learning, the students must discover facts and information for

themselves (Schiro, 2008). Teachers can assist students in class by making suggestions,

leading and guiding them, whereby helping students to maintain focus. Students should

also share in the planning of programs at school and in the decision process for the

delivery of the curriculum in the classroom. The teacher’s role as an evaluator though

still remains, but with students assisting in the evaluation process. All students could


benefit from an engaging learning experience and they deserve to be treated with respect

(Subban, 2006).

Many times teachers, who have material that must be covered in class, will

present instruction to cover that content in great detail. This could appear that the teacher

knows everything. Neither the teacher nor the administrator believes the students can

figure things out for themselves. But with detailed planning, students can be allowed to

uncover information or discover the content through research and inquiry (Schiro, 2008).

Most times the content being taught is not optional. Teachers are usually told what to

teach from the district’s central office and the district’s central office is required to meet

the standards handed down from the state’s educational department. Thus, there is little

flexibility or very few opportunities for change when it comes to curriculum. However,

there should be different instructional methods that promote mastery of the content for

the students.

Strategies should be used in class that engage the students and motivate them to

learn. The more engaged the students are in relevant activities, the less disruptive their

behavior will be (Marlowe & Page, 2005). In the traditional classroom, silence is the

ideal classroom atmosphere. A new approach would be to remove the ban from speech

and encourage communication among students. This can be a great tool in allowing

students to discuss or demonstrate their understanding and also to assist others in the

pursuit of their understanding (Marlowe & Page, 2005).

Not only is communication between students important in class, it is also

important for there to be appropriate communication between the teacher and student. A

vertical communication system where the teacher is at the top, sending messages to the


bottom may not be appropriate for a student centered classroom. However, a reciprocal

communication system may be appropriate where students and teachers would both

initiate classroom dialogue and raise questions (Marlowe & Page, 2005). This dialogue

can be concerning the understanding of the curriculum or it can be about choices in what

they will study, how they will study, and how they will demonstrate their understanding.

Learning can be most effective when students control what, when, and how they will

learn.

In math class, students tend to be more engaged if they are able to relate their

content to real life situations (Martin, 2007). Students are aware that they need to know

how to add, subtract, multiply and divide. But they also need to recognize how

percentages, geometry and algebra are used daily.

Academic Achievement in Mathematics

Many studies have shown that people learn in different ways. With hands on

activities and discovery learning, students have the opportunity to work at their own pace

and choose the strategy that is best for them. Respect is shown for all types of learners

and the anxiety of the struggling learners is reduced. Opportunities for advanced

learners are therefore extended (Dodge, 2005). When an individual experiences

happiness or enjoyment while engaging in a given activity, he or she is more likely to

seek opportunities to engage in that activity again, in an attempt to replicate the positive

experience (Shumow, Schmidt, & Kacker, 2008).

Marlowe and Page (2005) give a great example of how proper strategies used in

class will transform a student from one with little self-determination to an energetic

student willing to help others. They tell of a teacher named Matt Manino who taught


grades 5-8 in northwestern Vermont. He developed his classes in a manner which

required his students to initiate, investigate, problem-solve, and discover. Matt taught

Language Arts, Science, and Social Studies. A new student came to school named

Michael. Michael came from a traditional elementary classroom. Michael was an at risk

student with a poor home environment. His mother was deceased, his father was an

alcoholic, and his brother was in prison. Michael was spending much of his time in the

principal’s office for discipline purposes. Michael was failing all of his classes and was

receiving little if any support at home. The following year Michael was placed in Matt’s

classroom. With much work, Michael learned the skills to educate his self and identify

his learning style. Matt modeled the strategies he wanted Michael to master. Michael

practiced them and became an actively engaged member of a learning community. His

behavior problems diminished and he was willing to help new students learn the skills he

had mastered.

Not all research supports the leaner centered classroom. Chall (2000) presents

research that compares the teacher-centered to the student-centered educational programs

in elementary schools and found the teacher-centered educational program to be a better

approach for schools with low income children. Stallings and ABT Associates’ findings

(as cited in Chall, 2000) show higher achievement in reading, math, and language for the

teacher centered approach than the student centered approach. The teacher centered

approach was a more highly structured educational approach that focused more on

teaching basic academic skills.

Gage (as cited in Chall, 2000) also found that students in schools that were more

open, or student-centered schools, had lower academic achievement than students in the


teacher-centered schools. This was especially noticeable for students of low-income

families. Gage was quite concerned about the possible negative effects of student-

centered classrooms on the academic achievement of children from low-income families.

When students fail to learn in a student-centered environment, a lack of maturity is

usually the explanation. But often the reason is that the students have failed to receive

the necessary instruction. Some studies show that the student-centered learning may be

harmful for low SES students who are unable to take responsibility for effective learning.

However, academic achievement was the same for student-centered and teacher-centered

programs for students of middle-class families. Rothenberg (as cited in Chall, 2000)

concluded that progressive education (student-centered) was not widely practiced

because it was very demanding of teachers and did not seem to improve achievement, on

average. Gage also noted that student-centered education prepared teachers inadequately,

it was inadequately monitored, and it allowed teachers and students to neglect important

parts of the curriculum.

According to Chall (2000), a few research studies that compared the effects on

nonacademic learning were favorable toward the student-centered programs. There were

fewer discipline problems in class and students’ attitudes were better toward

mathematics.

Changes in Student Attitudes and Behaviors

As we discuss students’ attitudes toward mathematics, we are talking about

whether a student likes or dislikes the subject. According to Erwin, (2003), when

students are intrinsically motivated, they assume most of the responsibility for that


motivation. This will keep the student curious and interested in the concept and then

their learning will increase. Teachers should identify a students’ learning style and teach

to accommodate them. This can assist students in achieving better results academically

and improve their attitudes toward learning (as cited in Subban, 2006). Students’

attitudes towards mathematics determine their success in the subject. Information is most

likely to get stored if it makes sense and has meaning to the student. Also, teachers

should plan activities around their students’ interest. They should implement lessons

using cooperative learning, allowing for student choice, and hands on activities (Shumow

et al., 2008). Differentiated activities allow students an opportunity to choose their most

comfortable way to process, or make sense of the information. If a student constantly

fails in mathematics, he or she may believe that they can never do well in mathematics

(Marlowe & Page, 2005).

Class assignments should be challenging, but they should be tailored to fit the

interests and capabilities of the students. They should also be creative activities that

capture the interest of students. By designing activities that interest students, motivation

to complete or participate in the activities will increase. Student learning should increase

and students’ attitudes about learning will then become more positive (Jacobs, 2010).

The use of basic powerful differentiation strategies in math class will lead to

much higher engagement levels for the students. They will be required to think more and

therefore they will learn more. These actions will promote a more positive attitude

toward math for most students (Marlowe & Page 2005).

Collaboration among students can enhance their achievement and their attitudes

toward school. There are times when some students find it difficult to ask questions of


the teacher. They may be shy or possibly they just don’t want other students to think of

them as not smart (Tomlinson, 2004). Collaboration will allow students to share their

questions or concerns with each other before approaching the teacher. It is possible for

them to discover the necessary information while talking or working together. One

strategy used by teachers in class when students have questions about the curriculum is a

three step process. First the student will research the information in a text book or other

literature. If the answer is not found, the student would then ask another student and they

will possibly research it together. If the answer is still not found, the student may ask the

teacher for guidance. This will give the student a feel of success if the answer is found

without the assistance of the teacher. Also, when students share their strategies and

thinking processes, they do not get the idea that some students can do mathematics while

others cannot (Marlowe & Page, 2005).

