the effects of technology enriched instruction on 6...

THE EFFECTS OF TECHNOLOGY ENRICHED

INSTRUCTION ON 6th

GRADE PUBLIC SCHOOL STUDENTS’

ATTITUDES AND PROBLEM SOLVING SKILLS IN

MATHEMATICS

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

ORHAN CURAOGLU

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR

THE DEGREE OF DOCTOR OF PHILOSOPHY

IN

COMPUTER EDUCATION AND INSTRUCTIONAL TECHNOLOGY

OCTOBER 2012

ii

Approval of the thesis


INSTRUCTION ON 6th



MATHEMATICS

submitted by ORHAN CURAOGLU in partial fulfillment of the requirements for

the degree of Doctor of Philosophy in Computer Education and Instructional

Technology Department, Middle East Technical University by,

Prof. Dr. Canan Özgen

Dean, Graduate School of Natural and Applied Sciences ______________

Prof. Dr. Soner Yıldırım

Head of Department, CEIT ______________


Supervisor, CEIT Dept., METU ______________

Examining Committee Members:


CEIT Dept., METU ______________

Prof. Dr. Zahide Yıldırım

CEIT Dept., METU ______________

Prof. Dr. Sinan Olkun

ES Dept., AU ______________

Assoc. Prof. Dr. Yasemin Gülbahar Güven

Informatics Dept., AU ______________

Assist. Prof. Dr. Gulfidan Can

CEIT Dept., METU ______________

Date: September 2012

iii

I hereby declare that all information in this document has been obtained and

presented in accordance with academic rules and ethical conduct. I also

declare that, as required by these rules and conduct, I have fully cited and

referenced all material and results that are not original to this work.

Name, Surname: Orhan CURAOGLU

Signature :

iv

ABSTRACT


INSTRUCTION ON 6th



MATHEMATICS

CURAOGLU, Orhan

Ph.D., Department of Computer Education and Instructional Technology

Supervisor : Prof. Dr. Soner YILDIRIM

October 2012, 166 page

This research presents an experimental study evaluating two main purposes under

the main aim. These purposes are to describe differences among the groups in

terms of problem solving skills and attitudes towards to mathematics. While

conducting this study, a combination of qualitative and quantitative research

methods was employed. Both qualitative and quantitative data were gathered

through questionnaire for attitude towards mathematics, Problem solving skill

scale, problem solving achievement test and interviews for the study. The

qualitative data were analyzed according to qualitative data analysis techniques

and quantitative data were also analyzed using SPSS statistics software.

The results of the study demonstrate that effects of Technology Enrichment

Instruction on the sixth grade public school students’ attitudes and problem

solving skills in mathematics have both positive and negative results. The

students’ problem solving skills in the groups which token technology enrichment

mathematics instruction had a positive improvement. On the contrary, there was

no significant difference between experimental group that received technological

enhanced instruction and those received traditional instruction in terms of

attitudes towards mathematics.

Keywords: Problem solving skills, attitude towards mathematics, Solomon

research design, technology enriched instruction.

v

ÖZ

TEKNOLOJİ İLE ZENGİNLEŞTİRİLMİŞ ÖĞRETİMİN

ALTINCI SINIF ÖĞRENCİLERİNİN MATEMATİK DERSİNE

KARŞI TUTUMLARINA VE MATEMATİK DERSİNDEKİ

PROBLEM ÇÖZME BECERİNE ETKİSİ

CURAOĞLU, Orhan

Doktora, Bilgisayar ve Öğretim Teknolojileri Eğitimi Bölümü

Tez Yöneticisi : Prof. Dr. Soner Yıldırım

Ekim 2012, 166 sayfa

Bu araştırma teknoloji ile zenginleştirilmiş öğretimin altıncı sınıf öğrencilerinin

matematik dersine karşı tutumlarına ve matematik dersindeki problem çözme

becerine etkisini değerlendirme çalışmasıdır. Bu temel hedefin altında iki amaç

vardır. Bu amaçlar gruplar arasındaki problem çözme becerileri ve matematiğe

karsı tutumları arasındaki farkları tanımlamaktır. Bu araştırma için nitel ve nicel

araştırma yaklaşımları birlikte kullanılmıştır. Uygulama süreci boyunca eşzamanlı

olarak nicel veri hem de nicel veri toplama ve analiz işlemi yapılmış. Nicel veriler

SPSS veri analiz programında analiz edilirken nitel veriler nitel veri analiz

teknikleri kullanılarak analiz edilmiştir.

Çalışmanın sonuçları teknoloji ile zenginleştirilmiş öğretimin altıncı sınıf

öğrencilerinin problem çözme becerileri bakımından pozitif yönde etki yaptığını

göstermesine rağmen matematiğe karşı tutumların bakımından yansız olduğunu

göstermektedir.

Anahtar Kelimeler: Problem çözme becerileri, matematiğe karşı tutum, Solomon

araştırma tasarımı, teknoloji ile zenginleştirilmiş öğretim.

vi

ACKNOWLEDGEMENTS

I would here like to express my thanks to the people who have been very helpful

to me during the time it took me to write this thesis. First and foremost I would

like to express my gratitude to Prof. Dr. Soner Yildirim for her valuable guidance,

patient, and warm supports. His inspiring suggestions and encouragement helped

me in all the time of the research study and for writing of this thesis.

I would like to thank the students, the teachers/lecturers and colleagues in the

participating schools and universities for their hospitality and friendly co-

operation.

And most of all, I would like to express my gratitude to my family for their love

and encouragement.

This thesis would not have been written without all this support. I am deeply

indebted and most grateful.

vii

TABLE OF CONTENTS

ABSTRACT ........................................................................................................... iv

ÖZ ............................................................................................................................ v

ACKNOWLEDGEMENTS ................................................................................... vi

TABLE OF CONTENTS ...................................................................................... vii

LIST OF TABLES ................................................................................................... x

LIST OF FIGURES ............................................................................................. xiii

CHAPTERS

1.INTRODUCTION ................................................................................................ 1

1.1. Background of the Study ........................................................................... 1

1.2. Purpose of the Study .................................................................................. 5

1.3. Research Questions ................................................................................... 5

1.4. Significance of the Study .......................................................................... 6

1.5. Definition of Terms ................................................................................... 8

2. REVIEW OF LITERATURE ............................................................................ 10

2.1. Introduction ............................................................................................. 10

2.2. Technology in Education ......................................................................... 10

2.3. Integrating Technology in Turkey ........................................................... 12

2.4. Integrating Technology into Mathematics Education ............................. 13

2.5. Mathematical Problem Solving Skills ..................................................... 20

2.5.1. Problem solving process ........................................................................... 23

2.5.2. Problem Solving Strategies ....................................................................... 25

2.5.3. Problem Solving in Classroom ................................................................. 28

2.6. Attitude towards Mathematics ................................................................. 30

2.7. Summary ................................................................................................. 34

3. METHODOLOGY ............................................................................................. 35

3.1. Problem Statement and Research Questions ........................................... 35

3.1.1. Research Questions ................................................................................... 36

3.2. Overall Design of the Study .................................................................... 37

3.2.1. The Quantitative Approach ....................................................................... 38

3.2.2. The Qualitative Approach ......................................................................... 42

3.2.3. Content analysis ........................................................................................ 43

viii

3.3. Subjects and Context (Math Courses) ..................................................... 44

3.3.1. Subjects of the Study................................................................................. 44

3.3.2. Math Courses ............................................................................................ 46

3.4. Instrumentation ........................................................................................ 48

3.4.1. Problem Solving Skill Scale ..................................................................... 49

3.4.2. Attitude towards Mathematics Questionnaire ........................................... 50

3.4.3. Rubric for Student Response Evaluation .................................................. 52

3.5. Data Collection Procedure ....................................................................... 53

3.6. Data Analysis .......................................................................................... 54

3.6.1. Quantitative Data Analysis ....................................................................... 55

3.6.2. Qualitative Data Analysis ......................................................................... 57

3.7. Pilot Study ............................................................................................... 58

3.7.1. Subjects of the Pilot Study ........................................................................ 59

3.7.2. Data Collection Instruments for the Pilot Study ....................................... 60

3.7.3. Results of Pilot study ................................................................................ 62

3.8. Reliability and validity ............................................................................ 68

3.9. Assumptions, Limitations and Delimitations for the Study .................... 69

4. FINDINGS ......................................................................................................... 71

4.1. Descriptive Results .................................................................................. 71

4.2. Quantitative results .................................................................................. 72

4.3. Qualitative results .................................................................................... 95

4.3.1. Summary of qualitative results of problem solving achievement test....... 96

4.3.2. Summary of qualitative results of students` interviewed about problem

solving and attitude towards mathematics .............................................................. 102

4.3.2.1. What was the first thing you did when you saw the math problem?....... 102

4.3.2.2. Describing strategies that you used to help you solved the math problem.103

4.3.2.3. How did you know when you solved the problem, right? ...................... 104

4.3.2.4. What words do you use to describe your feelings when you see the math

problems? ................................................................................................................ 105

4.3.2.5. Level of student`s expression about how to solve their math problems. 106

4.4. Summary ............................................................................................... 107

4.4.1. Problem Solving Skills............................................................................ 108

4.4.1. Attitude towards Mathematics ................................................................ 111

5. DISCUSSION AND CONCLUSION .............................................................. 113

5.1. Introduction ........................................................................................... 113

ix

5.2. Discussion of Findings .......................................................................... 114

5.2.1. Problem Solving Skills............................................................................ 114

5.2.2. Attitude towards Mathematics ................................................................ 118

5.3. Implications and Recommendation ....................................................... 120

REFERENCES ..................................................................................................... 123

APPENDICIES .................................................................................................... 141

A: INTERVIEW PROTOCOL ............................................................................ 141

B: MATHEMATICS ATTITUDE SCALE ......................................................... 142

C: PROBLEM SOLVING SKILLS SCALES ..................................................... 144

D: ACTIVITIES ................................................................................................... 152

E: LESSON PLANS ............................................................................................ 154

F: ACTIVITY SHEET ......................................................................................... 156

G: SAMPLES OF STUDENT ACTIVITY NOTES ............................................ 157

H: STUDENT SELF EVALUATION FORM ..................................................... 159

I: RUBRIC FOR MATH PROBLEM SOLVING ............................................... 160

J: PROBLEM SOLVING ACHIEVEMNT TEST ............................................... 161

K: PERMISSION FORM from the MoTNE ........................................................ 163

CURRICULUM VITAE ...................................................................................... 164

x

LIST OF TABLES

TABLES

Table 2.1. Problem-solving Strategies cited from Babbitt & Miller (1996) ......... 26

Table 2.2. Problem-solving Strategies cited from Babbitt & Miller (1996) (cont’d)

............................................................................................................................... 27

Table 3.1. Experimental designs ........................................................................... 40

Table 3.2. Solomon Four-Group Design adapted from Frankel&Wallen, (2000) 40

Table 3.3. Participants of the Study ...................................................................... 45

Table 3.4. The numbers of participants in this research. ...................................... 46

Table 3.5. Indicators table of Problem Solving Skill Scale .................................. 49

Table 3.6. Item analysis results of Problem Solving Skills................................... 50

Table 3.7. Numbers of Groups in the Pilot Study ................................................. 59

Table 3.8. Mean and standard deviations of attitude toward mathematics ........... 62

Table 3.9The results of ANOVA test in terms of pretest and posttest score

experiment groups and control groups. ................................................................. 63

Table 3.10. Number of students means and standard deviation among groups for

each question according to categories of problem solving; understanding the

problem, planning a solution, and getting an answer ............................................ 64

Table 3.11. Descriptive Statistics for the level of understanding the problem,

planning a solution, and getting an answer ........................................................... 66

Table 3.12. Multivariate tests results of students problem solving skills scores .. 66

Table 3.13. Tests results of Between-Subjects Effects ......................................... 67

Table 4.1. The numbers of participants ................................................................. 72

Table 4.2. Descriptive Statistics in terms of problem solving skills .................... 73

Table 4.3. Tests of Between-Subjects Effects for students` problem solving

achievements ......................................................................................................... 74

Table 4.4. Difference between the control group that did not receive treatment and

the experimental group that received treatment with pretest in terms of problem

solving skills - Mann-Whitney U test ................................................................... 76

xi


the experimental group that received treatment without pretest terms of problem

solving skills ......................................................................................................... 77

Table 4.6. Descriptive Statistics for Analysis Variables ....................................... 78

Table 4.7. Tests of Between-Subjects Effects for Students’ attitude towards the

mathematics........................................................................................................... 79

Table 4.8. Difference in students’ attitude towards mathematics post-test scores

between control group and experimental group with pretest ................................ 80


between control group and experimental group without pretest ........................... 81

Table 4.10. Mean and standard deviations of attitude toward mathematics

understanding problem, making plan, implementation of plan and review their

solutions in terms of pretest and posttest .............................................................. 82

Table 4.11. The results of ANOVA test for problem solving skills scale in terms

of pretest and posttest score experiment groups and control groups. ................... 83

Table 4.12. The results of ANOVA test for levels of problem solving skills scale

in terms of pretest and posttest score experiment groups and control groups. ..... 84

Table 4.13. The results of ANOVA analysis concerning the level of

“understanding the problem” ................................................................................ 85

Table 4.14. The results of ANOVA analysis concerning level of make a plan .... 86

Table 4.15. The results of ANOVA analysis concerning level of utilize the plan 87

Table 4.16. The results of ANOVA analysis concerning level of making a revision

............................................................................................................................... 88

Table 4.17. Box's Test of Equality of Covariance Matrices ................................. 89

Table 4.18. Levene's Test of Equality of Error Variances .................................... 89

Table 4.19. Multivariate Tests .............................................................................. 90

Table 4.20. Tests of Between-Subjects Effects for MANOVA ............................ 90

Table 4.21. Multivariate Tests .............................................................................. 91

Table 4.22Tests of Between-Subjects Effects for ANOVA.................................. 92

Table 4.23Pairwise Comparisons across pretest and treatment ............................ 93

xii

Table 4.24. Mean scores and standard deviation among groups according to

categories of problem solving; understanding the problem, planning a solution,

and getting an answer ............................................................................................ 97

Table 4.25. Table for Total Scores means and standard deviation for each group

with pretest according to categories of problem solving; understanding the

problem, planning a solution, and getting an answer ............................................ 99

Table 4.26. Frequency table for each question concerning categories of problem

solving; understanding the problem, planning a solution, and getting an answer

according to problem solving achievement test. ................................................. 101

Table 4.28. Codes/themes after interview analysis. ............................................ 102

Table 4.29. Mann-Whitney U test scores in terms of problem solving

achievements post-test scores with / without pretest. ......................................... 109

Table 4.30. Mann-Whitney U test scores in terms of attitude towards mathematics

post-test scores with / without pretest. ................................................................ 112

xiii

LIST OF FIGURES

FIGURES

Figure 3.1. Rating scale in the attitude questionnaires........................................... 51

Figure 3.2. An analytic rubric for evaluating students’ work by Charles, Lester,

and O'Daffer ........................................................................................................... 53

Figure 3.3. Concurrent mixed method design adapted from Tashakkori and

Teddlie (2003). ....................................................................................................... 54

Figure 3.4. 2x2 Analyses of Posttest Scores .......................................................... 55

Figure 3.5. Mean plots about pretest and posttest score experiment groups and

control groups ........................................................................................................ 63

Figure 3.6. Total Scores means and standard deviation for each question according

to categories of problem solving; understanding the problem, planning a solution,

and getting an answer ............................................................................................. 65

Figure 4.1. The interaction effect of pretest and treatment on students’ problem

solving skills .......................................................................................................... 75

Figure 4.2. The interaction effect of pretest and treatment on students’ attitude

towards mathematics .............................................................................................. 80

Figure 4.3. Changes in the mean difference scores of level of understand the

problem .................................................................................................................. 85

Figure 4.4. Changes in the mean difference scores of level of making a plan....... 86

Figure 4.5. Changes in the mean difference scores of level of utilize the plan ..... 87

Figure 4.6. Changes in the mean difference scores of level of making a revision. 88

Figure 4.7. Treatment*Pretest with respect to problem solving skills ................... 94

Figure 4.8. Treatment*Pretest with respect to attitude towards mathematics........ 95

Figure 4.9. Total Scores means and standard deviation according to categories of

problem solving; understanding the problem, planning a solution, and getting an

answer .................................................................................................................... 98

Figure 4.10. Figure for total Scores means and standard deviation for each group


problem, planning a solution, and getting an answer ........................................... 100

xiv

Figure 4.11. Result of “What was the first thing you did when you saw the math

problem?” ............................................................................................................. 103

Figure 4.12. Result of strategies that students’ used to help them solve the

mathematics problem. .......................................................................................... 104

Figure 4.13. The result of “How did you know when you solved the problem,

right?” ................................................................................................................... 105

Figure 4.14. The result of “What words do you use to describe your feelings when

you see the math problems?” ............................................................................... 106

Figure 4.15. The result of the student`s expression levels about how to solve their

math problems. ..................................................................................................... 107

1

CHAPTER 1

INTRODUCTION

This research describes an experimental study evaluating the effects of

technology-enriched instruction on 6th

grade students’ mathematics attitudes and

the students’ problem solving skills. This section focuses on the justification of the

research by presenting the background, significance and the purpose of the study

as well as the research questions. At the end of this section, essential terms for the

study were defined and finally limitations of study were explained.