Throughout a student’s school career, he or she experiences many different

teaching styles and strategies. These strategies should be creative activities that capture

the interest of students while reinforcing concepts taught in the classroom.

Chall (2000) concluded that student-centered education may be somewhat

superior in its effects on attitude. Hands on activities will keep students engaged and will

help all students achieve their fullest potential. This approach proposes that students be

guided to follow their unique interests and to work at their own individual pace. Students

tend to be happier when they are able to choose what they will learn and how they will

learn it.


CHAPTER 3: METHODOLOGY

Research Design

I used an action research design where students were engaged in discovery

learning and a variety of other hands on activities. I also used several different methods

that assessed the effects of the math curriculum and practices on students’ achievement.

The purpose of an action research design is to investigate and improve our practice in the

classroom (Hendricks, 2009). Studying ways to improve student learning while focusing

on methods and desired outcomes is a necessary part of the research. Action research

allows the researcher a chance to investigate and evaluate their work so that they may

improve on their teaching and learning and influence the leaning of others (McNiff &

Whitehead, 2006). I also collected and analyzed data and made adjustments in the

classroom procedures to positively affect my student’s learning and positively affect my

professional performance. Action Research should be conducted by the person

empowered to take action concerning their own actions, for the purpose of improving

their future actions (Sagor, 2005). My research focus of this study was to explore the use

of motivation techniques and differentiated instruction strategies in a mixed ability sixth

grade math class. Methods of data collection are assessments (pre and post tests), student

attitudinal surveys, and a reflective journal. Data were used to assist me in determining

the impact of the specific strategies and motivation techniques.

Setting

This research took place in a middle school in North Georgia, where most

families were low income families. The school was a federally designated Title One

school. The school population consisted of 789 students, 49 teachers, and 3


administrators. There were three sixth grade teams in this school and each team had

three math classes. There was also one sixth grade honors math class. Since I was the

math teacher for the sixth grade honors class, I chose this setting to conduct my study and

students were easily accessible.

I requested and received permission to conduct the action research study from the

principal at this school. All of my subjects (students) were minors and I requested and

received permission from their parents or guardians to allow them to participate in the

study. This study was approved by the LaGrange College Institutional Review Board.

Subjects and Participants

There were seven hundred ninety eight students enrolled at this school and two

hundred seventy six of them are sixth graders. Of the three hundred sixth grade students,

a sample of twenty four participated in this study. The average age of students in this

class ranged from 11years old to 12 years old. The student ratio of this class according to

gender was eight males (33.33%) and sixteen females (66.67%). The student ratio

according to ethnicity was 71% African-American, 21% Hispanic, and 8% Asian/Pacific

Islander. There were no students in this class receiving services for a disability and no

students were on a SST (Student Support Team) plan due to poor academic performance

or behavior problems in class. I have conducted an analysis of the student learning data

for this class from the 2010 Georgia CRCT and found that 42% met standards and 58%

exceeded standards. Sixteen of the twenty four in this class have been labeled as gifted.

Students in this research study were placed in the honors math class either because they

were labeled gifted, their fifth grade teacher recommended honors math, or their parent(s)

requested they be place in sixth grade honors math.


Procedures and Data Collection Methods

Below in Table 3.1, the research design is prearranged by focus question and the

table outlines how data were collected and analyzed.

Table 3.1 Data Shell

Focus Question Literature sources

Type: Method, Data , Validity

How are data analyzed?

Rationale

How do you engage students in ways that motivate them to learn?

Sealy, 1966

Marlowe & Page, 2005

Schiro, 2008

Martin, 2007

Sabban, 2006

Instructional plan and rubric, student observations, learning style inventory and reflective journaling.

Data type: Qualitative Data

Qualitative: coded for themes

Look for categorical data

How do the applied motivation techniques and differentiated instruction strategies affect academic achievement in the math class?

Dodge, 2005

Shumow, Schmidt, & Kacker, 2008


Chall, 2000

Assessment

Data type: Quantitative Data

Quantitative: Descriptive and inferential statistics

Dependent T tests

Effect size

Quantitative: Will determine if there are significant differences.

How do students’ attitudes and behaviors change within the classroom when educators apply intrinsic and extrinsic motivation techniques?

Erwin, 2003

Subban, 2006


Jacobs, 2010

Tomlinson, 2005

Chall, 2000

Focus group, reflective journal, observations

Data type: Qualitative Data

Qualitative: Coded for themes

Qualitative: look for categorical and repeating data

I have created a rubric to critique the instructional plan for this unit. The

instructional plan was reviewed by six of my colleagues who are experienced math and


science teachers. These six colleagues have given feedback concerning the design of the

lesson and planned activities. I interviewed these colleagues about their responses to help

determine if I need to make any modifications to the instructional plan. The questions I

used in the interviews are as follows: 1) Does the essential question address the enduring

understanding? 2) In what ways can the use of instructional technology be improved? 3)

Are there other materials that would be appropriate? 4) To what degree are the needs of

special learners being met? 5) Do the assessments align with the standards stated? 6)

Are there other assessments that would yield better data? 7) Does the concept yield

relevance to students’ learning? See Appendix A for the instructional plan and Appendix

B for the rubric used for evaluating the instructional plan.

All students in this research study took the learning styles inventory (see

Appendix C) to help them determine their learning styles. This helped the students

identify and develop their own learning strategies. There were three methods I used to

collect data. All students were given a pre- and post- assessment, (See Appendix D)

student attitudinal surveys, (See Appendix E), and a reflective journal (See Appendix F).

The pre- and post-assessment was given to determine what impact the strategies had on

student achievement. The twenty four students in the honors math class took a pre test

then they engaged in discovery learning where students conducted research by using the

computer, review content from their text books, and engaged in hands on activities to

master the content. Then a post test was given to see if the strategies applied caused

significant gains in their learning.

Student attitudinal surveys were used to analyze student’s attitudes and feelings toward

mathematics. The reflective journal was used to record the daily class routine, student


behavior, changes in attitude, and different types of communication (see Appendix F for

prompts). I also conducted a focus group. The focus group discussion (see Appendix G)

was recorded and the data collected helped to ensure that the teachers were using best

practices in their class to facilitate student learning. When the study was complete, I

analyzed the data and shared it with three colleagues. I asked them to review the data and

answer the following questions: 1) How would you interpret the data? 2) Do you think

my interpretation is correct or incorrect? Why? 3) What additional activities should be

added to improve performance on this content? 4) Based on your review of the research

and your observations, what changes should I make in my approach to instruction for the

future?

Validity, Reliability, Dependability and Bias

Focus question one state: What is the process for implementing differentiated

instruction strategies in the math class so that students will be motivated to learn? For

this focus question, data were collected using an instructional plan and rubric. This type

of data is qualitative because it shows how the strategies impact the outcome. I spent

time observing students, talking with students and analyzing their artifacts and products

in class during this study (Hendricks, 2009). There is construct validity for this focus

question. Six mathematics and science teachers critiqued the instructional plan and were

then interviewed by me. The teachers gave their beliefs and opinions of the instructional

plan. I have selected an adequate number of students for my research. The data was

accurately recorded with the use of protocols, audio and/or videotaping, and therefore it

showed dependability.


Focus question two states: How do the applied motivation techniques and

differentiated instruction strategies affect academic achievement in the math class room?

The data gathering methods used to answer this focus question were teacher made tests,

quizzes, essays and performance tasks. This is interval data. Students took a pre and

post test and I was able to see the difference in the performance on each test (Salkind,

2007). The validity for focus question two is content validity because the subject matter

addresses the Georgia Performance Standards for sixth grade mathematics (Popham,

2008). The data from focus question two also showed proof of content mastery. Since I

used a pre and post test, I used a Test-Retest correlation for dependent t-test to ensure

consistency (Salkind, 2007). I have selected an adequate number of subjects for my

research. The data collection and treatment were kept consistent and I maintained well

organized data.

All instruments were checked for unfairness, offensiveness, and disparate impact.

According to Popham (2008), assessment bias refers to the qualities of an assessment

instrument that offends or unfairly penalizes a group of students based on their gender,

race, ethnicity, socioeconomic status, religion, or other such group defining

characteristics.

Focus question three states: How will student’s attitudes and behaviors change

within the classroom when educators apply motivation techniques and differentiated

instruction strategies? The data gathering methods used to answer this focus question

were reflective journals, surveys, focus groups, and student observations. Students were

surveyed concerning their attitudes towards mathematics and about their learning


environment, which were measured using ordinal variables on a five point Likert scale.

For reliability, I used Cronbach’s Alpha. It showed if there was internal consistency.

All instruments were checked for unfairness, offensiveness, and disparate impact.

According to Popham (2008), assessment bias refers to the qualities of an assessment

instrument that offends or unfairly penalizes a group of students based on their gender,

race, ethnicity, socioeconomic status, religion, or other such group defining

characteristics.

Construct validity was used for focus question three because it deals with

student’s attitudes (Popham, 2008). Journal prompts were used to make the data more

reliable. Several mathematics and science teachers critiqued the instructional plan and

were then interviewed by me. The teachers gave their beliefs and opinions of the

instructional plan. These teachers were also a part of a focus group at the conclusion of

the research. The responses to the focus group questions were used to ensure best

practices were used in the classroom. The data from focus question three is dependable

because the data collection and treatment was kept consistent. There was complete and

accurate supporting data through an established chain of evidence such as being able to

connect the research question to theory, to focus questions and to conclusion.

According to Popham (2008), assessment bias refers to the qualities of an

assessment instrument that offends or unfairly penalizes a group of students based on

their gender, race, ethnicity, socioeconomic status, religion, or any other group defining

characteristics. Therefore, all instruments used in this study were checked for unfairness,

offensiveness, and disparate impact.


Analysis of Data

The instructional plan was analyzed qualitatively, coded for themes, looking for

recurring, dominant and emerging data. This method was used because I was looking for

categorical and repeating data that form patterns of behaviors.

In focus question two, the quantitative data was analyzed statistically using the

following methods of analogy: a dependent-t test and an independent-t test. A

dependent-t test was used to determine if there were significant differences between

means from the pretest and the post test. To determine if there were significant

differences between means from one group tested twice. The decision to reject the null

hypothesis has been set at p < .05. The independent-t test was used to determine if

there were significant differences between means from the girls and boys in the pre test

and again in the post test. This test was used to determine if there were significant

differences between means from two independent groups. The decision to reject the null

hypothesis has been set at p < .05.

I used the effect size r with the dependent-t test and the Cohen’s d for the

independent-t test. The effect size r is a measure of the difference in the pre and post test

data. It showed how significant the hands on treatment have been. I calculated the effect

size r and use the outcome to make a judgment about the treatment. Cohen’s d effect size

data was used to make judgments about the independent-t test.

Focus question three, data was analyzed qualitatively, coded for themes, looking

for recurring, dominant and emerging data. This method was used because I was looking

for categorical and repeating data that form patterns of behaviors. Survey data from

Focus Question Three was analyzed by using the Chi Square method (Salkind, 2007).


The Chi Square method was used to test to see which of the survey questions were

significant and which questions were not significant. The significance level is reported at

the p < .05, p < .01 and the p < .001 levels. This data was useful in determining how

students feel about math and how teachers are instructing their students. Crobach’s

Alpha was computed for each survey question. The Crobach’s Alpha reliably determined

whether the survey measured the total score accurately (Salkind, 2009).

This research study has consensual validation because it has been approved by

faculty (Eisner, 1991). The research study also has epistemological validation because I

have reviewed the literature and the results will be compared to the literature (Denzin &

Lincoln, 1998).

This study does have credibility because I have used multiple data sources

showing structural corroboration. Opposing points of view are presented. Therefore, I

have fairness. There is also rightness of fit. Great care has been taken to ensure

precision and accuracy so that I can present a tight argument, coherent case, and have

strong evidence to assert judgments (Eisner, 1991).

This study has transferability. It can be replicated by others and easily used for

future research. This study has catalytic validity and is transformational. It has caused a

positive change in my view of classroom management and instructional practices (Eisner,

1991).

Summary

The research design gave an explanation of procedures used for collecting,

analyzing, and reporting the research. The setting tells why the class, school, and county

were chosen and how access was gained to conduct the study. The subjects were the


students in this research study and the participants were the teachers who volunteered to

participate. This section explains how and why they were selected. The procedures and

data collection methods describe in detail the procedures used for conducting the

research. An explanation was given as to how validity, reliability, and dependability

were strengthened through procedures used in the design of the research and how bias

was revealed and/or mitigated. Finally, the analysis of data explained how the data were

collected, organized, and analyzed. The holistic analysis describes the concepts of

dependability, credibility, and transferability.


CHAPTER 4: RESULTS

Our math classrooms are driven by the desire for our schools to make annual

yearly progress [AYP] . As a result of AYP teachers are spending a lot of time making

sure all material being presented on the CRCT is covered in class. Our curriculum is

continuously changing causing many of our students to struggle because they are not

receiving the help they need in class to be successful. There were a total of 24 students

who participated in this study. Hands on discovery learning, using differentiated

instruction strategies was used in the classroom to determine if it would significantly

impact student achievement.

Focus Question 1 was measured by using an instructional plan, instructional plan

rubric, student observations, learning style inventory and reflective journaling. The

instructional plan and rubric interview were used to determine if the study was conducive

for the students, and planned for accurate results. The students were studying geometric

solids. The unit essential question was “What properties of solids determine their

volumes and surface area.” The instructional plan was reviewed by six of my colleagues

who are experienced math and science teachers. These six colleagues have given

feedback concerning the design of the lesson and planned activities. I interviewed these

colleagues about their responses to help determine if I need to make any modifications to

the instructional plan. After the instructional plan interviews some changes were made

based on suggestive commentary from the veteran teachers.

I asked “Does the essential question address the enduring understanding of the

lesson?” Four of the teachers agreed that the essential question did in fact address the

enduring understanding. Teacher one suggested rewriting some of the essential questions


using the language of the Rigor Meter (Levels 3 and 4) throughout the plan. Teacher

three said “All of the essential questions address the enduring understanding. In fact, the

essential questions provide a more concrete grasp of the concepts presented in order to

ensure that the students have a thorough understanding of how the formulae are derived.”

When asked in what ways could the use of instructional technology be improved:

Teacher one responded “Students might benefit from using a computer based interactive

assessment, such as Turning Point throughout the unit.” Teachers three and six agreed.

Teacher two believe that instructional technology can be improved by providing either a

computer for every student while in the classroom. This way every child can be provided

the opportunity to engage in some experiences that perhaps only a few students would get

to be involved in. This would not only promote excitement but enhance learning to the

educational environment. Teacher four believe that the use of webcasts of three

dimensional figures, computer-assisted programs, and PowerPoint presentations may

activate student imagery and analytical thinking skills.