1.1. Background of the Study

The rapid growth of computers and Internet has aroused an interest in the area of

education. Computers have changed the lives of people and naturally of society

since it was first developed. Reducing the time and effort spent on repetitive work

and helping people to concentrate on more important aspects of their job can be

viewed as the most essential features of computers. In short, they are used

especially to produce more accurate and reliable outcomes, increase productivity,

reduce costs, and encourage research and development. Moreover, many

educational institutions provide their learners with technologically enriched access

in different ways. Ill-structured exercises in the classroom, as well as simulations,

games, and tutorial programs can be included these kinds of enrichments.

According to Ertmer et al. (1999), the statement is that using technology enables

users in the classroom to change their practices toward more student-centered

methods. Moreover, it is emphasized that teachers’ using technologies in the

classroom change students’ learning (Barron, Kemker, Harmes, & Kalaydjian,

2003). Morrison and Lowther (2004) illustrates this stating that computers can

make a change in student learning if teachers let their students use computer

2

technology in the classroom.

According to Tsay (1998), computers have a significant impact upon learning.

Using computer technology in classrooms supported for two reasons: a) to

facilitate and enhance learning; and b) to improve students’ ability to function in

an information-based society. In order to achieve these, many educators have

supported computer-based instruction. Although computer-based instruction has

brought some advantages, such as high quality and interactive instruction and

increased retention, these efforts have only recently been able to influence

computer supported instruction. Computer Supported Instruction or interactive

multimedia training are acclaimed to be effective for technological innovations in

education and enhancing instructional practices by stimulating learners’ senses in

learning. Many research emphasized the significance of using technology in the

classroom effectively by way of a learning tool. According to Jonassen (2000), for

example, learning with computers that supports meaning making by students is not

the same concept with learning from computer.

As regards the goals of the Turkish national education system, some of them are

united in national awareness and thinking, the training to enable students to think

along scientific area with intellectually developed their outlooks on world matters.

In addition to this, being productive happy individuals, who contribute to the

prosperity of the society by their skills. In order to achieve this goal, Ministry of

Turkish National Education takes advantage of new developments. In the schools

under Ministry of Turkish National Education (MoTNE), computers have been in

place in elementary and secondary schools for more than ten years, which means

that there is almost no primary school providing education without computer

support (OECD report, 2005). Nevertheless, putting computers in class does not

exactly mean that they are automatically being used as a tool in our national

curriculum.

In parallel with these reforms, MoTNE has decided to change curricula in

elementary and secondary education in Turkey. According to the MoTNE

3

authorities, it is mandatory to change the curriculum because it is clearly realized

that there have been many changes and developments in the country, such as the

demographic structure, parents’ qualities, cultural area, human rights, political

area, science and technology (Cakir, 2006). Therefore, it is necessary to integrate

these developments into our education system.

Similarly, many efforts have been made about the integration of technology into

classrooms all over the world. For example, according to Ertmer (2005), in the

USA the computer connected activities in which instructors most regularly engage

their learners include doing research using the internet, improving their computer

skills, , use the computers as a free-time activity, doing drill and practice and

expressing themselves in writing, (Ertmer, 2005, p2).

As there are a few efficient materials in our classrooms, mathematics as mentioned

above is difficult for instructing and learning because the boards in the classrooms

are not capable of computing and demonstrating advanced level geometric figures,

functions etc. In order to fill the gaps in classrooms, Technology Enriched

Instruction can be utilized as an intellectual partner to engage and facilitate

students’ skills and thinking.

This study also focuses on the attitudes of these students towards mathematics and

how these attitudes have changed in the course of this study. For this research,

attitude refers to feelings and emotions of an individual toward mathematics.

Student attitudes and mathematics achievement are typically high in elementary

school when the introduction of material is slow and repetitious, but the

achievement and attitude towards to mathematics levels begin to lower as the

curriculum content becomes more abstract (Ma & Xu, 2004).

Another focus of the current study is on students’ problem solving ability. This

ability is an important skill for people, especially today. Even though this fact

might be perceived from today’s features, John Dewey expressed this reality

almost in the beginning of the 20th

century in his important book Democracy and

4

Education (1916). Dewey (1916) stated that students should be thinkers and

problem solvers via more relevant education.

Educators have sought ways about how to improve problem solving skills and

critical thinking for years. Depend on the amount of literature on the subject;

improving these skills is always essential. Problem solving skills and critical

thinking skills are generally considered as essential cognitive activities in daily

and business environment. Person is often obliged to solve problems and is

rewarded to do so. Problem solving has been recognized and encouraged through

several disciplines, such as mathematics, psychology, science and many other

fields. All disciplines employ problem solving process in different contexts and

different ways. Likewise, all kind of educators considers this process important

(Wager, 1997).

In the curriculum, students are seldom engaged with meaningful problems similar

to the ones they may encounter in daily life. Although educators claim that

improving students' problem solving skills is a vital goals of today's education,

Gagne (1996) expressed that this kind of skill has not been given enough time and

importance (cited Askar, 1988). After school, students face problems that are ill-

structured in nature. Therefore, students’ problem solving abilities should be

improved in the teaching and learning process in order to solve these kind of

problems in their everyday lives, professional lives as well as school lives.

All over the world and in Turkey, mathematics education, especially the basics of

mathematics has always had top priority. The Student Selection Exam (SSE) is a

vivid example of this. The test is a highly important test as the score of this test is

used as a requirement to be accepted to universities in Turkey. In this exam,

mathematics items have great effects on students’ success as they have a high

weighting in grade calculation. Therefore, teaching and learning mathematics is

more important both teachers and students who are to take this exam.

5

After international comparisons, like the Second International Mathematics and

Science Study (SIMSS), the third study (TIMSS) and the Evaluation of

Educational Achievement (IEA); cross-national studies gained a ground on

wide scale to explain the difference in students’ mathematics achievement.

Countries like Singapore, Taiwan and other eastern countries where students

showed a higher performance in mathematics put a lot of emphasis on strategy

training in problem solving open-ended discussions and organize their programs

with a primary focus on problem solving (Cai, 2003; Kaur, 2001).

1.2. Purpose of the Study

The aim of this quasi-experimental research was to evaluate the effects of

technology-enriched instruction on the 6th

grade students’ mathematics attitudes

and the students’ problem solving skills. More specifically, this research aims to

examine the effects of technology integration, which is through instructor

demonstration, required assignments and direct intervention, on students’ problem

solving achievement and attitude towards to mathematics.

1.3. Research Questions

The main research question was ‘What are the effects of Technology Enrichment


solving skills in mathematics?’

Under this question, there were eleven sub research questions which were related

to problem solving and attitude towards to mathematics. Sample of the research

questions follows.

• Is there a difference among the groups with pretest and without pretest in

terms of problem solving skills?

6

• Is there a difference between the control groups that did not receive

treatment and experimental group that received treatment in terms of

problem solving skills?

• Is there a difference in students’ attitude towards mathematics among

groups that who are given pretests and groups than that is not given

pretest?

• Is there a difference in students’ attitude towards mathematics between

control groups and experimental groups?

• Is there a difference among the control groups that did not receive


principles, which are understanding the problem, making a plan,

implementing the plan and reviewing the solution, of problem solving

skills?

• Is there a difference among experimental and control groups in terms of

students’ attitudes towards the mathematics scores and the students’

problem solving skill scores?

1.4. Significance of the Study

In recent years, educational institutions have been influenced from the rapid

development in new technologies. Today’s students are growing up with

technology. In order to prepare students for life after school, educational

institutions are enhancing their own facilities and teaching abilities to offer to their

students. The International Technology Education Association is an example of an

organization that advocates teaching technology using hands-on experiences

within the context of mathematics, science, and other disciplines and focuses on

improving technological literacy in order to prepare students for the workforce

(Roblyer, 2006).

On the other hand, one of the aims of mathematics education is to improve

students’ problem solving skills. Mathematics education aims to develop students’

7

problem solving skills since students use not only their mathematical knowledge

they already learned also improve their knowledge to have a better mathematical

insight in problem solving process (Olkun & Toluk, 2002). Similarly, Altun (2001)

expressed that problem solving does not have specific rules but has its own

systematic way.

Moreover, many reports have recently indicated that the improvement of problem

solving skills of students is an important issue in mathematics education.

However, Turkish students' performance was not good enough as expected. Mullis

et al. (2000) stated that Turkish students in TIMMS had high performance in

solving the problems that required low or moderate cognitive behavior; however,

their problem solving performance were highly low in solving the high cognitive

demand problems.

Therefore, the Ministry of Turkish National Education (MoTNE) has restructured

mathematics education curriculum of elementary and secondary (from grades 1 to

12) schools. By this means, improving students’ problem solving skills has

become a key level.

Not only the MoTNE but also other education authorities in many countries agree

that using technology in classrooms is inevitable. Roblyer (2006) stated that using

technology in classrooms will enable students to become technologically literate in

order that they can be successful in today’s society. Students live in a digital world

expecting them to use technology at home and at school. Thus, educators have to

figure out educational activities connected to their lives and technologies. As a

result of all these efforts, students might be more prepared for their life after

school.

Considering the above-mentioned realities, the consequences of this study can be

deemed beneficial for a variety of stakeholders. Educators may enhance their own

mathematics education, improve their teaching skills and use different

instructional materials in their teaching. Moreover, the results of research are

8

hoped to help teacher educators and to improve teacher education. Besides,

students will be given chances to develop a comprehensive understanding of the

concept of mathematics. Having been examined in detail, study outcomes might

also contribute to the education, especially to mathematics lessons. As a result, the

results may encourage teachers to think about how to use computers to get better

achievement results.

Finally, considering the fact that problem solving ability is an important skill for

people and is generally considered as an important cognitive activity in daily and

professional contexts, it would be fair to state that this research will find evidence

on how to improve students’ problem solving abilities so that they are able to solve

these kind of problems in their everyday, professional or their school lives. Thus,

students will be prepared for professional life and educators will be informed

about how to use technology enriched instruction to get better results in terms of

problem solving skills. In addition, programs of pre-service and in-service

education may be redesigned to update teachers about how to improve students’

attitudes towards mathematics and integrate problem solving into their teaching.

1.5. Definition of Terms

Math Attitude: Confidence, value, enjoyment, emotions, feelings and motivation

toward mathematics including (Tapia & Marsh, 2002).

Computer Based Instruction (CBI): This term denotes instruction delivered by a

computer rather than by an instructor in the classroom. CBI can deliver lessons,

provide simulations, test learners, and generate and manage administrative data.

Achievement: Measured by differences in pre-test scores and post-test scores,

using comprehensive problem solving skill exam for both pre- and post-tests for

each traditional and treatment section.

9

Computer Supported Instruction (CSI): This term is used to imply the use of

Computer as an aid or as a supplement in teaching/learning process. In addition,

drill and practice exercises are incorporated to help students practice and reinforce

some skill or concept that has previously been taught.

Enrichment: It is defined as providing children with extra cognitive stimulation.

This term is used to “refer to any supplementary activity, intervention, or

opportunity added to child’s daily life experiences” (Children with Challenges,

2009, p. 1).

Technology Enrichment: For the purposes of this study, the computer provides

relatively unstructured exercises of various types. These are simulations, tutoring,

games, etc. to supplement the classroom experience, motivate and stimulate to

learners.

Traditional instruction: Instruction in which course content is delivered by lecture

in a face-to-face classroom setting in which students listen passively and take

notes. Homework was assigned and graded. In the control group, students took

traditional instruction.

Problem Solving: It is defined as having students engage in a problem or

assignment that requires them to think systematically about what is needed and

identifies a strategy to solve the problem (NCTM, 2000).

10

CHAPTER 2

REVIEW OF LITERATURE

2.1. Introduction

The literature review section includes theoretical perspective to the study by

discussing relevant research studies and the information previously documented

related to the broad topics of Technology in Education, Technology in

Mathematics Education, Integrating Technology into Education, Mathematical

Problem Solving and Attitudes and Achievement in Mathematics.

2.2. Technology in Education

Technology has extensively influenced the whole society and its surrounding all

over the world. Cellular phones, text messaging, email and social media are

primary tools of communication for adults and children alike. This means that

technology invades almost all sides of our society. Kitchens (1996) stated that

through the years, technology has most often been used to deliver ways. These

ways include present and exchange the information. Computers, voice recording,

video recording devices and projectors represent a couple of the technological

devices which have resulted from technology and have been integrated into

schools as a media for delivery information, which makes the delivery of

information possible in ways other than traditional lectures and paper based

formats (Edwards, Roblyer, and Havriluk, 1997). Hence, using information

technology in education is gaining unavoidable motion as it enhances teaching

and learning opportunities for all ages. When looked at the historical

developments, education technologies have found a significant application field

11

for a long time instead of a short period of time (Hannafin and Savenye, 1993;

Seels and Richey, 1994; Gentry, 1995; Spector, 2001; Reiser, 2002; Molenda

2004).

Many institutions or educators try to define what educational technology is.