The next question asked was “Are there other materials that would be appropriate

for this study? All of the teachers agreed that the extensive list of materials and

manipulatives listed were appropriate for the completion of the lesson and they could not

think of more. The teachers were then asked if the assessments were aligned with the

standards stated and if there were other assessments that would yield better data? All the

teachers agreed that the assessments were aligned with the standards stated and the

assessments listed were the most appropriate. Teacher three stated “The use of the

multiple assessment tools listed will address the different learning styles of the students”.


The last question asked was, does the concept yield relevance to student learning? All of

the teachers agree that the concept yields relevance to student learning. However, teacher

two said “The hands-on opportunities will keep the students focused on solid figures and

their properties”. Teacher three then said “The task will allow students to conceptualize

the relationship of area and volume of similar objects. The tasks along with the

investigations are engaging providing authentic learning”. Teacher six then stated “All of

the concepts yield relevance to the students’ learning, especially where the students get to

explore. Wonderful things seem to occur when students get to explore verses sitting and

listening to lectured material for 30 minutes to an hour. Allowing the students to explore

is a well thought out and engaging activity”.

The students involved in the study were all given a learning styles inventory.

They were able to identify their learning style and understand the different approaches

and ways of learning that is best for them. There were eight students identified as visual

learners, those who learn best by seeing, five students identified as auditory learners,

those who learn best by listening, and eleven students identified as kinesthetic learners,

those who learn best by moving, doing and touching. Once the students identified their

learning style, they were prepared to choose the activity that would best assist them in the

learning activity.

To answer Focus Question 2 about how applied motivation techniques and

differentiated instruction strategies affect math achievement, the sixth grade math concepts

explored were estimating the surface area and volume of simple geometric solids. Pre and post

tests were used to show student progress. There were 30 questions on the pre and post test.


Table 4.1 Pre Test and Post Test Dependent t-test Results

Pre Test Post Test Mean 49 75.5Variance 148.8695652 107.5652174Observations 24 24Pearson Correlation 0.388937395Hypothesized Mean Difference 0df 23t Stat -10.32815986P(T<=t) one-tail 2.07125E-10t Critical one-tail 1.713871528P(T<=t) two-tail 4.1425E-10t Critical two-tail 2.06865761 T =10.32, p< .05 Reject the null

The results showed that all of the students showed an increase of knowledge in

estimating the surface area and volume of simple geometric solids. The pre test scores

ranged from 28% to 76% and an examination of the pre test scores showed that the mean

score was 49 percent. The post test scores ranged from 56% - 94%, and the mean score

of the post test was 75.5 percent. One hundred percent of the students increased their

scores. This indicates that no student’s academic achievement was harmed due to the

strategies provided.

In Table 4.1 the dependent t-tests shows the differences in the pre and post test at

p < .05 for all tests given. The effect size must be calculated to help determine if a

difference between the mean of the pre test and the mean in the post test is statistically

significant and meaningful. A small effect size ranges from 0.0 to .20, a medium effect

size ranges from .20 to .50 and a large effect size is any value above .50 (Salkind, 2007).


The effect size for the pre-posttest of this experiment is r = -0.76. This data concludes

that there is a significant difference in scores of the students. Therefore, the null

hypothesis must be rejected.

How students’ attitudes and behaviors change when motivation techniques and

differentiated instruction strategies are applied was examined by the use of an attitudinal

survey completed by all students at the end of the research. The survey consists of 20

questions about students’ attitudes and the way they learn mathematics. The survey was

completed by each student participating in the study. The survey was used to determine

whether the discovery learning and hands on approach affects student’s attitudes in

mathematics. To make this determination a chi square test was used. Chi Square was

computed for each survey question and then tested for a significance level. Table 4.2

arranges the chi square value for each survey question.


Table 4.2 Chi Square Student Survey Survey Questions n = 24 χ2

1. I have always hated math 13.92**2. I stop working as hard after I do badly 11.83**3. I rarely ask questions during math class 6.834. Knowing math will help me in my future 31***5.Males are naturally better at math than females 2.676. Math is a fun subject 2.677. Math has been my best subject 2.678. Math has been my worst subject 1.839. Females can do just as well in math as males can 13.08**10. I like to do hands on activities in math 23.08***11. Math is just memorizing formulas 6.4212. Math is not important in everyday life 34.33***13. In math, you can be creative and discover things by yourself

10.17*

14. I try to learn math because it helps me develop my mind and helps me think more clearly

23.92***

15. Using the internet (or a computer) is a good way for me to learn math

7.67

16. Working with other students helps me have a better attitude towards math

7.67

17. I keep trying even if the work is hard for me to do 22.67***18. I work as hard as I can in math 21.42***19. I worry that I will get poor grades in math 620. I only do math because I have to 20.58***

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

The data in Table 4.2 shows how the students feel about math and how important

math is to them. The data in question 1 shows that most students in this class have not

always hated math and question 10 shows that most students enjoy hands on activities in

math. The result of question 13 shows that many of the students in this class believe that

you can be creative and discover things by yourself in math. The data in question 4

shows that most of the students believe that math will help them in their future and the

results of question 12 shows that most students do not agree that math is not important in

everyday life. The data in question 17 and 18 shows that most students in this class


believe that they work as hard as they can in math and they keep trying even if the work

is hard for them.

Crobach’s Alpha reliably determined that the total score was measured accurately.

The results from questions 5, 9 and 19 show a neutral response, so they were excluded

from the Cronbach calculation. Cronbach’s alpha was computed for all other survey

questions and the Cronbach alpha is .35 (see Table 4.3). The responses showed little

consistency. Cronbach’s alpha was used because internal consistency reliability is used

to see if the items on a test are consistent with one another and that they represent one

area of interest (Salkind, 2007).

Table 4.3 Cronbach’s Alpha Student Survey

Survey α = .35

Reflective journaling is another method used to collect data about the attitudes of

students in the mathematics classroom. Information was gathered about how students

used the manipulatives to generate answers and how the hands on approach helped them

to understand the concept. The reflective journal also recorded the student attitudes

towards mathematics and how the students felt using the different strategies in class.

Several of the students liked the more hands on approach. One student wrote “I was able

to figure some things out on my own that I did not think that I could. That made me feel

good and it was also a lot of fun.” Another student wrote “Class today was better than it

usually is. I like talking to my friends while working.” One other student wrote “Mrs.

Dorsey always allow us to talk to other people in our group when we are working but it

was nice to be able to get up and walk around the room without permission. Working


with the geometric objects was interesting and fun also.” On day two, three students

wrote “I had fun in class today.” All of the students did not like this approach. One

female student wrote “Miss Dorsey did not teach anything today. I like it better when she

teach us. I don’t like it when I have to learn by myself.”

The next method used to answer Focus question 3 was a focus group. I conducted

a focus group with 6 math teachers to determine if there was any categorical or repeating

data. These teachers were from sixth, seventh and eighth grade levels. These six math

teachers reviewed my findings at the conclusion of the study. During the focus group, 4

questions were asked. The first question was “How would you interpret the data from the

pre and post tests?” Each of the teachers agreed with the finding of great gains for the

students. However, 2 of the teachers believed that if the traditional style of teaching was

added to the hands on approach, the students would have improved even more.

Question three of the focus group questions asked “What additional activities

should be added to improve performance on this content?” One teacher stated that I

should add more problem solving questions to allow students to practice what they have

learned. Another teacher said “You should add a teacher led content review before

assessing students. It is good to allow them to construct their own knowledge, but it is

better if you review with them what it is that they have learned to clear any

misunderstanding.”

The final focus group question stated: Based on your review of the research and

your observations, what changes should I make in my approach to instruction for the

future? One of the sixth grade math teachers stated “I would extend the time of the study

and give the students more tasks. This will allow the students a greater opportunity to


retain what they are learning.” One of the seventh grade teachers said “I would allow the

students an opportunity to present ideas for activities in class.”

The last method used to answer Focus Question 3 was student observations.

Student observations were used to determine the understanding the students showed

throughout the lesson as well as what their behavior and attitude was like. During the

first two days, I spent a lot of time discussing what appropriate behavior should be during

these kinds of activities. There was a lot of talking, but much of it was not about the

content. After the third day, their conversations were more about geometry than it had

been. During a 90 minute block, before the research began, I usually excuse 3 to 5

students to go to the rest room. On day 5, I noticed that only one student went to the rest

room during class and on day six, only one student went to the rest room during class.

The students had now become engaged and participating during class. They seem to

enjoy using their manipulatives and working with their partners. There were a lot of

discussions, but their energy was mostly spent on completing the activities. As the

students entered the class each day, someone would ask with excitement “What are we

doing today?” I had one student who asked on 4 different occasions for permission to

come into my class during homeroom to spend some extra time on his activities.


CHAPTER 5: ANALYSIS AND DISCUSSION OF RESULTS

Analysis

The purpose of this study was to discover if the use of motivation techniques and

differentiated instruction strategies would benefit students by fostering a deeper

understanding of sixth grade math concepts. Hands on discovery learning, using

differentiated instruction strategies was used in the classroom to determine if they would

significantly impact student achievement.

Focus question one deals with the process for implementing differentiated instruction

strategies in the math class so that students will be motivated to learn. This focus question

was measured by using a peer reviewed instructional plan, instructional plan rubric, learning

style inventory, student observations and reflective journaling. The qualitative data from

Focus Question One was coded for themes to look for categorical and repeating data that

form patterns of behaviors.

According to Schiro (2008), supporters of a student centered classroom believe that

the classes should be enjoyable places where students develop naturally, and in curriculum

learning, the students must discover facts and information for themselves. The instructional

plan and rubric interview were used to help determine if the researcher needed to make any

modifications to the instructional plan, to determine if the study was conducive for the

students, and planned for accurate results. The interview was done with six colleagues who

are math and science teachers.

Planning is a very important part of the implementation process for a student

centered classroom. Teachers who which to establish a strong student centered

classroom should invest a significant amount of time in working out the details before


beginning instruction and a large amount of time planning instruction each week. Most

of the research agrees that frequent and effective planning is a necessary part of any

effective teaching program (Sileo & Garderen, 2010).

Teachers should identify a students’ learning style and teach to accommodate

them. This strategy can assist students in achieving better results academically and

improve their attitudes toward learning (Green, 1999).

The learning styles inventory was used to help the students and the teacher

identify their learning styles and understand the different approaches and ways of

learning that was best for them. They were then prepared to choose the activities that

would best assist them in their learning.

In Chapter 2 the literature states that removing the ban from speech and

encouraging communication among students can be a great tool in the classroom. It

allows students the opportunity to discuss or demonstrate their understanding and also to

assist others in the pursuit of their understanding (Marlowe & Page, 2005). This theory

was supported during this study when the students were able to communicate freely with

each other while working in collaborative groups, during peer learning, math games, and

discovery learning.

Focus Question 2 was about how the applied motivation techniques and

differentiated instruction strategies affect academic achievement in the math classroom.

Students were given a pre test prior to any teaching strategies being applied. They were

then given a post test at the end of the unit. The data from the pre and post test were

analyzed by using a t-test to determine if there were significant differences in the pre-test


and post-test scores. The results from the t-test show that there is significant difference in

the pre-test and post-test scores.

According to the literature review in Chapter 2, students have the opportunity to

work at their own pace and choose the strategy that is best for them with hands on

activities and discovery learning. Therefore, respect is shown for all types of learners.

According to Dodge (2005), the anxiety of the struggling learners should be reduced, and

opportunities for advanced learners should be extended. This was experienced during the

research in this mixed ability honors math class. As students were working

independently, in groups, with manipulative, or on the computer, they were able to

continue on to the next concept if they were comfortable with the material, or they were

able to repeat an activity or review with a partner if they did not understand it. Marlowe

and Page (2005) discussed how proper strategies used in class will transform a student

from one with little self-determination to an energetic student willing to help others.

During this research, many students were asking questions of the teacher, especially

during the first few days of the research. Once they realized that their questions would be

answered with more probing questions to help them find their answers, they began to

question each other more and have more meaningful conversations about the content.

Research from Stallings and ABT Associates (as cited in Chall, 2000) show

higher achievement in reading, math, and language for the teacher centered approach than

the student centered approach. Gage (as cited in Chall, 2000) also found that students in

schools that were more open, or student-centered schools, had lower academic

achievement than students in the teacher-centered schools. This research did not support

their theories. Each student in this class increased their score on the post test and the


class as a whole experienced academic success while leaning in a student-centered

classroom. In Table 4.1 the t-tests shows the differences in the pre and post test at p < .05

for all tests given. The effect size was calculated to help determine if a difference

between the mean of the pre test and the mean in the post test was statistically significant.

The effect size was calculated at r = -0.760215, which is a large effect size, and therefore

showing a significant difference.

Focus Question 3 was about how students’ attitudes and behaviors change within

the classroom when educators apply intrinsic and extrinsic motivation techniques. This

focus question was examined by the use of an attitudinal survey completed by all students

at the end of the research, reflective journaling, student observations and a focus group.

Students’ attitudes towards mathematics determine their success in the subject.

According to Green (1999), teachers should identify a students’ learning style and teach

to accommodate them. This can assist students in achieving better results academically

and improve their attitudes toward learning. Teachers should also plan activities around

their students’ interest. They should implement lessons using cooperative learning,

allowing for student choice, and hands on activities (Shumow et al., 2008). All students

participating in this research project were given a survey concerning their attitude about

math and the way they learn math. The survey was used to determine whether the

discovery learning and hands on approach affects student’s attitudes in mathematics. To

make this determination a chi square test was used. The result of this survey shows that

most students believe you can be creative and discover things by yourself in math and

they also enjoy hands on activities in math. This survey also show that students believe


math is important in everyday life and in the future and therefore they work as hard as

they can in math class and they keep trying even if the work is hard for them.

Reflective journaling is another method used to collect data about the attitudes of

students in the mathematics classroom. When designing activities that interest students,

motivation to complete or participate in the activities will increase (Green, 1999).

Student learning should increase and students’ attitudes about learning will then become

more positive (Jacobs, 2010). Most students had positive comments about the hands on

approach used during the research. They made comments such as “I had fun in class

today” and “Class was better than it usually is”. All students were not excited about the

hands on approach. Some students preferred the traditional approach.

Research shows that the use of basic powerful differentiation strategies in math

class will lead to much higher engagement levels for the students and it will promote a

more positive attitude toward math (Marlowe & Page 2005). According to Chall (2000),

hands on activities will keep students engaged and will help all students achieve their full

potential. As the students were observed during the research, they became more engaged

each day. All students were participating in the hands on activities. At first, the

conversations were not always about the content and the students would have to be

redirected. However, after the third day, there were more conversations about the

geometry content and students did not have to be redirected as much.

Discussion

The results of this study indicate that a student centered classroom will motivate

students to increase their achievement and yield academic success. Most of the students


enjoyed the hands on activities and they displayed positive attitudes throughout the study.

However, some of them did prefer direct instruction.