Pertaining to this issue, Gentry (1991) expressed that the technology’s purpose

and meaning is not always clear in education. However, Association for

Educational Communications and Technology (AECT) made a definition which is

the widely used an educational technology’s explanation.

“Educational technology is complex, integrated process

involving people, procedures, ideas, devices and

organization for analyzing problems and devising,

implementing, evaluating, and managing solutions to the

problems involved in all aspects of human learning

(AECT, 1977).”

Computers, textbooks, blackboards, smart boards, slide projectors and

videocassette recorders are regarded as tools that allow us to teach more

effectively. However, the material and methods used in educational technologies

should be well organized to obtain positive results. The studies conducted about

technology in education show that technology has helpful developments on on

basic and advanced skills in the instructional process. For instance, Rice (1984, as

cited in Chou, 2003) indicated that the “new media” which are computers and

Internet, has allowed or facilitated the provision of the important feature of

interactivity in educational applications in order to enhance learning potential.

Regarding this, Borsook & Higginbotham (1991, as cited in Chou, 2003) argue

that “the computer’s interactive potential makes it unique in the history of

educational/instructional technology and sets it apart from all other instructional

devices” (p, 267).

Also, many research studies about educational technology disclose strong

http://courses.ceit.metu.edu.tr/ceit626/week1/AECT_Definition%20of%20Educational%20Technology.pdf

12

connection between technology and students’ outcomes at all subject areas and

school levels. These researches reveal that students in a technology enrichment

environment complete their work more quickly, show more work cooperatively,

express positive attitudes about the class, self-motivation and understand the

information in a variety ways (Keller & Suzuki, 1988; Kramarski & Feldman,

2000; Lee, 2000; Waxman et al., 2002; Edyburn, Higgins, Boone, 2005; Fox,

2005 and Viadero, 1997).

To sum up, the views on what exactly educational technology may include can be

explained in four major perspectives. The first perspective is educational

technology as media and audiovisual communications. This view emphasizes the

use of films, slides, and videos instead of books and lectures as a more effective

way of conveying information (Roblyer, 2006). The second one is also

educational technology as instructional systems, which focus on developing

efficient systems of instruction and training using both teachers and technology.

The third perspective considers educational technology as technology education or

vocational training. Roblyer (2006) summarized that they advocate teaching

technology using hands-on experiences within the context of mathematics,

science, and other disciplines and focus on improving technological literacy in

order to get ready learner for the work wold (Roblyer, 2006). The last perspective

is instructional technology as educational computing or computer systems used to

support administrative and instructional personnel. These computer systems help

educators in all educational levels use technology to assist instruction (Roblyer,

2006). Using technology in classroom is essential for increasing their productivity

as well as enhancing teachers’ instructional strategies. Hence, integration of

technology expands classroom instruction and management.

2.3. Integrating Technology in Turkey

As far as the integration of technology in Turkey is concerned, Yildirim (2007)

has recently conducted a study with 402 basic education teachers about teacher's

13

current use of Information and Communication Technology (ICT) in the Turkish

basic education schools and the barriers of effective technology integration.

Although teachers have been usually held responsible for the success or failure of

ICT in schools, there are indeed a number of barriers for the diffusion of ICT

(Yildirim, 2007). Some of the findings of his study are as follows:

Teachers largely used ICT to create handouts and tests, rather than to

use it to promote students’ higher order cognitive abilities.

Due to the lack of pedagogical and in-service support, teachers ranked

the lowest frequency for the use of instructional software.

Accessing computers technology is another important issue in the

technology integration process.

Lack of principal support, lack of collaboration among teachers and

inflexible curricula are also negative factors impeding the integration

of technology into the curriculum.

The most recent project of the Ministry of Turkish Education "Movement of

Enhancing Opportunities and Improving Technology" known as FATIH is the

most expensive educational project of Turkey and the World. It is estimated that

the project will cost approximately 3 billion TL in three years. For example, this

projects includes that all schools around the country will be equipped with smart

boards. In addition, more than twelve thousand tablet computers were equipped in

almost fifty schools in seventeen provinces in a pilot part. Then, the project will

spread all over the Turkey. This means that according to MoTNE (2012), almost

forty thousand schools and more than six thousand classes will be distributed with

the these information technologies and turn into computerized education classes

(Smart Class) (MoTNE, 2012)

2.4. Integrating Technology into Mathematics Education

Information technology is now seen as a part of our life, and the field of education

is no exception. When used appropriately, educational technology can have an

14

immense impact on students, instructors, and administrators in our education

system. To emphasize the necessity of educational technology, Alkan (1991)

maintained that it is necessary to utilize educational technologies to provide

educational service to masses of people, to serve high quality education, to meet

different needs and demands of the society, to use human resources more

effectively and to increase equal opportunity in education. Yildirim (2007) also

supports that there seems to be a widespread agreement among researchers,

practitioners and policy makers on the field of education that the using technology

in education improve the teaching and learning process. Another statement about

the implementation of technology was made by Besnoy & Clarke (2010). They

suggest that teachers can use wikis, math casts and the Texas Instruments (TI)

graphing calculators in their classrooms student response systems.

Especially in mathematics education, technology is generally considered as a

vehicle of information which is calculators and computers. They may be used in

the classroom (Simonson & Thompson, 1997). Many articles in the literature

emphasize the need for in-service activities for teachers learning how to use

calculators and computers. Moreover, there is also necessary how to integrate into

the classroom. Using technology in classrooms, for example, will enable students

to become technologically literate in order to be successful in today’s society

(Roblyer, 2006).

Considering that technology serves today’s students well in educational settings, it

would be true to claim that using technology in mathematics education can

expand the range of the math content and problem situations that were previously

beyond the grasp of students and can facilitate higher-order learning, such as

posing problems, solving problems, and making decisions by using tools for

computations and visual illustrations (NCTM, 2003).

Whether the benefits of technology in the classroom outweigh the costs of

implementation or not is a controversial issue. However, time for the teacher to

plan, assess, and work with students is one of the major benefits gained from

15

technology. Because these educational media have become more influential,

smaller, and inexpensive; they have already become accessible for use of students

and teachers, which has resulted in the perception that technology use has

increased simply as technological equipment is being used nowadays (Sorensen,

1996).

Technologies, especially the use of the interactive whiteboard, allow teachers to

create more concise and focused lessons, as well as to move forward and

backward in their lessons with ease. In addition to this, teachers are able to

conduct quick reviews of entire lessons, instead of taking the time to rewrite the

information on the board again for the next class. With the use of the computer,

the lesson is already there, so the teacher simply has to open up the document and

review the information. The students or parents could also get the lessons via e-

mail from instructors if they missed a class. Certain technology programs allow

the teacher to provide instant feedback to the students as well (Kent, 2008).

Traditional way of teaching mathematics, on the other hand, generally causes

students to replicate mathematical routines without developing much conceptual

understanding. In other words, students do not see the point in plotting a graph,

performing computations, or writing papers by hand when they realize that the

workplace will require technological literacy (Heide & Henderson). Allowing

students to perform these activities using technology will give them more

experience in using higher-order thinking and problem-solving, other demands in

the workplace (Heide & Henderson, 1994). Besides, the incorporation of new

technology such as TI-Nspire graphic calculators quickly motivates teachers to

confront with basic educational issues. This new technology rebuilds relationship

among the fundamentals of pedagogy, content and technology (Curaoglu, et al.,

2010).

One of the studies dealing with the incorporation the mathematics classroom and

technology is TI-Nspire conducted by Curaoglu et al. (2010), which employ a new

instructional tool in order to engage pre-service secondary mathematics teachers

16

and to support mathematics instruction in exploring new ways of teaching

mathematics. The study aims to find out positive and negative evidences in how

pre-service mathematics teachers use the graphing calculator in teaching concepts

and procedures of mathematics. Various experiences containing an imaginary

teaching scenario involving TI-Nspire, class reflections, and lesson plans were

completed in the study. At the end of the study, evidences about aspects of

teaching with technology were gathered form participants (Curaoglu, et al., 2010).

The findings of the study are following:

The technology used in the study helped as stimulator and a tool in

encouraging pedagogical consideration within the learners.

Confronted with the strength and limitation of the new technology,

learners practiced the tension between their instructional materials

which they had to recreate and traditional curricular materials (e.g., the

handouts and textbook).

The new technology made encounters between learners’ awareness of

new changes devices and their traditional view of mathematics

teaching. It means that the traditional approach to mathematics class

causing a pressure on learners.

Another result of study is that innovates encouraged among the pre-

service teachers a willingness to learn on their own and with their

students. Innovates may provide the emergence of certain openness in

their instructional methods for teaching. Participants also expressed

that it is essential for training, peer assistance and further support.

Learners who participated to this study have different beliefs and prior

experience about teaching and assessment. These properties of

participations played a significant role in their justification of

instructional approach which formed their learning practices on the TI-

Nspire project.

Computers in classrooms can contribute to education in terms of active learning

which helps the presentation of information in a variety of manners in addition to

17

giving students maintained attention and reliable feedback. Some examples of

effective computer usage in instruction are the interactive computer in class

(Hughes et al., 1999; Naatanen, 2005; Baptist, 2005) and video storybook with

interactive screen (Hughes et al., 1999). Moreover, technology usage is

surprisingly low although situations like accessing technology in schools in order

to maintain successful technology integration, enriching the education for teachers

and adjusting necessary political organizations have been constituted (Ertmer,

2005).

Olkun, Altun, and Smith (2005) examined the potential effects of computer

technologies on geometry scores of students as well as their geometry learning.

One of major outcomes was that students in experimental groups performed better

on geometry learning than those in control groups. The researchers recommend

that schools should integrate technology and mathematical content in a method

that facilitates students to discover and understand the connection between 2D

geometric figures. A similar research study was conducted by Isiksal and Askar

(2005) working on the effects of dynamic geometry software and spreadsheet on

mathematics self-efficacy and mathematics achievement of students. One of the

main findings of the study was that students’ mathematics achievement was

improved in group which employed technology as a learning tool.

In the report written by Kulik (2003), studies measuring the effect of computer

enrichment on mathematics tests, writing and reading were mentioned. The results

of the examined researches revealed about effects on computer enrichment

programs. In most of the studies, whereas computer enrichment programs had

trivial positive effects on student writing, they had much higher effects in

mathematics achievement. In the remaining study, this program had a trivial

negative effect on students’ writing but this result was statistically significant.

Another research study was conducted in an Irish primary school by Ryan (2002)

to see the effects of computer use integrated into the sixth class. The effects of the

computer use were found to be students’ creativity, self-esteem, academic self-

image, academic achievement as well as their motivation and attitude towards

18

computers. The findings of the study are as follows:

Positive impact of using computer on the self-esteem of lower

students and the academic self-image of high and average

students

High and average students benefiting from computer use

according to creativity scores

Some positive evidences were realized about computer use on

attitude towards learning, student motivation and learning

environment

Enhanced learning with computers rather than traditional

methods

Another interesting research was conducted by Tall and Chae (2001) about visual

meaning attached to symbolic ideas in mathematics. An experimental approach

was used in the study through a computer program to give visual meaning to

symbolic ideas and to be a source for further generalization. The motivation of

this study stems from the fact that participants desired to think algebraically rather

than geometrically while they were solving. However, computer assisted learning

which uses graphical representations can improve students’ mathematical

understanding in general because graphic software can provide students with

facilitated intuitive thinking previous the construction of a formal concept. The

result of the study shows that visualizing concepts and manipulating symbols

provide some benefits to students helping them to better develop concepts. This

means that interacting with computer software might help students who did not

achieve highly in mathematics, especially in conceptual knowledge which is

difficult to understand.

Depending on the properties and difficulty of the problem, several approaches

may help students on mathematical problem solving. While a couple of them

19

targets the procedural and declarative knowledge problems, a couple of them

emphasis on learners’ trouble with conceptual understanding and others

concentrate on improving students’ critical thinking and reasoning.

Anchored instruction is an approach using video technology to produce materials

about daily life mathematics problems (Cognition and Technology Group at

Vanderbilt, 1997). This instruction can be also used with regular and special

education students effectively. In this manner, this approach may show the

importance of situating or anchoring mathematical knowledge in meaningful and

daily life applications. Therefore, this approach helps students overcome their

challenges. Moreover, these anchored instruction environments combine audio-

video technologies in a story format. Because students deal with the characters or

events in the story, they are already situated in the problem and motivated to find a

solution for these problems.

The researchers have carried out several studies about the effectiveness of

anchored instruction environments. For instance, learner who received the

anchored instruction environment achieved significantly higher than leaner in the

traditional instruction groups on a variety of transfer tasks, contextualized video

problems, including complex text problems, and applied construction problems on

the mathematical problem solving (Bottge and Hasselbring, 1993; Bottge, 1999;

Bottge et al., 2002; Bottge et al., 2004)

There are many other studies proving that visualization increases the attention and

curiosity of students and helps students for conceptual learning. To illustrate,

Soylu and Ibis (1998) stated that using computer for teaching, teachers take

advantage of opportunity of visualization of the physical phenomenon to show

their students in there dimensions.

Interactive whiteboards are one of the current trends of instructional electronic

devices designed for teachers' use in the classroom to support students' learning.

Although this technology was first used in the beginning of 1990 in the United

20

Kingdom, it is still believed as a new tool of technology equipment for the

education system. According to Betcher and Lee, (2009), the interactive

whiteboard provides teachers with all the advantages of a computer, but with a

large screen, enabling larger groups to view the information. Everyday technology

companies are trying to enhance interactive white board software in order to make

it smarter. Roblyer (2006) assumes that this interactive software can also provide

supplemental activities for students that would be difficult to include otherwise.

Students are also able to visualize concepts that are generally difficult to

understand without using interactive software (Heide and Henderson, 1994).

To sum up, more research studies implemented so as to investigate the effects of

methodology on learners’ accomplishment should be done in a technology

enrichment environment. Some studies acknowledge technology-supported

education. For example, research on educational technology concludes that

student motivation and attitudes definitely reflect improvement when technology

is used in the classroom (Clements and Sarama, 2005). However, technologically

enhanced classrooms widely prefer constructivist learning as a learning theory.

Wetzel (2004) also stated that technology promotes constructivist learning

(Wetzel, 2004). However, there is a confliction about assessment standards

because of constructivism principles. Evidence is not as conclusive in evaluating

the degree of knowledge attained (Veronesi, 2004).

2.5. Mathematical Problem Solving Skills

Problem solving is usually considered equally a vital cognitive activity in daily

and business contexts and has become an important survival skill in our

technologically advanced society (Wu, Custer and Dyrenfurth, 1996). It has been

also recognized and encouraged by various disciplines, such as psychology,

science, mathematics and other. Instructional theories help us to find a path to

enrich the process of learning and teaching in all those disciplines. For instance,

cognitive theory has existed for complex forms of learning requiring higher-level

21

skills. Similarly, behavioral theory is for strengthening stimulus-response

associations or constructivism is for advanced knowledge acquisition. However,

this is only one point of view; the content or in other words, subject matter.

Likewise, it is believed that behavioral approach can effectively help mastering the

content (knowing what), cognitive strategies are beneficial for problem solving

procedures (knowing how) and constructivism for dealing with ill-defined

problems through reflection interaction. (Ertmer and Newby, 1993).

The subject of problem solving is important in the mathematics studies. Improving

the skills to solve complex mathematics problems is a primary aim of mathematics

teaching and learning which includes abstracting, classifying, analyzing, searching

for patterns, comparing, conjecturing, generalizing, convincing, explaining,

proving, modeling (Putnam, Lampert and Peterson, 1990, Krulik and Rudnick,

1983). In the literature, many research studies, opinions and theories were

published so that the act of problem solving in mathematics and science could

have tried to explain and better comprehend (Polya 1957; Henderson and Pingry

1953).

In addition, researchers and practitioners in education have seek ways to

comprehend the learner’s abilities to solve complex problems and to encourage

them problem solving in science and mathematics (Kilpatrick, Swafford, and

Findell 2001; Lester 1980; Schoenfeld 1988, 1992; Silver 1985). Moreover, the

concept of problem based learning is another popular research area. Many

researchers carry out studies to inquire ways to solve the problems about daily life.

Improving problem solving skills effects creativity, achievement, logical thinking,

attitude and concept learning as an indicator of the quality in science education

(Yaman and Yalcin, 2005; Akinoglu and Tandogan, 2007).

Another study was conducted by Pimta, Tayruakham, and Nuangchalerm (2009)

who gave a mathematic problem solving ability test and questionnaires to 1027 6

grade students. The results of their study revealed factors that affect mathematic

problem solving ability. The result of the study was that factors influencing

mathematic problem-solving ability were attitude towards self-esteem,

22

mathematics, teachers’ teaching behavior in the classroom, motivation and self-

efficacy. It was also revealed that the visual data had an influence on mathematic

problem-solving skills. As the implication of the study, the researchers suggest

that the teachers should study the methods to develop mathematic problem-solving

skills and prepare activities to enable students to be enthusiastic to learn and

improve positive attitude toward mathematic learning.

There are various ways of highlighting problem solving in learning environments.

Placing students in the center of ill-structured, complex, real life and meaningful

problems which has mysterious solutions is one of mutual properties of these

approaches (Lavonen, Meisalo and Lattu, 2001). In these kinds of authentic and

student centered environments, students behave as expert in the learning

environment and challenge the problems which do not enough information, entire

limits. Students have to find the finest likely solutions until its due date. Many

kinds of authentic and student centered environments, for example, open-ended

learning context was of them (Hannafin, Hall, Land, and Hill, 1994; Land and

Hannafin, 1996), problem-based learning (Barrows, 1985; Barrows and Tamblyn,

1980) and goal-based scenarios (Schank, Fano, Bell, and Jona, 1994) have

mentioned in the literature as ways of focusing on problem-solving outcomes.

In order to solve mathematical problems, it is better to be processed systematically

which is separated into the pieces in the process of making solutions. The four-

stepped model (understanding the problem, making a plan, implementing the plan,

and review your solution) of Polya, who is considered as the father of the modern

focus on problem solving in mathematics education (Passmore, 2007), has widely

been accepted by educators by way of improving student problem solving skills in

the classroom. After the publication of “How to Solve It”, the two books

“Mathematics and Plausible Reasoning” and “Mathematical Discovery” were

published respectively in 1962 and 1965.

The four stages of Polya’s (1957) problem solving are as follows:

23

1. Understanding the problem. Understand the verbal statement of the

problem. Study the data and the condition. Determine the unknown.

Draw a figure and develop a suitable notation for the problem.

Separate the parts of the condition in order to get a better

understanding.

2. Making a plan. Try to find a connection between the data and the

problem. Consider whether the earlier methods can be used now.

Develop a plan considering which calculations, computations, or

constructions to perform in order to obtain the unknown.

3. Implementing the plan. Examine the details of the plan. Check each

step carefully. Implement the plan step by step.

4. Review your solution. Examine the solution and the path to obtain it.

Consider how to apply the result to other problems.

In the first stage of Polya’s model, students must read the given information. Then,

they have to decide what to ask, what they need to find out and which information

presented is relevant to this goal. The students who have difficulties in reading

mathematical text for understanding hold the idea that mathematics is a language

all its own (Philips at all 2009). Students have to make a broad plan and choose

applicable strategies or appropriate drill and practice so as to solve the problem in

the second phase of Polya’s process. This stage includes relating information in the

problem to the problem-solving schema which provides students to shape and

identify their thought processes. The third stage also deals with students'

performance in the computations to implement the plan created in the second stage

and find the solution. The last stage is the looking back phase in which students

looked back what they have done, review their solutions if it is correct or not, and

reflect how to use these finding in other problems.

2.5.1. Problem solving process

Problem solving, which is also a process, takes place in several pattern relaying on

the situation, task, and the context. First of all, it is worth mentioning what the

problem includes. Anderson (1985) maintains that every problem consists of three

24

parts: givens, a goal, and obstacles. In this process, defining or understanding the

problem, interpreting data, drawing a schema, designing, creating a model,

utilizing and testing may be considered as means to solve problem and obtain

result.

Assessment methods of the problem solving process should be considered before

investigating the problem solving process of the students. Several approaches,

such as thinking aloud, introspection, retrospection, and written inventories could

be employed in this process (Lester, 1980). Think aloud approach is also an

important one that has led to a lot of research and ideas in the literature. For

example, think aloud techniques have been used as a research technique to access

people’ thought while they were dealing with a task in several content areas, such

as reading, history, and chemistry (Bowen, 1994; Crain-Thoreson, et al., 1997;

Weinburg, 1992). In mathematics, this method is generally used in order to

investigate processes which has includes the problem solving properties

(Kantowski, 1977; Kilpatrick, 1969, 1978) and to analyze individual differences

(Rowe, 1980).

Polya (1947) describes the process of problem solving as a strait development from

one phase to the following phase while solving a problem. Non routine problems

associated to mathematical subject in the literature are related to different

mathematical content areas. Obviously, these problems may have affected the

students’ processes of problem solving and their solutions depend on complexity

and diversity. Because of this, the evaluation of process while solving the

mathematical problem might give the educator more evidence instead of its result.

On the other hand, the ability to solve simple real life-based non routine addition

and subtraction operations is the basis for developing the ability to deal with

complex problems in mathematics. Huang, Liu and Chang (2012) conducted a

research study on Taiwanese students. Results showed that students who have

mathematical learning difficulties turned out more upset when the difficulty and

complexity level reached upper levels.

25

2.5.2. Problem Solving Strategies

The results of many research studies showed that students who has high problem

solving skills develop a representation of the problem they are attempting to solve.

Furthermore, students with higher problem solving skills construct a mental model

of the information and the relationships among the elements of the problems

(Riley, Greeno, and Heller, 1983). Students may take this information to select a

solution strategy and apply the strategy to find the answer. According to O’Connell

(2007), improving problem-solving skills through the teaching of strategies

requires attention to building both mathematical skills and the thinking process.

Babbitt and Miller (1996) create a list of strategies used to improve problem

solving skills (see Table 2.1). The most common components of these strategies

are: “reading the problems carefully, thinking about the problem via self-

questioning or drawing, visualizing, underlying, or circling relevant information,

determining the correct operation or solution strategy, writing the equations, and

calculating and checking the correct answer” (Babbitt and Miller, 1996, p. 392).

These components are also challenging for a variety of reasons for students to

solve mathematical problems. Hasselbring, Lott, and Zydney (2006) classified

these challenges about problems; declarative knowledge, procedural knowledge,

and conceptual knowledge. From their perspective, learners to be able to solve

mathematics problems have to get kinds of knowledge such as declarative,

procedural, and conceptual. In addition, students need know fundamental

mathematical facts and the strategies and procedures which implemented in order

to solve the problem. Moreover, they have to apply their knowledge into the

mathematics problem solving process.

26

Table 2.1. Problem-solving Strategies cited from Babbitt & Miller (1996)

Researchers Strategy Steps Strategy Steps

Babbitt (1993) Read the problem

Underline the problem

Choose solution strategy and solve

Check, “Is the question answered?”

Check, “Does the answer make sense?”

Consider applications and extensions

Bennett (1981) Read the problem

Underline numbers

Pre-organize Reread the problem

Decide on the operation

Write the mathematical sentence

Post-organize Read

Check operation

Check math statement

Check calculations

Write labels

Case, Harris, and Graham (1992) Read the problem out loud

Look for important words and circle them

Draw pictures to help tell what is happening

Write down the math sentence

Write down the answer

Fleischner, Nuzum, and Marzolla -

1987 Read

Reread

Think

Solve

Check

Kramer (1970) Read the problem

Reread the problem

Use objects to show the problem

Write the problem

Work the problem

Check your answer

Show your answer

27

Table 2.2. Problem-solving Strategies cited from Babbitt & Miller (1996) (cont’d)

Miller and Mercer (1993) Find what you‟re solving for

Ask what are the parts of the problem

Set up the numbers

Tie down the sign

Then to compute the answer… Discover the sign

Read the problem

Answer, or draw and check

Write the answer

Montague and Applegate (1993) Read

Paraphrase

Visualize

Hypothesize

Estimate

Compute

Check

Polya (1957) Understand the problem

Devise a plan

Carry out the plan

Look back to verify that the answer is reasonable

Snyder (1988) Read the problem

I know statement

Draw a picture

Goal statement

Equation development

Solve the equation

Watanabe (1991) Survey the question

Identify key words and labels

Graphically draw problem

Note type of operation (s) needed

Solve and check problem

28

2.5.3. Problem Solving in Classroom

Reviewing the literature, it would be true to state that problem solving skills have

received a lot of attention. Several authors maintained that getting solution in

learning mathematics successfully requires better problem solving skills (Gagne,

1985; Mayer, 1992). In this modern computer technology age, the focus of many

research studies have been switched from the traditional learning and teaching

environments to online, interactive teaching methods and mediums by tablet

computer and mobile devices in the classroom. The use of computers and its

practice results obtained research related to problem-solving teaching strategies

will support learners to get more effective learning (Huang, Liu, and Chang, 2012).

In addition, teacher and curriculum design studies are increasingly calling for more

emphasis on “higher order thinking skills” and technological problem solving. The

classroom and instructional activities are the most important ones for students'

learning and the outcomes for education (Webster and Fisher, 2000; NCTM, 2000).

Moreover, Toluk and Olkun (2002) stated that in order to develop children’

problem solving skills, children have to take opportunities to practice in real life

problem conditions in their mathematics classrooms.

Problem solving has special attention in the mathematics class. The brief summary

made by Stanic and Kilpatrick (1989) is as follows:

“Problems have occupied a central place in the school mathematics

curriculum since antiquity, but problem solving has not. Only

recently have mathematics educators accepted the idea that the

development of problem solving ability deserves special attention.

With this focus on problem solving has come confusion. The term

problem solving has become a slogan encompassing different views

of what education is, of what schooling is, of what mathematics is,

and of why we should teach mathematics in general and problem

solving in particular.”

29

More importantly, pre-service mathematics programs should be organized to

prepare the teacher to teach mathematics using problem solving approach. In

addition, problem based activities aim to learners to improve an understanding of

the subject knowledge (Sprague and Dede, 1999). Technology should be used as

instructional tools to assistance students solve the problem. Therefore, teacher

educators and researchers should be well informed about ways of exploring

methods of enhancing the problem solving skills of their students. According to

Lester (1994), a widely acceptable rule is that problem difficulty should organize

not a function of numerous task but rather characteristics of the student. Thus,

teachers have an important role to create a learning environment setting up

situations for students allowing them to explore mathematics.

Problems used in the classroom should be proper for students' level, suitable for

their knowledge and experience to solve the problems. Otherwise, problem solving

success of the student appears to be below than expected. The reasons of this may

be the lack of some of the appropriate abilities of students, such as reading,

translating and representing ability to understand the problems. The factors

affecting the problem solving process are as follows:

The problem difficulty and complexity

Students’ learning styles and their strategy preferences

The problem solving instruction is also a popular topic in the field of education in

general. Many research studies are available in the literature. Verschaffel et al.

(1999) showed that students on the fourth and fifth grade received helped to solve

mathematical application problems in order to learn problem solving strategies. At

the end of the study, the instruction on ill-structured problems effect the students’

pattern how they solved the problems an their cognitive strategies and their

consciousness about their solutions in the fourth grade (Follmer, 2000)

Developing student’s cognitive strategies provide students different perspectives

while analyzing problems. These are making syntheses, generalize the solution

30

methods and benefit from solutions to similar problems (Niederer and Irwin,

2001). Moreover, Ridlon (2004) stated that traditional drill-and-practice does not

help many students learn mathematics. Whereas, students performed better and

their attitudes improved, which made them excited about learning by means of

involving students in the center of the mathematics problems related to their life

(Ridlon, 2004).

Investigating the professional development of teachers about how to integrate

problem solving into third grade mathematics curriculum, Hartweg and Heisler

(2007) included in their studies three third grade teachers and mathematics

education consultant who were observed modeling the teaching of problem

solving. Students were given about ten minutes before problem solving to have the

problem presented, ask question, and clarify meanings. After working together to

solve problem, all students in class discussed strategies, methods and solutions.

The result of the study showed that mathematical understanding and mathematical

writing skills of the students improved. In addition, considering teacher surveys

and student attitude surveys, they noticed that students’ confidence in problem

solving and their writing of mathematical explanation improved (Hartweg and

Heisler, 2007).

MoTNE organizes programs including professional development, coaching and

technical support for teachers as an in-service training. For teachers to encourage

their students to boost their problem solving techniques and critical-thinking skills,

they are provided a course in order to use multimedia tools and other ICT

components. After taking this training, integrating the technology of their subject

are expected to improve students’ problem solving skills and achievements.

2.6. Attitude towards Mathematics

Developing technology and its integration to education have conveyed new and

impressive changes in the educational environment. Instructional technology has

played an influential role in these changes as it is found to be an effective tool to

31

redesign the instructional learning environment and to improve students'

achievement and attitudes towards learning (Salomon, Perkins, & Globerson,

1991). In addition to this, adequate budget, qualified mathematics teachers,

motivating and challenging curriculum, positive attitudes towards mathematics,

and real-life experiences involving mathematics are some of the basic factors to

perform higher in terms of mathematic achievement level among all countries. One

of the reasons for students’ failure might result from their feelings of failure and

inadequacy, hatred about the subject of mathematics and more possibly a great

defeatist prejudge.

Therefore, it could be suggested that positive attitudes towards mathematics are

needed for students to take the mathematics course. To illustrate this point,

Marzono (1992) expressed that a positive attitude towards mathematics is

necessary so that student can develop confidence in his or her ability to do the

mathematics. This is followed by the teachers’ responsibility to provide

mathematics instruction and to improve students’ attitudes. More specifically,

students’ attitudes towards mathematics are dependent upon the instruction that the

student received (Jackson and Leffingwell, 1995).

Beliefs and attitudes of teachers can be significant indicator of technology uses.

Teachers’ choices to accept and rate the technology use in the classroom rely on

their beliefs and attitudes toward technology. In other ways, improving teachers’

technology usage in class involves shifting their beliefs about technology

positively. It is obvious that one of the ways to changing teachers’ beliefs is to

make available chances for teachers to gain familiarity with technology.