The study was complete in two weeks which is a short period of time to complete

this unit. The results of the post-test may have increased even more if the students could

have completed a wider variety of tasks, more tasks, or repeated the already completed

tasks to assure mastery. This study found that a student centered classroom yields

positive results for middle school mathematics. However, it may not be the best method

for all subjects.

Steps were taken throughout this study to ensure credibility. Structural

corroboration was achieved through the use of multiple data sources focusing on three

specific focus questions. Quantitative and qualitative date were gathered and recorded as

accurately as possible. The pre-test and post-test showed test reliability. The tests were

identical and the students were tested on the exact same content both times. Content

validity was increased by having other math teachers review the instructional plan and

rubric to verify the subject matter addressed the Georgia Performance Standards for sixth

grade mathematics. The study also showed fairness because it presented opposing views.

These opposing views were adequately researched and considered. Assessment biases

were decreased by checking the instruments for unfairness, offensiveness, and disparate

impact. Validity and reliability were considered when determining data collection

methods for each focus question. There is also rightness of fit. Great care was taken to

ensure precision and accuracy.


Implications

The quantitative results of this study showed that there was a significant

difference between the pre-test and post-test after the hands on strategies had been

applied. This study shows that discovery learning had a great impact on student

achievement. On the post-test, all students’ scores increased from their pre-test scores.

The students developed a positive attitude and maintained proper behavior throughout the

study. They enjoyed the hands on activities and working in groups. Many of the students

became eager to come to math class. I learned that taking extra time to prepare engaging

activities was well worth it. This study was conducted using a small sample. It would be

difficult to assert judgment on a much larger population.

Mathematics teachers generally have classes of students who are performing on

multiple academic levels and the one-size-fits-all curriculum is no longer appropriate. I

was positively impacted by learning new methods of teaching and new ways to try to

motivate students to learn. There is no longer a feeling of giving students’ knowledge,

but assisting them in creating their own knowledge. This study can be easily replicated in

any middle school math classroom.

Impact on Student Learning

This study impacted student achievement by applying discovery learning in a

child centered classroom. Motivation techniques and differentiated instruction strategies

had a positive impact on the students’ attitudes and behaviors as well. Students were

given the opportunity to expand their ideas by trying new ways of learning that they

previously may not have used in a mathematics classroom. The students spent a lot of

time investigating the geometry concepts by use of manipulatives, virtual manipulatives,


online research and group discussions. I learned that if there are strategies in place to

keep students focused and consistently engaged, academic achievement will increase and

behavior issues will decrease. While some students were not comfortable in the non-

traditional student centered classroom, all students were given the opportunity to try new

ways of learning that may benefit them in their educational career. Most students in this

study were eager to come to class and were actively engaged throughout the study.

Most of the teachers interviewed for this study said they would apply some of the

strategies in their classrooms and try to present more student centered lessons as well.

Recommendations for Future Research

Based on the results of this study, there are several recommendations for future

research. The first recommendation is to increase the sample size to include participants

of all ability levels in mathematics. The current study was with a 6th grade honors class

where all students were performing at or above current grade level. Also, an increase in

sample size would accommodate two groups of students. One group of students could

receive hand on discovery learning strategies and the other could receive the traditional

teaching approach. With these two strategies in place, their scores could be compared to

see which approach most affect student achievement. The second recommendation is to

include the socioeconomic status, gender differences, and race in the study. This will

show how behaviors and attitudes changed during the study based on their socioeconomic

status, gender or race as well as how their academic achievement is affected. The third

recommendation is to extend the time of the study. This study was for 2 weeks and more

time was needed to ensure mastery of the content by all students. It will also allow more

opportunity for students to showcase what they have learned in a variety of ways. The


next recommendation is to include accommodations and modifications for students with

special needs. Even though the students in this research did not include any student with

special needs, future research projects should include larger sample sizes and students of

all ability levels, including students with special needs. The final recommendation is to

include a session during the study where students who are still struggling can work with

teachers in a traditional setting. The traditional approach is a strategy that is necessary

for some students to feel comfortable and confident in their learning.

Results from this research shows that the use of motivation techniques and

differentiated instruction strategies in a mixed ability sixth grade math class will

positively affect academic achievement and improve students’ attitudes and behaviors in

the classroom.


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Appendix A

Instructional Plan

INSTRUCTIONAL PLAN

Unit Title: SOLIDS Course Title: 7th Grade Math GPS Standards: M6M3.a, b, c, d; M6M4.a, b, c, d Date/Length of Unit: 2 Weeks M6G2.a, b, c, dUnit Essential Question:

What properties of solids determine their volumes and surface areas?

Enduring Understandings: Approximate volumes of simple geometric

solids may be found using estimation. Formulas may be used to determine the

volume of fundamental solid figures. Appropriate units of measure should be used

when computing the volumes of fundamental solid figures.

Approximate surface area of simple geometric solids may be found using estimation.

Manipulatives and the construction of nets may be used in computing the surface area of right rectangular prisms and cylinders.

Formulas may be used to compute the surface area of right rectangular prisms and cylinders.

Volumes of right prisms and pyramids may be compared and contrasted.

Volumes of cylinders and cones may be compared and contrasted.

Various views of solid figures may be interpreted and sketched to provide a 2-dimensional representation of a three dimensional figure.

Nets for prisms, cylinders, pyramids, and cones may be constructed.

Essential Questions: How can I estimate the volumes of simple

geometric solids? How can I use formulas to determine the

volumes of fundamental solid figures? How can I determine the appropriate units

of measure that should be used when computing the volumes of fundamental solid figures?

What kinds of problems can be solved using volumes of fundamental solid figures?

How can I estimate the surface area of simple geometric solids?

How can I use manipulatives and nets to help compute the surface areas of right rectangular prisms and cylinders?

How can I use surface areas of plane figures to derive formulas for the surfaced areas of solid figures?

How can I use formulas to compute the surface area of right rectangular prisms and cylinders?

What kinds of problems can be solved using surface areas of right rectangular prisms and cylinders?

How do the volumes of right rectangular prisms and pyramids compare?

How do the volumes of cylinders and cones compare?

How can I interpret and sketch various views of solid figures?

How can I construct nets for prisms, cylinders, pyramids, and cones?


Supplies. Manipulatives such as… Centimeter cubes Power solid models Nets Various containers (boxes and cylinders) Text book Computers Rulers Measuring Tape & cups Scissors Graph paper Paper plates Bags of sand Cardboard Tape

Students will be able to… Decipher and draw views of solid figures

from a variety of perspectives. M6M3. Determine volumes of basic solid

figures. M6M4. Determine surface areas of basic

solid figures. M6G2.a,b Compare and contrast

properties of solid figures. M6G2.c,d Interpret and sketch various

views of solids and construct nets for solids.

Recognize the figure determined by a given net.

Pre-Test

Wherever we look, we see three-dimensional shapes. Buildings, furniture, plants, even people themselves: all are solid objects. Whenever we look at the world around us, we see it in three dimensions: length, width and height.

Many students tend to memorize, without understanding, formulas that we use in geometry or other mathematic areas. The following activities allow students to discover formulas to solve problems dealing with circumference, area, surface area, and volume.

Activating Prior Knowledge

1) Students will work in groups to create guided activity sheets that include information they have previous learned about measuring figures. They will add to this unit sheet as we progress and use it as a review as new activities are added to the lessons.

a) Students will review perimeters.

Use a number of unit squares. Make as many patterns as you can. Remember to use the same number

of squares each time. Make diagrams of each pattern on graph paper. Estimate perimeter. Which pattern has the greatest perimeter? Which has the smallest perimeter?

b) Students will review area.