Moreover, students’ attitudes are affected by several factors. Computers and

calculators are popular technological tools which are appropriate for some

educational situations or all mathematical subjects. In the literature, it is argued

that the use of graphing calculators in mathematics instruction takes sufficient

attention, research evidence. Besides this, using calculators and computers in

mathematics classes showed positive evidences in students’ attitudes towards

mathematics and in the performance in their coursework (Sheingold and Hadley,

32

1990; Honey and Henriquez, 1993).

Another study by Bilican, Demirtaşli and Kilmen (2011) was carried out to

conclude if the attitudes of the students participating in the both TIMSS 1999 and

2007 projects towards the “Mathematics course” had changed in the course of the

study during the project. The sample of TIMSS 1999 was comprised of almost

eight thousand 8th

grade students and the sample of other TIMSS was comprised of

4498 8th

students. Stratified sampling method was used the selection of the students

within the ratio of seven geographical regions and schools. The results of the study

showed that by means of cooperative learning activities, students can establish a

relationship between daily life and their mathematics learning. Consistent with the

findings of the study related to the attitudes of the students towards mathematics

and self-efficacy beliefs, it can be realized that students could develop more

positive attitudes towards mathematics and perceive themselves more adequate in

mathematics in years.

Ellington’s report was also a good example to summarize their result. Along with

the results of the report, the improvement of problem solving skills had substantial

outcomes when materials were designed especially for using with the calculator

and similarly for graphing calculator. Ellington (2003) made a meta-analysis in

order see whether working with calculator improved students’ attitudes toward

mathematics improved or not. According to Ellington, results indicated that

working with calculators had affected positively students’ attitudes toward

mathematics.

There is not large amount of research evidence for the effect of mathematics games

despite teaching mathematics with technology has a difficult process which

composed of cultural, social, and technical factors. The issue of computer

mathematics games is one of the popular topics to work on. A research study

conducted by Abrams (2008) about the influence of computer mathematics games

on students’ mathematics motivation and achievement in different school levels

yielded positive evidence on student’s attitudes and achievements. He explains that

33

an analysis of all pre-post data which was collected from students, teachers and

parents showed that playing games on computer motivates children to learn

mathematics and improve students’ self-efficacy for learning mathematics, their

attitudes towards mathematics instruction and their curiosity in mathematics

activities.

Similarly, Spotnitz (2001) also conducted an experimental study to investigate how

mathematics games affected intrinsic motivation, task involvement, self-efficacy

and achievement. The sample of the study includes 83 fourth through sixth grade

students diagnosed as learning disabled in mathematics. Games were chosen for

the students in the treatment class. The students played the computer games related

to a fantasy design, personalization and manipulation for four, 30-minute sessions

over four weeks rather than receiving traditional instruction. Self-reported

questionnaires and the total of correct responses of the experimental and control

groups on pencil and paper mathematics tests were instruments to collect data. At

the end of the data analysis, the researcher reported that positive results were

reported for intrinsic motivation, task involvement, and self-efficacy for the

students who played the computer games. In addition to this, parent observations

and responses also favored the use of computer games as a tool. A qualitative

analysis of parent observations and responses indicated approval for using

computer games as a tool. However, there was no significant increase in the rate of

improvement about mathematical achievement in both groups.

Another relevant study was done by Asante (2012) who stated that school

environment, teachers’ attitudes and beliefs, teaching styles and behavior and

parental attitudes were identified as factors that influence students’ attitudes

towards mathematics. The researcher also suggested that the teachers ought to

develop good connection with their students and emphasize teaching activities used

for classroom. These activities should be based on active teaching and learning

properties and participation of students in the class. Besides, educators such as

teachers, researchers, school administrators and other stakeholders in education

34

ought to prepare some events like workshops and seminars in order to develop

positive attitudes towards mathematics for students, parents.

Another study conducted by Mahmud, (2001) indicated that compared to average

and weak students, successful students have strong positive attitudes towards

solving mathematics problems. Positive attitudes towards problem solving play a

vital role to achieve the success in students’ lifetime as well (Effandi and Normah,

2009; Mohd and Mahmood, 2011). To sum up, positive attitudes affect problem

solving skills which are believed to play a significant role in mathematics

achievement.

2.7. Summary

This chapter includes the necessary literature review with special focus on the

background perspectives and main standpoints in the study. Moreover, the findings

of other relevant studies about issues like achievement, technology integration to

education and classrooms, student’ problem solving skills and student’ attitude

towards mathematics were discussed. It could be concluded that if technology is

used appropriately, it is able to be very helpful to enhance educational productivity

with its power to have an impact upon achievement, learning style, attitude,

motivation etc. (Lee, 2000; Byrom & Bingham, 2001; Kulik, 2002; Waxman et al.,

2002; Barron et al., 2003; Clements & Sarama, 2003; Waxman et al., 2003;

Edyburn et al., 2005; Fox, 2005; Hew & Brush, 2007, Yildirim, 2007). The use of

technology in problem solving, attitude of students and technology integration are

the main titles of the chapter.

35

CHAPTER 3

METHODOLOGY

The purpose of this chapter is threefold: (1) to set out the main aim of the study

and research questions, (2) to provide an overview of the research design and

methods employed to address the research questions, and (3) to describe some

methodological issues that arise from the design and how these issues were

addressed.

3.1. Problem Statement and Research Questions

The aim of the study and the research questions introduced in Chapter 1 is to

evaluate the effect of technology-enriched instruction on the 6th grade students’

mathematics attitudes and the students’ problem solving skills. More specifically,

the purpose of this study is to examine the effect of technology integration such as

through direct intervention, instructor demonstration, researching on the web and

outside of classroom and weakly assignments on the students’ attitudes and

problem solving skills in the mathematics course with technology enriched

instruction. The study had four groups in two schools and addresses the following

research questions:

36

3.1.1. Research Questions

The main research question was “what are the effects of Technology Enrichment


solving skills in mathematics?” Under this question, there were eleven items

related to four sub research questions.

1. What are the effects of Technology Enrichment Instruction on the sixth

grade public school students’ problem solving skills in mathematics?

a) Is there a difference among the groups with pretest and without

pretest in terms of problem solving skills?

b) Is there a difference between the control groups that did not receive



c) Is there an interaction between pretest and treatment of problem

solving skills?

d) Is there a difference between the control group that did not receive

treatment and the experimental group that received treatment with


e) Is there a difference between the control group that did not receive

treatment and the experimental group that received treatment

without pretest in terms of problem solving skills?

2. What are the effects of Technology Enrichment Instruction on the sixth

grade public school students’ attitude towards mathematics?

a) Is there a difference in students’ attitude towards mathematics

among groups that given pretests and groups than not given pretest?

b) Is there a difference in students’ attitude towards mathematics

between control groups and experimental groups?

c) Is there an interaction between pretest and treatment on students’

attitude towards mathematics?

37

d) Is there a difference in students’ attitude towards mathematics

between control group and experimental group with pretest?

e) Is there a difference in students’ attitude towards mathematics

between control group and experimental group without pretest?

3. Is there a difference between the control groups that did not receive


principles, which are understand the problem, make a plan, utilize the plan

and reviewing the solution, of problem solving skills?

4. Is there a difference between experimental and control groups in terms of

students’ attitudes towards the mathematics scores and the students’

problem solving skill scores?

3.2. Overall Design of the Study

This study includes a combination of quantitative and qualitative research

methods. That is to say, a mixed method design was employed in the study. The

aim of the mixed method design is to answer research questions that the other

methods cannot provide better inferences (Tashakkori and Teddlie, 2003). In other

words, both quantitative and qualitative methods using together help reaching best

answers from the research. Johnson and Onwuegbuzie (2004) stated that the mixed

methods research could be defined as the class of research in which the researcher

mixed or combined qualitative and quantitative research approaches, methods and

techniques into only one research. They also characterized this research approach

as the third research paradigm. It may be used for fill in the gap between the

qualitative and quantitative research methods (Johnson and Onwuegbuzie, 2004).

Mixed methods research offers the chance to present a better diversity of views.

Qualitative and quantitative approaches ought to be diverse in a manner has

balancing each other’s strengths and weaknesses (Creswell and Clark, 2007).

There appears to be three main points that mixed methods research is better to

single research methods approach:

38

• Mixed methods approach is able to solution research questions which

only one research methodologies cannot.

• Mixed methods approach provides enhanced (stronger) inferences.

• Mixed methods approach offers the chance on the presentation of a larger

variety of contrary sights

In the study, both quantitative and qualitative data collection methods were

simultaneously addressed in both collection and analysis procedures. According to

Creswell and Clark (2007), QUAL + QUAN was utilized in this study, which

means that both qualitative and quantitative methods were utilized at the same

time during the research and both have equal emphasis in this study. Then

inferences were made on the foundation on the collected data. The most favorable

design is the triangulation design in order to validate or expand quantitative

results. Creswell and Clark (2007) stated that the triangulation design is used for

expecting to validate or enrich quantitative results with qualitative data. This study

was designed based on convergence model of triangulation design. After

collecting quantitative and qualitative data independently, the researcher analyzes

separately sticking into the same phenomenon. At the end of the research, the two

types of results are converged in the interpretation part (Creswell & Clark, 2007).

3.2.1. The Quantitative Approach

The quantitative part of this study was a quasi-experimental Solomon four-group

research design that is a kind of the quasi-experimental design (Fraenkel &

Wallen, 2000). This quasi-experimental design was necessary for this research

because of the current circumstances in educational settings which was the

limitation of the true randomization of samples in the schools. However, groups

are assigned randomly as control and experimental groups according to this

research design. Solomon four groups (Solomon, 1946) is a very valuable

experimental design to investigate the role of the pretest. In addition to this, he

added that this research design has potentialities for revealing and weighting

certain interaction effects. These interaction effects may shed light on attentional,

39

attitudinal and perceptual factors which are mostly important in three types of

psychological experimentation: (1) transfer of training; (2) induced changes in

opinions, values, and attitudes; and (3) the effect of controlled experience on

response skills, or performances which already exist in the behavior repertoire.

Moreover, Van Engelenburg (1999) says that the treatment effect, pretest effect,

and interaction of pretest and treatment can be separated through this design.

When this design is examined as an aspect of pretest effect and internal validity, a

couple of different opinions can be seen in the literature about the one-treatment

condition experimental research designs. Campbell and Stanley (1963) compared

the Solomon four group design with the two other designs -the pre- and post-test

control group design and the post-test only control group design (see Table 3.1).

All designs mentioned above are sufficient to evaluate the treatment effects and

eliminates of the most threats to internal validity. Nevertheless, the Solomon four-

group design enhances the advantage of evaluating the existence of pretest

sensitization. Define of pretest sensitization is that exposure to the pretest

increases the effect of the experimental treatment, thus preventing generalization

of results from the pretested sample to without pretested population (Huck &

Sandier, 1973).

40

Table 3.1. Experimental designs

O = outcome measure; X = treatment; R=Randomization

In Table 3.2, Frankel and Wallen, (2010) also mentioned the Solomon Four-Group

Design which is similar to the one utilized in this study.

Table 3.2. Solomon Four-Group Design adapted from Frankel&Wallen, (2000)

O = outcome measure; X = treatment;

Design Group Pretest Treatment Post test

Solomon four-groups 1

2

3

4

R

R

R

R

O1

O3

X

X

O2

O4

O5

O6

Pre and post-test

control groups

1

2

R

R

O1

O3

X

O2

O4

Post-test only control

group

1

2

R

R

X

O2

O4

Pretest Treatme

nt

Post test

School A Experimental O1 X O2

Control O3 O4

School B Experimental

Control

X O5

O6

41

Two control groups and two experimental groups in two different schools in the

same county were employed to conduct this research study. The instructors taught

concepts and skills to their classes in the control groups as explained in the

National Curriculum of Elementary School Mathematics. Therefore, the

instruction given to the control group was called as traditional instruction. Those

classes received 4-week instruction and 16 lectures each of which was 40 minutes.

Students did not use any technological device, computer software etc. in the

control group. One of the control groups, which were randomly chosen, took

Problem Solving Skill Scale (Appendix C), Problem solving Achievement Test

(Appendix J) and Mathematics Attitude Scale (MAS) as pre-test before the unit

(Appendix B). The teacher clarified the aim of the attitude scale and both problem

solving tests to the students.

Taitt (1985) conducted a quasi-experimental research that lasted ten weeks about

the effects of the instruction on basic computer programming on the problem

solving abilities of prospective teachers. The Solomon four-group design was

employed to minimize the both internal and external validity threats. The subjects

enrolled in “Teaching Elementary Mathematics” and experimental group were

registered in “Microcomputer for Teachers” classes. The treatment, instruction of

the basic computer programming, was utilized to students in the experimental

group. Random assignments were made within both the control and experimental

groups to determine who would receive the pre-test.

Another Solomon type experimental research was conducted by David Seagraves

to measure the self-esteem of students, if ninth grade students study a novel using

theatre arts standards or not in 2008. It was considered the advantage of the

Solomon four group design that protects external and internal validity. It also used

random assignment which controlled several of the variables, such as differential

selection and statistical regression that threatened the internal validity of the study.

Seagraves (2008) stated that first two groups practiced almost the same pretest

processes. In addition, threats for history and maturation were protected in same

point. External validity was also considered. The post-test groups were also

42

protected the effects of the pre-test sensitizing since both third group and forth

group did not take any pre-tests. Therefore, they were not any pre-test effect to the

post-test data.

3.2.2. The Qualitative Approach

Qualitative study is an inquiry of understanding social or human problems based

on building a complex holistic picture formed with words, reporting detailed views

of informants and conducting the research in natural setting (Creswell, 1994).

Qualitative research has a diverse collection of procedures; however, many have

some distinguishing characteristic. As suggested by Miles and Huberman (1994), a

triangulation of various types of qualitative instrumentation is recommended to

validate the data and to provide rich descriptions of the study group. Qualitative

research contains the empirical collection of data. Therefore, the researcher

personally becomes situated in the subjects' natural setting. Miles and Huberman

(1984) described the reasons for selecting a qualitative research approach for this

type of study.

“The researcher has a fairly good idea of the parts of the phenomenon that

are not well understood, and knows where to look for these things--in

which settings, among which actors within which processes or during what

class of event. Finally, the researcher usually has some initial ideas about

how to gather the information--through interviews, observations, document

collection, perhaps even with a well-validated instrument that will allow

for some comparison between the proposed study and earlier ones. (Miles

& Huberman, 1984, pp. 27-28)”

Eisner (1991) defined six distinguishing features of qualitative study that a

researcher might consider in designing a qualitative study. These are:

1. Qualitative studies tend to be field focused

2. Qualitative studies relates to the self as an instrument

3. Interpretive character makes a study qualitative

4. Qualitative studies display the use of expressive language

5. Qualitative studies' attention to particulars

43

6. Qualitative research becomes believable because of its

coherence, insight, and instrumental utility. (pp. 32-41)

In the light of these facts and based on the literature review, this study is also

designed as a qualitative study in order to explore the differences in students’

attitudes toward mathematics scores and the students’ problem solving skill scores

comparing experimental and control groups.

To collect qualitative data, interviews were conducted and a student self-

evaluation form was used (see Appendix H). Moreover, a problem solving

achievement test and rubric were utilized in the process of collecting qualitative

data.

3.2.3. Content analysis

Content analysis is defined as developing a systematic, objective, and replicable

method for reducing words in a text into content categories centered on coding

(Holsti, 1969; Krippendorff, 2004; Weber, 1990). In other words, it is a technique

that researcher employs to make his content data in content analysis more

understandable. Qualitative content analysis was utilized to interpret and analyze

the text according to the pre-constructed constructs defined by the coding schema

(Merriam, 1988).

Content analysis concentrates on six questions according to Krippendorff (2004):

What is the text that will be studied?

What is the question that will be answered?

What is the population that will be studied?

What is the measurement of the concept?

What are the inferences?

What is the validation of the inferences?

44

Content analysis is a device that allows a researcher to achieve an unbiased

analysis of recorded evidence while sorting through and categorizing vast amounts

of information in a systematic approach with ease (Krippendorff, 2004). It is

crucial that contextual phenomenon in content analysis has to be evaluated in order

to obtain a valid inference of the context for findings. This type of methodology is

a “technique for making inferences by objectively and systematically identifying

specified characteristics of messages” (Holsti, 1969, p.14) and for studying the

patterns and trends according to recorded communication of people (Babbie,

2004).

Curricula, paintings, policies, and transcripts are all a part of “the study of

recorded human communication” (Babbie, 2004, p. 314). In particular, a

curriculum conveys information that is intended for a learner to learn. This method

is a convenient tool for concentrating on an institutional group, individuals, and

social awareness topics (Weber, 1990).

As this study seeks to understand and learn from the experiences of both students’

attitude and problem-solving skills on technology enriched instruction in a

mathematics course, observation notes and students’ class works were analyzed as

a part of the data collection procedure for this study. The primary goal for using

different data collection sources was to triangulate the information to validate the

accuracy and adequacy of the information.

3.3. Subjects and Context (Math Courses)

3.3.1. Subjects of the Study

Purposeful sampling strategy utilized to select the sample in this study. This

sampling can be seen a principal sampling strategy in qualitative research. It was

preferred on cases that have considerable amount of data, which need be studied in

depth (Patton, 1990). In addition, Fraenkel and Wallen (2000) stated that the

45

strengths of the purposeful sampling from convenience sampling are that

availability is not just an issue for researchers but also their decision which based

on their backgrounds to select a sample that they believe will provide what they

need.

The subjects of this study were selected from Pasakoy Primary School (School A)

and Milli Egemenlik Primary School (School B), Bolu, Turkey. Several schools

were investigated to select suitable schools in Bolu, which was a pilot project city

for the new mathematics curricula. Although many of the schools have been in the

center of the Bolu, there were not any computer labs in the school. Some of the

schools have computers but the physical conditions of schools did not allow them

to set up the computer labs. After the school managers were interviewed, the

schools were selected for the pilot study. The researcher obtained permission to

conduct research from the university that was currently enrolled and from the

Ministry of Turkish National Education (see Appendix A). Classes were randomly

assigned to treatment and control groups as it can be seen in Table 3.3.

The groups were selected randomly as control and experimental groups by

drawing lots. Only six students in the experimental group randomly selected in the

classroom list were interviewed in the study.

Table 3.3. Participants of the Study

Treatment class Control class

School A 6/B 6/A

School B 6/A 6/B

Those schools have very big computer labs and their computers have excellent

hardware configuration. In addition, the physical condition of the computer lab

was very convenient for this study. The administrators of the schools and

mathematic course teachers were eager to participate in this study in their school.

46

The teachers also used supplementary scenarios during the unit that focused on

problem solving skills. The numbers of participants of study are presented in

following Table 3.4.

Table 3.4. The numbers of participants in this research.

Treatment Group Control Group

Pilot Study School A Group 1 19

Group 2 21

School B Group 3 17

Group 4 24

Main Study School A Group 1 27

Group 2 32

School B Group 3 16

Group 4 13

3.3.2. Math Courses

The aim of this research is to integrate technology into education. That is to say,

relatively unstructured activities and projects of various types, such as games,

simulations, tutoring, and spreadsheet template were provided to fill in the cells

with mathematics formulas to express what they understood in the mathematics

class. According to NTTM (2000), using technology in mathematics instruction

ought to facilitate and support problem solving, conceptual development,

reasoning, and exploration. Activities aiming to engage students in a given case, to

develop problem solving skills and to increase students' understanding of how to

use mathematics in real-life situations with technology were used. Spreadsheet that

is often considered as one of the components of computer literacy and web

browser was chosen as a learning tool in the mathematics class. Therefore, an

enriched classroom experience was built to encourage and motivate students in the

lab setting. In this study, students acquire how to apply mathematics to real-life

situations using technology. They learn about how much it costs to build a regular

47

basketball field, and then use the Internet browser and Excel to collect data. The

students analyze their own basketball field then present it by PowerPoint.

In this study, the control and the experimental groups were taught by the same

teachers. In the control group, the teacher used traditional methods to conduct

their lessons and to help students achieve the goals set by the Ministry of National

Education. Whereas, in the experimental groups, the teacher taught half of the

weekly lessons in the classroom and covered the remaining two forty-minute

lessons in the computer laboratory using Technology enriched instruction. The

instruction applied in the experimental group was provided by the teachers

according to the lesson plans prepared by the researcher.

Lesson plans: Lesson plans which are developed to guide teachers to organize

materials used to help the students to achieve intended learning outcomes were

developed according to National Educational Standards. Improving the integration

of the technology into teaching will enhance students' problem solving skills. The

aim of the lesson plan is to illustrate students many important concepts, such as

cost, time, planning, designs, teamwork, and application in learning about real life.

Students also deal with tasks that require transferring mathematical knowledge to

project on the computer lab. Lesson plans are attached as Appendix E. Sample of

the lesson plan presented in the following;

Students were asked to design their study rooms. However, in order to convince

their families, they were asked to prepare a list after searching the furniture prices.

By this means, students were expected to complete a real life problem by applying

technology, research and problem solution skills into mathematics. The suggested

activities for this task are as follows:

Showing students how to use Excel calculation tables.

Showing them how to write formulas into cells in Excel.

Explaining the ways of using internet to do research.

Measuring the room (walls, windows, doors, armchairs etc.).

Entering the measurements into an Excel file and naming this file

as “measurements”

48

Drawing the new shape of the room by opening a new Word file.

Designing the new plan for the room using the measurements.

Entering the names and the prices of objects in the new room into

the Excel file previously opened.

Calculating the cost and the value-added cost of the objects by

means of mathematical formula in the Excel.

Activities: The classroom activities promote interactive and open-ended

exploration of mathematical concepts, take advantage of web searching and

spreadsheet capabilities that allow the students to extend further or significantly

enhance what could be done using paper-and-pencil environment. They also give

teachers and students an opportunity to discover mathematical concepts and

improve problem-solving abilities in a laboratory-like setting. Sample activity

sheet is attached as Appendix D.

To sum up, the control group learned through the traditional teaching method in

which the teacher taught student with minimal technological aids. In other words,

no computer programs, games or no technological devices were used. The

experimental group used both the traditional teaching methods and the approved

computer programs for this study. In this case, teachers taught the class for one

day and allowed students to practice the concepts with the computers in order to

offer them with, in theory, a more interactive lesson in the computer lab.

3.4. Instrumentation

This section provides detailed information about the instruments used for data

collection. In this study, data were gathered through three scales (Problem Solving

Skill Scale, Problem solving achievement test and Attitude toward Mathematic

Scale) and the rubric for content analysis of students’ responses.

49

3.4.1. Problem Solving Skill Scale

Problem solving achievement scale, which was designed according to George

Polya’s principles, was utilized in this research. These principles are follows;

First, you have to understand the problem.

Make a plan.

Utilize the plan.

Look back on your work (reviewing).

This scale based on a revised version of Ozsoy's (2007) problem solving

achievement scale which is composed of mathematics problems include practice of

multiplication, addition, subtraction and division in order to evaluate students’

problem solving achievement. There are 20 multiple-choice items in this scale that

has five items for each of the following principles: understanding, making plan,

solution, and revision. Details of the scales are presented in the indicator (Table

3.5). After making necessary revisions, the pilot study was conducted to determine

the reliability and validity of the survey. In the literature, it was suggested that if

discriminating power of items is higher than discrimination index above .20, items

are regarded as much better (Patel, 1993). Remmers, Gage and Rummel (1967)

also have similar views.

Table 3.5. Indicators table of Problem Solving Skill Scale

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Understand

the problem

Make a plan

Utilized the

plan

Reviewing

the solution

50

Ozsoy (2007) stated that the overall Cronbach-alpha reliability of the survey was

found to be 0.84 for problem solving achievement scale, as it can be seen in the

item analysis results in Table 3.6,

Table 3.6. Item analysis results of Problem Solving Skills

N Number of questions Mean Std. Deviation reliability

200 20 11.8 3.6 0.84

After the pilot study was carried out, the selection of items were done in line with

the above criteria. The pilot study was also specifically done for this instrument.

At the end of the piloting stage, some minor revisions were deemed necessary. For

instance, questions 5 and 12 were revised as each of the questions was zero

variance and was removed from the scale. Also, expert views about the scale were

obtained and considered in the revision process. The overall Cronbach-alpha

reliability of the survey was found to be 0.84. The results of the pilot study were

presented in detail in the pilot study section of the study.

3.4.2. Attitude towards Mathematics Questionnaire

A questionnaire is frequently defined as an inexpensive way of collecting data

from a large group of respondents. It enables the researcher to obtain the

information about “the thoughts, attitudes, feelings, beliefs, values, perceptions,

personality, and behavioral intentions” of a large group of people with a minimum

cost (Johnson & Christensen, 2004, p. 164). The multiple-choice questions in the

attitude questionnaire were carefully designed to provide an accurate picture of the

learners’ opinions. The questions were closed-ended and required participants to

51

choose from a limited number of responses with “a fully anchored rating scale”

(Johnson & Christensen, 2004, p. 171).

Mathematics Attitude Scale developed by Askar (1986) was administrated in this

study as a part of study (see Appendix B). The MAS was administered to students

at METU while developing stage of this scale. It consists of twenty items about the

attitude towards mathematics both ten positive and ten negative items. The items

have five-point Likert type scale which are strongly disagree, disagree, undecided,

agree and strongly Agree. Positive items were coded starting from Strongly Agree

as 5 to Strongly Disagree as 1 (Figure 3.1). Negative items were coded from 1 to

5. This scales prepared in Turkish and 0.96 alpha reliability coefficients was found

with SPSS statistical software package program. The participants completed the

questionnaire in Turkish as well.

5 4 3 2 1

Strongly

Agree Agree Neutral Disagree

Strongly

Disagree

Figure 3.1. Rating scale in the attitude questionnaires

After conducting factor analysis, only one factor was determined by general

attitude towards mathematics. In addition, the Principal Component Analysis was

utilized same data then it was obtained similar result with factor analyses using the

SPSS package program. In this study, MAS was used to investigate students’

scores of control and experimental groups in terms of attitude towards

mathematics according to research design procedures.

52

3.4.3. Rubric for Student Response Evaluation

Rubric is a grading scale for students that shows what is required in order to

receive a particular grade or rating on an assignment (Andrade & Du, 2005). In

other words, rubrics offer the teacher an opportunity to evaluate the student's

process of a problem solving skill by levels of performance on mathematical

problems. Charles, Lester, and O'Daffer (1987) developed an analytical rubric to

evaluate students’ works. This scale has three phases or categories of problem

solving such as understanding the problem, planning for a solution, and getting an

answer. For all these problem-solving categories, 0, 1, or 2 points are assigned. A

separate score is recorded for each section: understanding, planning, solution, and

presentation. In this study, the rubric, which was developed by Charles, Lester,

and O'Daffer (1987), was used to evaluate students’ works (Figure 3.2). The aim

of this was to determine the specific strengths and weaknesses of student’s

problem solving skills in this research. Therefore, this allows the researchers to

guide for improvement for further studies.

53

Scale I: Understanding the Problem

2 Complete understanding of the problem

1 Part of the problem misunderstood or misinterpreted

0 Complete misunderstanding of the problem

Scale II: Planning a Solution

2 Plan could have led to a correct solution if implemented properly

1 Partially correct plan based on part of the problem being

interpreted correctly

0 No attempt, or totally inappropriate plan

Scale III: Getting an Answer

2 Correct answer and correct label for the answer

1 Copying error; computational error; partial answer for a problem

with multiple answers

0 No answer, or wrong answer based on an inappropriate plan

Figure 3.2. An analytic rubric for evaluating students’ work by Charles, Lester,

and O'Daffer

3.5. Data Collection Procedure

The study was conducted in almost 5 weeks, in the spring semester from beginning

of April to the mid-May. Quantitative and qualitative data were collected and

analyzed concurrently as seen in Figure 3.3.

54

Figure 3.3. Concurrent mixed method design adapted from Tashakkori and

Teddlie (2003).

3.6. Data Analysis

Creswell (2003) stated that the process of data analysis involves moving into a

deeper understanding of the data by representing the data, and interpreting the

deeper meaning of the data. Data triangulation was applied to overcome the

weakness or intrinsic biases and the other problems that come from one single

method; thus, qualitative data was collected by self-assessment reports, follow-up

face-to-face and focus-group interviews during and after the implementation. As

known, data triangulation is described as one of the most important criteria to

maintain the validity and reliability of a study and to test the plausibility of the

findings (Yıldırım & Şimşek 2005). In the study, the data triangulation was

considered; in other words, qualitative and quantitative techniques with lots of data

collection and analyzing were employed concurrently in the spring semester of the

2010 educational years.

Purpose/Question

Data Collection

Data Analysis

Inferences

Data Collection

Data Analysis

55

3.6.1. Quantitative Data Analysis

Descriptive statistics (i.e., frequencies, percentages, means, and standard

deviations) were employed to analyze the results. This analysis was done by SPSS

Statistical software. In this study, the mean pre-test and post-tests scores of the

experimental and control groups were presented descriptively in Figure 3.4.

There are many statistical procedures that utilize all six set of observations (Braver

1990; Campell and Stanley, 1963). Campell and Stanley (1963) recommend a 2 x 2

analysis of variance design for the Solomon Four-Group research. However,

Braver (1990) states that their representations was incomplete. They suggest

performing a separate additional analysis for Groups 1 and 2. The test could be a

two-group analysis of covariance (ANCOVA). Therefore, the most powerful

results can be gathered from the data.

Pretest Treatment (X)

Yes No

Yes

No

O2 O4

O5 O6

O= Outcomes measure. X=Treatment

Figure 3.4. 2x2 Analyses of Posttest Scores

The researcher used a 2 x 2 factorial ANOVA to statistically analyze and compare

scores on the Mathematics Attitude Scores (MAS) to reveal main effects as well as

interactions between variables. A 2 (i.e., pretest/no pretest) x 2 (i.e., use of

treatment /no use of treatment) factorial ANOVA compared the posttest scores

according to the pretest and no pretest scores of the MAS depending on whether or

not they are subjected to treatment as a within-groups factor and a between-groups

factor.

56

Similarly, a 2 x 2 factorial ANOVA were conducted to statistically analyze and

compare scores on the Problem Solving Skills Scores (PSS) for main effects as

well as interactions between variables in this research. A 2x2 mixed-design

factorial ANOVA also compared the posttest scores according to the pretest and

no pretest scores of the PSS depending on whether they received the treatment or

not.