Cut shapes from cardboard. Using graph paper, find which shape has the largest area? How did you find which has the largest area? What information did you find interesting with this activity?

Vocabulary


Base, Cone, Cube, Cylinder, Edge, Face, Net, Polyhedron, Polygon, Prism, Pyramid, Surface Area, Volume.

Exploring and comparing shapes and sizes.

1. Select an object shaped like this:

2. Find other objects that are the same size and shape as yours. 3. Paragraph - Tell how you checked to find out whether it was the same size and

shape.

Exploring Surface Area

Different types of geometric objects will be given. (Pyramids, prisms, cylinders, and cones)

1. Name the geometric objects.2. Estimate the surface area of these basic solids.3. Compute the surface area of these basic solids. (Students may cut objects along their

edges)4. Sketch a net of the basic solids. Compare with your team mates. Be prepared to share

with class.5. Create a formula for computing the surface area of these basic solids.6. Write a summary of what you have found in your exploration. What questions do you

still have?7. Class discussion and class presentation of nets.8. Mini task to assess understanding of surface area.


Exploring Volume

Let's start by making a 3D cube out of a 2D piece of cardboard. Cut, fold, and tape the three cubes as shown. Measure the length of each cube:

CUBE Length (cm)

A

B

C

The length of a side of Cube B is _______ times the length of Cube A. How many times bigger do you think the volume of Cube B is compared to Cube A? _______ times

In the following steps, keep the cubes over the paper plate to make clean up easier.

Pour sand into Cube A until the cube is full. Shake the cube gently so that the sand is flat across the top of the cube. Note: do not use the cube as a scoop because it is not strong enough to keep its shape.

Pour the sand from Cube A into Cube B. Repeat this until Cube B is completely full. Keep count of how many times you have to fill Cube A and record it in the table. Make sure Cube A is filled completely and is level each time. Now repeat this for Cube C.

CUBE Length Predicted Volume Measured Volume

B _____ times Cube A _____ times Cube A _____ times Cube A

C _____ times Cube A _____ times Cube A _____ times Cube A

How close were your predictions?

On your own.


1. More geometric objects of various types will be given. (Pyramids, prisms, cylinders, and cones)

2. Estimate the volumes then use formulas to compute the volumes. (Students may use the internet or textbooks to research the formulas for finding the volume.)

3. Compare with your team mates. 4. Write a summary of what you have found in your exploration. What questions do

you still have? Be prepared to share your questions with the class?5. Mini task to assess understanding of volume.

Post Test


Appendix B

Instructional Plan Rubric

Criteria Describe & State Open-ended Questions

Essential Question (s) How can I estimate the volumes of simple geometric solids?

How can I use formulas to determine the volumes of fundamental solid figures?

How can I determine the appropriate units of measure that should be used when computing the volumes of fundamental solid figures?

What kinds of problems can be solved using volumes of fundamental solid figures?

How can I estimate the surface area of simple geometric solids?

How can I use manipulatives and nets to help compute the surface areas of right rectangular prisms and cylinders?

How can I use surface areas of plane figures to derive formulas for the surfaced areas of solid figures?

How can I use formulas to compute the surface area of right rectangular prisms and cylinders?

What kinds of problems can be solved using surface areas of right rectangular prisms and cylinders?

How do the volumes of right rectangular prisms and pyramids compare?

How do the volumes of cylinders and cones compare?

How can I interpret and sketch various views of solid figures?

How can I construct nets for prisms, cylinders, pyramids, and cones?

Does the essential question address the enduring understanding?

Instructional Technology

Computer, Math Textbook, Inter-write pad In what ways can the use of instructional technology be improved?

Materials Centimeter cubes Power solid models

Are there other materials that


Nets Various containers (boxes and cylinders) Rulers Measuring Tape & cups Scissors Graph paper Paper plates Bags of sand Cardboard Tape

would be appropriate?

Accommodations for special needs

N/A To what degree are the needs of special learners being met?

Standards covered M6M3.a, b, c, d M6M4.a, b, c, d M6G2.a, b, c, d

Do the assessments align with the standards stated?

Assessment (formative)

Essay – Each Student should be able to answer the unit’s essential question.

Each student should be able to explain the process for computing surface area and volume of three dimensional figures.

Each student should be able to complete a post test, multiple choice with 85 percent accuracy or better.

Are there other assessments that would yield better data?

Relevancy to childrenActivities should allow students to learn necessary concepts in a way that is educational and interesting. (Fun)

Does the concept yield relevance to student’s learning?


Appendix C

What's Your Learning Style?

For these questions, choose the first answer that comes to mind and click on a,b, or c. Don't spend too much time thinking about any one question. Question 1

When you study for a test, would you rather

a) read notes, read headings in a book, and look at diagrams and illustrations.

b) have someone ask you questions, or repeat facts silently to yourself.

c) write things out on index cards and make models or diagrams. Question 2

Which of these do you do when you listen to music?

a) daydream (see things that go with the music)

b) hum along

c) move with the music, tap your foot, etc. Question 3

When you work at solving a problem do you

a) make a list, organize the steps, and check them off as they are done

b) make a few phone calls and talk to friends or experts

c) make a model of the problem or walk through all the steps in your mind

Question 4When you read for fun, do you prefer

a) a travel book with a lot of pictures in it

b) a mystery book with a lot of conversation in it

c) a book where you answer questions and solve problems Question 5

To learn how a computer works, would you rather

a) watch a movie about it

b) listen to someone explain it

c) take the computer apart and try to figure it out for yourself


Question 6You have just entered a science museum, what will you do first?

a) look around and find a map showing the locations of the various exhibits

b) talk to a museum guide and ask about exhibits

c) go into the first exhibit that looks interesting, and read directions later

Question 7What kind of restaurant would you rather not go to?

a) one with the lights too bright

b) one with the music too loud

c) one with uncomfortable chairs Question 8

Would you rather go to

a) an art class

b) a music class

c) an exercise class Question 9

Which are you most likely to do when you are happy?

a) grin

b) shout with joy

c) jump for joy Question 10

If you were at a party, what would you be most likely to remember the next day?

a) the faces of the people there, but not the names

b) the names but not the faces

c) the things you did and said while you were there Question 11

When you see the word "d - o - g", what do you do first?

a) think of a picture of a particular dog

b) say the word "dog" to yourself silently

c) sense the feeling of being with a dog (petting it, running with it, etc.)


Question 12When you tell a story, would you rather

a) write it

b) tell it out loud

c) act it out Question 13

What is most distracting for you when you are trying to concentrate?

a) visual distractions

b) noises

c) other sensations like, hunger, tight shoes, or worry Question 14

What are you most likely to do when you are angry?

a) scowl

b) shout or "blow up"

c) stomp off and slam doors Question 15

When you aren't sure how to spell a word, which of these are you most likely to do?

a) write it out to see if it looks right

b) sound it out

c) write it out to see if it feels right Question 16

Which are you most likely to do when standing in a long line at the movies?

a) look at posters advertising other movies

b) talk to the person next to you

c) tap your foot or move around in some other way Total your a's, b's, and c's - or if you're on-line click on the submit button below.