The researcher used Man Whitney U test to explore possible differences between

participants’ pretest and posttest PSS tests and MAS questionnaires. This

nonparametric statistic was used due to data violations of parametric assumptions.

Sometimes variables may not distribute normally, or the samples are so small that

one cannot tell if they are part of a normal distribution or not. Howell (2002)

defined nonparametric tests as, “statistical tests that do not rely on parameter

estimations or precise distributional assumptions“(p. 467). In this study,

participants’ numbers in the groups are not normally distributed. The students`

numbers of groups in the second schools were below the 20. Using the t-test to tell

if there is a significant difference between samples may not be proper in this case.

The Mann-Whitney U-test can be used when the data do not meet the assumptions

about normality, homoscedasticity, and linearity as well as when one or more

variables are rank-ordered (Field, 2005; Howell, 2002).

Two-way MANOVA was employed in the SPSS to reveal the differences between

the scores of pretest and treatment, which are the independent variables, on

dependable variables that are problem solving skills and attitude towards

mathematics. Pretest and treatment situations are independent variables whereas

post test score of problem solving skills and attitude towards on mathematics were

included in the analysis as dependent variables at the significance alpha (α) level

of 0.05.

57

3.6.2. Qualitative Data Analysis

Structured interview questions and products that students prepared were utilized in

order to understand the process of students` problem solving and attitudes towards

mathematics. The transcripts of the interviewed students’ verbal explanations for

their problem solving processes were compared to the stages of problem-solving

skills by which results of problem solving achievement test had been classified.

The following interview questions were asked to the participants:

1. What was the first thing you did when you saw the math problem?

2. Please describe strategies that you used to help you solved the math

problem.

3. How did you know when you get the problem right?

4. What words do you use to describe your feelings when you see the math

problems?

5. Level of student`s expression about solving what he did.

In addition to interviews, the qualitative data also collected by open-ended

achievement test and student works were analyzed using content analysis.

Whereas the data collected by the Problem Solving Achievement test from the

students, descriptive and inferential analysis were utilized in the analysis phase of

the study. After data coding of the open-ended test by the problem solving skills

rubric, the similar characteristics of these codes were grouped together in order to

use for the common aspects of the categories. The frequencies and percentages

were analyzed for each category. In addition, after the interviews recordings were

listened, the transcriptions were read carefully to find out general aspects of their

content. Then, all quotes of the students were coded. These coded quotes related to

the topics obtained from the interviews were used for the definition of the

organized data. Triangulation was provided by a second scorer that was a

mathematics education professional with extensive experience in elementary

mathematics content and pedagogy.

58

In order to check reliability, all students’ works were coded by two independent

subject matter expert coders. The inter-coder reliability was found to be 85

percent, which is considered high (Ericsson and Simon, 1993). Inconsistencies

found were finalized after getting agreement between coders.

3.7. Pilot Study

The aim of pilot studies is to explore certain issues before implementing the main

study. Therefore, a pilot study was carried out in the semester prior to the

application of the study in same schools. With the pilot study, the researcher aimed

to get ideas from the learners about the treatment and testing materials so as to

collect feedback on the instructional design and its effectiveness. In order to

accomplish this aim, same research design, which is a quasi-experimental

Solomon four-group research, was utilized in the pilot study as well.

The pilot study was carried out in order to reveal whether the instruments to be

used in the current study assess what is intended to assess for the study before the

data collection procedure starts. By doing the pilot study, it was also aimed to

reveal the challenges that the researcher and the teachers are likely to encounter in

or out of the classroom and even after the data collection process in the evaluation

process. Finally, the pilot study was done to propose revisions in the case of

problems that are difficult to solve during the data collection phase. As a result of

the pilot study, it was realized that two of the items in Ozsoy’s (2007) Problem

Solving Scale do not work properly and necessary minor changes were made in

the scale. In addition, as a result of the piloting stage, a lot of experience has been

acquired by the researcher about the application of the Solomon four groups

research design which is a complicated research design.

For piloting, four groups in two public schools were focused by using all the data

collection instruments and data analysis methods before the actual study. As a

result of the analysis, the findings of the piloting stage were briefly summarized

59

below. The issues of reliability and validity in collecting and analyzing the data for

the study were also considered and discussed in this part of the study.

3.7.1. Subjects of the Pilot Study

The researcher started to implement the pilot study at two different public

elementary schools. Two control groups and two experimental groups in two

different schools in the same county were employed to conduct for the pilot study.

Eighty-one students were enrolled into groups in two public schools. The

following Table 3.7 shows numbers of participants in each group. Experimental

groups took treatment in 16 lectures in four weeks.

Table 3.7. Numbers of Groups in the Pilot Study

Sections

Number of

students

6/A Pasakoy 19

6/B Pasakoy 21

6/A Egemenlik 17

6/B Egemenlik 24

Total 81

Before implementing the study, lesson plans were developed in line with National

Educational Standards. The aim of integrating technology into teaching is to

enhance student problem solving skills and develop better attitudes toward

mathematics course in this study. Therefore, all lesson plans were prepared with

the worksheets. Then, activities through which students learn how to apply

mathematics to real-life situations using technology were developed. In this case,

students learn about ratios and a healthy diet, and then use the Internet search,

Excel to collect data. They analyze their chosen foods and make recommendations

to the principal on including healthier foods on canteen menus. The tasks that

require transferring mathematical knowledge to project on the computer lab were

embedded to lesson plans properly.

60

3.7.2. Data Collection Instruments for the Pilot Study

Mathematics Attitude Questionnaire: As a pretest and posttest,

mathematics attitude scale was utilized to students within the scope of

research project. Scale is composed of 20 items related to confidence to

math and usefulness of it.

A Problem Solving Achievement (PSA) test was also prepared by the

researcher to measure the mathematics knowledge of students about the

topic for the pilot study. After investigating level determination tests

utilized by Ministry of National Education, ten items related to the topic

were chosen. Final form of the achievement test was shaped after

consulting to an expert. The achievement test consisted of seven open-

ended items aiming to investigate the students’ mathematical achievement

and problem solving abilities. All of those scales are attached as an

appendix at the end of the paper.

Rubric: Rubrics offer the teacher an opportunity to evaluate the student's

process of a problem solving skill by levels of performance on

mathematical problems. Charles, Lester, and O'Daffer (1987) developed an

analytical rubric to evaluate students’ works. This scale has three phases or

categories of problem solving; understanding the problem, planning a

solution, and getting an answer. For each of these problem-solving

categories, 0, 1, or 2 points would be assigned. In this study, problem

solving achievement test scores was evaluated by this rubric. Each question

in the PSA test were divided by three categories of problem-solving and

scored by the researcher and a subject matter expert.

Self-assessment reports: Self-assessment reports used to collect data from

students is another useful technique to evaluate a number of important

problem-solving performance and attitude goals. However, the usefulness

of such assessments obviously depends on how candidly they report their

61

feelings, beliefs, intentions, thinking patterns, and so forth. Students are

asked to write or dictate on a tape recorder a retrospective report on a

problem-solving experience they have just completed (Charles, Lester, and

O'Daffer. 1987). While administrating self-assessment report, students

were asked to reconsider and describe how they solved the problem. The

items that were asked in the self-assessment report were:

• What did you do when you first saw the problem? What were your

thoughts?

• Did you use any problem-solving strategies? Which ones? How did

they work out? How did you happen to find a solution?

• Did you try an approach that did not work and have to stop and try

another approach? How did you feel about this?

• Did you find a solution to the problem? How did you feel about this?

• Did you check your answer in any way? Did you feel sure it was

correct?

• How did you feel, in general, about this problem-solving experience?

(Charles, Lester, and O'Daffer, 1987).

Interviews: The same interview protocol was used face-to-face and in the

form of focus-group interviews for the reliability. The interview protocol

covered the standardized close-ended questions of the student self-

assessment report and the interviewing process took approximately 15

minutes. Therefore, the interview included 5 main questions and follow up

questions. The interviewees were also made to comment on their replies by

the following “why” questions so that they can describe how they solved

the problem.

• Have you ever felt frustrated when solving the problem? Why?

• Have you ever felt that you want to give up and not solve the problem?

When?

• Have you enjoyed solving this problem? Why or why not?

• Would you rather have worked by yourself or with others when solving

62

this problem? Why?

The purpose of using a combination of these data collection and analyzing

techniques was to evaluate the problem-solving performance and attitudes of the

participants.

3.7.3. Results of Pilot study

A repeated measure analysis of variance (ANOVA) was conducted on students by

group, (control group vs. experimental group) and time (pre-study vs. post-study) to

find out if one group made more progress than the other group at the conclusion of

the study, and to measure each group's achievement from the pre- to the posttest.

Means and standard deviations on students by group and test are presented in Table

3.8.

The following Table 3.8 shows groups mean scores of students’ in terms of pretest

and posttest. In attitude pre-test, first treatment group’ (6/A) mean scores (M= 42.00,

SD= 4.63) were lower than control group (6/B) student scores (M= 42.25,

SD=4.55). Control group mean scores (M= 37.17, SD= 4.62) were higher than

experimental group mean scores (M= 36.53, SD= 2.13) in posttest.


Pretest Posttest

Groups Mean Std.

Deviation

Mean Std.

Deviation

6/A Pasakoy 42.00 4.63 36.53 2.13

6/B Pasakoy 42.25 4.55 37.17 4.62

In order to understand whether there is any significant difference between pretest

and posttest score of students in experimental and control groups, ANOVA was

conducted on students' test scores by group (control vs. experimental) and attitude

(pre vs. post). Results indicated that there was no group-attitude interaction on

students, F (1, 25) = 0.042, p = .084, Mean Square Error = 290.325 (See Table 3.9.).

63

Table 3.9The results of ANOVA test in terms of pretest and posttest score

experiment groups and control groups.

Source F Sig.

η2

Attitude

Attitude*Group

31.95 0.00 0.561

0.042 0.84 0.002

Mean Square Error 290.325

Although the results of ANOVA test in terms of pretest and posttest score between

experiment groups and control groups show that there was no statistically significant

differences in interaction about attitude towards to mathematics between

experimental and control groups, there was a significant main effect difference on

attitude towards mathematics (Table 3.9). As indicated by the above data, there was

a main effect of attitude on students, F (1,25) = 31.95, p < .001. Post-hoc tests were

conducted to further support that there was main effect of attitude and both groups

showed significantly negative improvement from the pretest to the posttest (see

Figure 3.3).

Figure 3.5. Mean plots about pretest and posttest score experiment groups and

control groups

42

36,53

42,25

37,17

33

34

35

36

37

38

39

40

41

42

43

Mean Mean

Pretest Posttest

6/A Pasakoy

6/B Pasakoy

64

Table 3.10. Number of students means and standard deviation among groups for

each question according to categories of problem solving; understanding the

problem, planning a solution, and getting an answer

N Sum Mean Std. Deviation

ss1a 75 21 0.28 0.583

ss1b 75 11 0.15 0.425

ss1c 75 4 0.05 0.324

ss2a 75 63 0.84 0.871

ss2b 75 46 0.61 0.804

ss2c 75 30 0.40 0.771

ss3a 75 72 0.96 0.892

ss3b 75 51 0.68 0.872

ss3c 75 39 0.52 0.844

ss4a 74 51 0.69 0.810

ss4b 75 39 0.52 0.777

ss4c 75 29 0.39 0.733

ss5a 75 111 10.48 0.795

ss5b 75 99 10.32 0.872

ss5c 75 85 10.13 0.963

ss6a 75 90 10.20 0.753

ss6b 75 61 0.81 0.849

ss6c 75 29 0.39 0.613

ss7a 75 84 10.12 0.770

ss7b 75 71 0.95 0.804

ss7c 75 32 0.43 0.661

As it can be realized from figure3.4, each answer given by the students to teach

question in the test used in the piloting stage was coded. Their answers were

assessed according to the rubric and a pattern decreasing from understanding the

problem to getting an answer was found. The mean scores about problem-solving

categories which are understanding the problem, planning a solution, and getting

an answer for first question are 0.28, 0.15 and 0.05. Even if the fifth question

which has highest mean is showed same pattern (See Table 3.10, Figure 3.4).

65

Figure 3.6. Total Scores means and standard deviation for each question according

to categories of problem solving; understanding the problem, planning a solution,

and getting an answer

A repeated measure analysis of variance (ANOVA) was conducted to examine the

research question “Is there a difference between the control groups that did not

receive treatment and experimental group that received treatment in terms of the

problem solving skills phases, which are understanding the problem, planning a

solution, and getting an answer?”

A summary of the group means and standard deviations for the level of

understanding the problem, planning a solution, and getting an answer according

to the control and treatment groups are shown in Table 3.11.

0

20

40

60

80

100

120

Understanding theProblem

Planning a solution

Getting an answer

66

Table 3.11. Descriptive Statistics for the level of understanding the problem,

planning a solution, and getting an answer

Pre test Post test

Mean Std.

Deviation

Mean Std.

Deviation

Understanding the

Problem

Control 6.69 3.75 8.15 2.38

Treatment 4.23 3.00 5.69 3.64

Total 5.46 3.56 6.92 3.26

Making a solution Control 5.69 3.95 6.77 1.96

Treatment 3.69 2.75 2.77 3.81

Total 4.69 3.48 4.77 3.60

Getting an answer Control 5.00 2.89 4.31 3.54

Treatment 2.77 2.59 1.62 3.15

Total 3.88 2.92 2.96 3.56

The multivariate tests indicate a significant difference between pre-test and post-

test scores of understanding the problem, planning a solution, and getting an

answer. Wilks’ Λ = .43, F (3.22) = 9.53, p < .001, partial η2= 0.57. Students’

problem solving skills scores was found to have significant difference over the

experimental period of the study (Table 3.12).

Table 3.12. Multivariate tests results of students problem solving skills scores

Wilks'

Lambda

Value

F Hypothesis

df

Error

df

Sig. Partial

Eta

Squared

treatment 0.70 3.20 3.00 22.00 0.04 0.30

test 0.43 9.53 3.00 22.00 0.00 0.57

test * treatment 0.70 3.20 3.00 22.00 0.04 0.30

For understanding the problem as a depended variables, the main effect of

treatment yielded an F ratio of F(1, 24) = 4.97, p = 0.04, η2 = 0.17 indicating that

the mean of understanding the problem score was a significantly difference for

treatment taken group than for treatment not taken groups. The main effect of

67

planning a solution yielded an F ratio of F (1, 24) = 7.29, p < 0.01, η2 = 0.23

indicating that the mean change score was significantly different in the group that

received the treatment and the group that did not. Lastly, the main effect of getting

an answer yielded an F ratio of was F (1, 24) = 4.90, p < 0.04, η2 = 0.17 point was

(see Table 3.13).