(James, 2009)((James, 2009)James, 2009)(James, 2009)377596

Appendix D

Pre- and Post-Test


1. Johnny used a trailer to haul dirt. The trailer is in the shape of a rectangular prism. The interior of the trailer has a length of 8 feet, and a width of 4 feet, and a height of 2 feet. What is the total number of cubic feet of dirt that the trailer can hold when it is filled so that the dirt is level with the top?

a. 14 cubic feetb. 56 cubic feetc. 64 cubic feetd. 112 cubic feet

2. What is the base of the prism pictured here?a. Cubeb. Hexagonc. Triangled. Rectangle

3. Gerald’s father has no tape measure but needs to estimate the area of a room to purchase carpet. All he has to measure with is string. If he wants to estimate the size of the room in square yards, he should use string as long as which of the following?

a. The width of his handb. The length of his footc. The distance from the floor to his headd. The distance from his nose to the end of his outstretched arm

4. Use the diagram below to answer this question.

A swimming pool is 6 yards wide and 10 yards long. A soccer field is 60 yards wide and 110 yards long. About how many swimming pools would fit in the space taken up by the soccer field?

a. 110b. 60c. 70d. 120

5. Jerome is shopping for a storage box for his sports card collection. He sees a box that is the same height but 3 times as long and 3 times as wide as the one he has at home. How does the volume of the store box compare with his own?

a. 3 times the volume of his boxb. 6 times the volume of his boxc. 9 times the volume of his boxd. 27 times the volume of his box


6. Which is the closest to the volume of the cone shown above?

a. 16.75 cu in.b. 20.94 cu inc. 43.98 cu ind. 67.02 cu in

7. The volume of a rectangular solid is 960 cubic inches. The dimensions of the base are 12 inches by 10 inches.

What is the height of the solid?

a. 4 inb. 8 inc. 120 ind. 840 in

8.


Which represents a two-dimensional view from directly above the figure?

9. This drawing shows cubic boxes stacked in the corner of a warehouse.

If each box will hold 8 cubic feet, what is the total capacity of the stack of boxes?a. 488 cubic feetb. 496 cubic feetc. 504 cubic feetd. 512 cubic feet

10. Which of the following nets can be folded along the dashed lines to form a cube?


11. The cylinders shown are similar.

What is the volume of the larger cylinder?a. 56π m3

b. 224π m3

c. 896 π m3

d. 3,584π m3

12. The base of a triangle is 3 units more than h, its height. Which expression represents its area?


13. Shelby made a rattle by putting some rice in an empty baking powder can and taping the lid on. Now she wants to cover the entire can in tissue paper and decorate it. Find the approximate surface area of the can to determine how much tissue paper she will need.

a. 94.2 cm2

b. 188.4 cm2

c. 270.1 cm2

d. 282.6 cm2

14. Michael is filling a wading pool. What is the amount of water needed to fill the pool to the top?

a. 5,200 in3

b. 1,300 in3

c. 860 in3

d. 432 in3

15. Alexis is helping her mother pack dinner plates for their move to their new house. She placed them in a cardboard canister. Then she placed the canister in a larger


rectangular box. She put packing material around the canister to fill the box. The canister and box are shown.

Estimate the surface area of the box?a. 2,000 in2

b. 2,100 in2

c. 2,200 in2

d. 2,300 in2

16. How much packing material did Alexis put around the cardboard canister inside the box?

a. 6,030.48 in3

b. 6,230.52 in3

c. 8,208.72 in3

d. 8,604.36 in3

17. How many 2-inch cubes will fit in the figure shown?

a. 10

b. 30

c. 300

d. 1,000

18. Which of the following nets matches the dimensions of a box?


Jordan built a house out of building blocks. He used a cube and a square pyramid to make the house.


19. The attic of Jordan’s house is represented by square pyramid. If the height of the attic is 6 inches, calculate the attic’s volume.

a. 36 in3

b. 72 in3

c. 108 in3

d. 144 in3

20. How many times greater is the volume of the main level of the house above than the attic?

a. 1

b. 2

c. 3

d. 4

21. A can of pie filling is 10 centimeters high and has a diameter of 6 centimeters. The company that produces the pie filling needs more paper for labels that go around the entire can. Calculate the area of one label.

a. 60.2 cm2

b. 94.2 cm2

c. 188.4 cm2

d. 282.6 cm2

22. What is the area of the figure shown below?


a. 28 ft2

b. 38 ft2

c. 48 ft2

d. 56 ft2

23. What is the perimeter of the figure shown above?

a. 28 ft2

b. 28 ft

c. 34 ft3

d. 38 ft2

Use the diagram to answer the following question.

24. What is the perimeter of the figure shown above?

a. 54 ft

b. 64 ft

c. 74 ft

d. 84 ft

25. Which of the following formulas can be used to find the volume of the prism shown?


a. 10 cm x 10 cm x 7 cm

b. 10 cm – 10 cm x 7 cm

c. 10 cm + 7 cm x 10 cm

d. 10 cm – 7 cm x 10 cm

26. Carly will ship some gifts to her relatives. She has two boxes she can use as shown below. Which of the following statements is TRUE?

27. Erika is packing a box of cookies to send to her brother at college. The box is 10 inches long, 8 inches wide, and 4 inches high. She is packing it in a larger box with


packing material around it to protect the cookies. The larger box is 20 inches long, 15 inches wide, and 10 inches high. How much packing material dies Erika need?

a. 320 in3

b. 2,680 in3

c. 2,780 in3

d. 3,320 in3

28. Anthony has cleaned his fish tank and is refilling it with a 2-liter bottle. The tank is 50 centimeters long, 35 centimeters wide, and 30 centimeters tall. A 2-liter bottle holds 2,000 cubic centimeters of water. How many bottles of water will Anthony need to fill the tank to the top?

a. 6

b. 12

c. 20

d. 24

29. What is the surface area of the solid figure that the net below will form?

a. 120 cm

b. 124 cm

c. 142 cm2

d. 142 cm3

30. Which solid figure will the net shown below form when folded?


a. A cylinder

b. A cylindrical prism

c. A rectangular pyramid

d. A rectangular prism


Appendix E

Student Attitudinal Survey

I am interested in your ideas about mathematics and this class. Your answers to the

questions that follow will help me understand what you think mathematics is all about.

This questionnaire is not something to be graded and your answers are completely

anonymous. Please tell me what you really think by putting an X in the box corresponding

to Strongly Agree, Agree, Undecided, Disagree, or Strongly Disagree.

Thank you for your help!

Student Attitude Survey

Question Strongly Agree

Agree Undecided Disagree Strongly Disagree

1. I have always hated math 2. I stop working as hard after I do badly 3. I rarely ask questions during math class 4. Knowing math will help me in my future 5.Males are naturally better at math than females 6. Math is a fun subject 7. Math has been my best subject 8. Math has been my worst subject 9. Females can do


just as well in math as males can 10. I like to do hands on activities in math 11. Math is just memorizing formulas 12. Math is not important in everyday life 13. In math, you can be creative and discover things by yourself 14. I try to learn math because it helps me develop my mind and helps me think more clearly 15. Using the internet (or a computer) is a good way for me to learn math 16. Working with other students helps me have a better attitude towards math 17. I keep trying even if the work is hard for me to do 18. I work as hard as I can in math 19. I worry that I will get poor grades in math 20. I only do math because I have to


Appendix F

Reflective Journal Prompt Questions

1) Three main things I learned from this session are…

2) What I most liked about this session was...

3) What I most disliked about this session was...

4) Interesting facts I learned in this session...

5) What I would like to do differently is…


Appendix G

Focus Group Questions

1. How would you interpret the data from the pre and post tests?

2. Do you think my interpretation is correct or incorrect? Why?

3. What additional activities should be added to improve performance on this

content?

4. Based on your review of the research and your observations, what changes

should I make in my approach to instruction for the future?

Documents

Statement of the Problem - LaGrange Collegehome.lagrange.edu/educate/Advanced Programs/M.Ed. Defense... · Web viewCrobach’s Alpha reliably determined that the total score was measured