Table 3.13. Tests results of Between-Subjects Effects

Source Measure Type

III Sum

of

Squares

df Mean

Square

F Sig. Partial

Eta

Squared

Observed

Power

Treatment Understanding 39.38 1.00 39.38 4.97 0.04 0.17 0.57

Planning 58.50 1.00 58.50 7.29 0.01 0.23 0.74

GettingAnswer 39.38 1.00 39.38 4.90 0.04 0.17 0.57

Error Understanding 190.15 24.00 7.92

Planning 192.62 24.00 8.03

GettingAnswer 192.96 24.00 8.04

Computed using alpha = ,05

To sum up, after completing data analysis, there was no significant difference

between mean scores of sixth grade students received instruction with technology-

enriched and those received instruction with traditional method in terms of attitudes

towards mathematics (p>0.05). However, the mean score of the students received

instruction with technology-enriched was lower (mean=42.00 and standard

deviation = 4.63) than the mean of those who received instruction with traditional

method (mean=36.53 and standard deviation =2.13). The results of the attitude

pretest and posttest are presented in Figure 3.3.

In order to analyze students’ problem solving achievement test scores, a rubric was

used developed by Charles, Lester, and O'Daffer (1987). The questionnaire mean

scores were converted to the same three levels of agreement used in the interview

rating to be able make comparison with the interview data. This scale has three

phases or categories of problem solving; understanding the problem, planning a

solution, and getting an answer. For each of these problem-solving categories, 0, 1,

68

or 2 points were assigned. A separate score was recorded by researcher and co-

scorer that was a mathematics education professional with extensive experience in

elementary mathematics content and pedagogy for each section: understanding,

planning, solution, and presentation in order to triangulate the data analysis. The

aim of this was to determine the specific strengths and weaknesses of student’s

problem solving skills in this research. Students’ means, standard deviation among

groups for each question according to the phases of problem-solving,

understanding the problem, planning a solution and getting an answer were coded

by the rubric and presented as follows (see Table 3.10).

3.8. Reliability and validity

The issues of validity and reliability are strongly related to the quality of research.

Definition of the validity is how accurately reflects or evaluates the particular

variables that the researcher tries to measure in the study. Validity involves the

research question to test what you intend it to measure. Another important issue is

reliability that a research study, test, experiment, or any measuring activities find

out the similar outcome on repeated measurements (Gall, Borg, & Gall, 2003). In

that reason, validity and reliability were both main concerns throughout this study.

First of all, problem solving achievement scale based on a revised version of

Ozsoy’s (2007) problem solving achievement scale has an internal consistency

reliability of 0.84 according to the Cronbach’s alpha. Secondly, Mathematics

Attitude Scale (MAS) has 0.96 alpha reliability coefficients. As a research model,

the Solomon four group design was employed in order to protect internal and

external validity. Groups were randomly assigned as control and experimental

groups. Solomon four groups (Solomon, 1949) is a very valuable experimental

design to investigate many of the variables, such as differential selection and

statistical regression that threatened the internal validity of the study. Group 1 and

group 2 were utilized almost the same pretest procedures because of the same

school and the same grade level, to secure internal validity issue of history and

maturation. As an external validity, pretest effect was also considered. The effects

69

of the pretest the groups to the posttest were also controlled because third and

fourth groups did not take the pretests. Therefore, the posttest scores were not

sensitized by pretest effects. This research design also had a replication effect

because, in essence, the experiment was with and without a pretest. The pretest

and non-pretest groups were compared to further validate this study’s findings.

Another issue of reliability is the consistency of the scoring of rubric items. To

measure the extent to which the researcher accurately and reliably, the rubric was

used to score mathematics performance according to problem solving stages.

According to research protocol, before any work is done by the second scorer, the

researcher conducted problem solving achievement test. The second scorer was a

mathematics education professional with extensive experience in elementary

mathematics content and pedagogy.

3.9. Assumptions, Limitations and Delimitations for the Study

For this study, the following assumptions can be stated:

The students responded accurately and honestly to all the instruments used

in this study.

The teachers participating in the study followed the guidance and lesson

plan provided.

The participant teachers understood the guidance and lesson plan materials.

The participant teachers did not involve in any other similar studies during

the research.

The treatment and control group teachers were at a similar proficiency

level with regard to handling and ability to teach elementary mathematics.

The measures of the pretest and posttest were reliable and valid.

The data is recorded and analyzed in consideration of ethical issues.

The following limitations were applied to the present study:

70

This study is limited to students participating in the study. Therefore, the

generalizability of findings is not possible.

The reliability of instruments that are used to collect data and the honesty

of the participants’ responses to the instruments are also the limitations of

the study.

The treatment and control teachers were both from the same schools.

Therefore, they had access to each other’s classroom.

The students involved in the study had taken the Fundamentals of

Information, Communication and Technology class at the previous

semester.

The following delimitations were applied for this study:

The treatment and control samples were from the same city and same

county; therefore, had similar educational and environmental experiences.

The length of time for the study was limited to 8-class session, each of

which last for 40 minutes.

The curriculum materials were designed specifically for treatment groups

and provided at the beginning of the study.

The project materials used to solve the mathematical problem were

provided.

71

CHAPTER 4

FINDINGS

The purpose of this study was mainly to identify the effects of technology-

enriched instruction on 6th

grade students’ mathematics attitudes and students’

problem solving skills. Using the methodology outlined in the previous chapter, a

large amount of data were collected and analyzed in two phases: quantitative and

qualitative. There are three scales (Problem Solving Skill Scale, Problem solving

achievement test and Attitude toward Mathematics Scale) and the rubric for

content analysis of students’ responses through such other data collection tools as

interviews and observations. Because of the several data sources, the data were

exceedingly complex and not readily convertible into standard measurable

objects. The answers filled in the entirely structured questionnaires that were used

to collect data through quantitative techniques were transferred firstly to the

digital environment. Then, the data collected from quantitative instruments were

analyzed through descriptive statistics by utilizing computer software.

In this chapter, the results of the study in regard to the research questions are

presented. At the end of the chapter, the findings of the study are summarized.

4.1. Descriptive Results

As previously mentioned in methodology section, participants of the study were

consisted of 88 sixth grade elementary school students. The Table 4.1 shows the

numbers of participants whether they took pretest and treatment or not.

72

Table 4.1. The numbers of participants

Pretest taken or

not

Treatment taken or

not

N

No No 16

yes 13

Total 29

yes No 27

yes 32

Total 59

Total No 43

yes 45

Total 88

4.2. Quantitative results

The data were analyzed using 2x2 ANOVA to seek the following questions. Then,

it was reported the results of major tests in factorial ANOVA with insignificant

interaction.

1. What are the effects of Technology Enrichment Instruction on the sixth grade

public school students’ problem solving skills in mathematics?”

a) Is there a difference among the groups with pretest and without pretest

in terms of problem solving skills?

b) Is there a difference between the control groups that did not receive



c) Is there an interaction between pretest and treatment of problem

solving skills?

73

Table 4.2. Descriptive Statistics in terms of problem solving skills

Pretest taken or

not

Treatment taken or

not

Mean Std.

Deviation

N

No No 7,1250 1,96214 16

yes 9,2308 2,12736 13

Total 8,0690 2,26670 29

yes No 8,0000 2,07550 27

yes 10,4688 2,38252 32

Total 9,3390 2,55025 59

Total No 7,6744 2,05543 43

yes 10,1111 2,35702 45

Total 8,9205 2,51991 88

The descriptive statistics (see Table 4.2) indicate that the assumption of normality

was not violated. In order to assess the assumption of equal variances, Levene’s

test for homogeneity of variances was computed. This procedure tests the null

hypothesis that the group variances of the group means are equal. The results of

the Levene’s test at F(3,84)=0.610, p=0.610, indicated that the null hypothesis

cannot be rejected. As a result, the variances of the group means were not found to

be heterogeneous, leading to the conclusion that the assumption of equal variances

was not violated.

74

Table 4.3. Tests of Between-Subjects Effects for students` problem solving

achievements

Source Type III Sum

of Squares

df Mean

Square

F Sig.

Corrected Model 152.417(a) 3 50.806 10.668 0.000

Intercept 5838.652 1 5838.652 1226.036 0.000

Pretest 21.495 1 21.495 4.514 0.037

treatment 100.747 1 100.747 21.156 0.000

Pretest * treatment 0.634 1 0.634 0.133 0.716

Error 400.026 84 4.762

Total 7555.000 88

Corrected Total 552.443 87

After completing this analysis of the assumptions, there appeared no problem to

conduct the factorial ANOVA. Problem solving achievements were subjected to a

two-way analysis of variance having two levels of pretest (taken, not taken) and

two levels of treatment (taken, not taken). All main effects were statistically

significant at the .05 significance level. The results are presented in Table 4.3.

The main effect of pretest yielded an F ratio of F(1, 84) = 4.51, p < .001, which

indicates that the mean of the problem solving achievement score was

significantly greater for the groups taking the pretest (M = 8.07, SD = 2.27) than

the group who did not take the test (M = 9.34, SD = 2.55). The main effect of

treatment yielded an F ratio of F(1, 84) = 21.16, p < .05, indicating that the mean

change score was significantly higher in the treatment taken (M = 10.11, SD =

2.35) than treatment not taken (M = 7.67, SD = 2.05). The interaction effect was

non-significant, F(1, 84) = 0.13, p > .05 (see Figure 4.1).

75

Figure 4.1. The interaction effect of pretest and treatment on students’ problem

solving skills

d) Is there a difference between the control group that did not receive

treatment and the experimental group that received treatment with


76

A Mann-Whitney U test was conducted to evaluate the research question “Is there

a difference in problem solving achievements post-test scores between control

group that not given an intervention and experimental group with pretest”.


the experimental group that received treatment with pretest in terms of problem

solving skills - Mann-Whitney U test

Section Post

Test

N Mean

Rank

Sum of

Ranks

U P

6/A 29 23.47 680.50 245.500 0.001

6/B 32 37.83 1210.50

A Mann-Whitney U test indicated a significant difference that problem solving

achievements post-test scores was greater for experımental group than for control,

group with pretest, U = 245.50, z = -3.18, p = .001. Experimental group had an

average rank of 37.83, while control group had an average rank of 23.47 (see

Table 4.4).

e) Is there a difference between the control group that did not receive

treatment and the experimental group that received treatment without



a difference in problem solving achievements post-test scores between control

group that not given an intervention and experimental group without pretest”.

77


the experimental group that received treatment without pretest terms of problem

solving skills

Section Post

Test

N Mean

Rank

Sum of

Ranks

U P

6/A 13 19.23 250.00 49.000 0.015

6/B 16 11.56 186.00

A Mann-Whitney test indicated a significant difference that problem solving

achievements post-test scores was greater for experımental group than for control

group without pretest, U = 49.00, z = -2.43, p = 0.015, p < 0.05. Experimental

group had an average rank of 11.56, while control group had an average rank of

19.23 (see Table 4.4).

2. What are the effects of Technology Enrichment Instruction on the sixth grade

public school students’ attitude towards mathematics?”

a) Is there a difference in students’ attitude towards mathematics

among groups that given pretests and groups than not given pretest?

b) Is there a difference in students’ attitude towards mathematics

between control groups and experimental groups?

c) Is there an interaction between pretest and treatment on students’

attitude towards mathematics?

The data were first examined to determine measures of central tendency and

distribution. The assumption of independence was met by having all students

complete their tests individually. The distribution of scores was analyzed to

ensure that the assumption of normality for the factorial ANOVA model was not

violated. Levene’s test of homogeneity of variances was used to ensure that the

78

assumption of equal variances was not violated. Descriptive statistics for ANOVA

is presented in Table 4.6.

Table 4.6. Descriptive Statistics for Analysis Variables

Pretest taken or

not

Treatment taken or

not

Mean Std.

Deviation

N

No No 58.8750 10.53170 16

yes 62.3077 5.21831 13

Total 60.4138 8.60862 29

yes No 63.6296 6.20885 27

yes 61.7500 5.99462 32

Total 62.4754 6.08990 61

Total No 61.8605 8.29969 43

yes 61.9111 5.72801 45

Total 61.8111 7.01827 90

In order to assess the assumption of equal variances, Levene’s test for

homogeneity of variances was computed. This procedure tests the null hypothesis

that the group variances of the group means are equal. The results of the Levene’s

test at F(4,85)=0.611, p=0.656, indicated that the null hypothesis cannot be

rejected. As a result, the variances of the group means were not found to be

heterogeneous, leading to the conclusion that the assumption of equal variances

was not violated.

According to this analysis of the assumptions, there appeared no problem to

conduct the factorial ANOVA.

The data were analyzed using 2x2 ANOVA with an alpha level set at 0.05 for

each effect. Students’ attitude towards mathematics was subjected to a two-way

analysis of variance having two levels of pretest (taken, not taken) and two levels

79

of treatment (taken, not taken). All main effects were statistically significant at the

0.05 significance level.

Table 4.7. Tests of Between-Subjects Effects for Students’ attitude towards the

mathematics

Source Type III Sum

of Squares

df Mean Square F Sig.

Corrected Model 252.473(a) 4 63.118 1.299 .277

Intercept 88138.294 1 88138.294 1813.407 .000

Pretest 84.802 1 84.802 1.745 .190

treatment 45.916 2 22.958 .472 .625

Pretest * treatment 135.866 1 135.866 2.795 .098

Error 4131.316 85 48.604

Total 348239.000 90

Corrected Total 4383.789 89

The main effect of pretest yielded (see Table 4.7) an F ratio of F(1, 84) = 1.74, p >

0.05, indicating that the mean attitude towards the mathematics score was not

significantly greater for pretest taken groups (M = 62.42, SD = 6.09) than for

pretest not taken groups (M = 60.41, SD = 8.61). The main effect of treatment

yielded an F ratio of F(1, 84) = 0.47, p > 0.05, indicating that the mean change

score was not significantly higher in the treatment taken (M = 61.91, SD = 5.72)

than treatment not taken (M = 61.86, SD = 8.30). The interaction effect between

the pretest and treatment was non-significant, F(1, 84) = 2.79, p > 0.05 (see figure

4.2)

.

80

Figure 4.2. The interaction effect of pretest and treatment on students’ attitude

towards mathematics

d) Is there a difference in students’ attitude towards mathematics

between control group and experimental group with pretest?


a difference in students’ attitude towards mathematics post-test scores between

control group and experimental group with pretest”.


between control group and experimental group with pretest

Section Post Test N Mean Rank Sum of Ranks U P

6/A 29 32.36 938.50 424.500 0.568

6/B 32 29.77 952.50

A Mann-Whitney U test indicated students’ attitude towards mathematics post-

test scores was not greater for experimental group than for control group with

pretest, U = 424.50, z = -0.57, p = 0.57, p > .05. Experimental group had an

81

average rank of 32.36, while control group had an average rank of 29.77 (see

Table 4.8)..

e) Is there a difference in students’ attitude towards mathematics

between control group and experimental group without pretest?


a difference in students’ attitude towards mathematics post-test scores between

control group and experimental group without pretest”.


between control group and experimental group without pretest

Section Post Test N Mean Rank Sum of Ranks U P

6/A 13 17.50 227.50 71.500 0.153

6/B 16 12.97 207.50

A Mann-Whitney test indicated that students’ attitude towards mathematics post-

test scores was not significantly different for experimental group than for control

group without pretest, U = 71.50, z = -1.43, p = 0.153, p > .05. Experimental

group had an average rank of 12.97, while control group had an average rank of

17.50 (see Table 4.9).

3. One-Way analysis of variance (ANOVA) was conducted to examine the

research question “Is there a difference between the control groups that did not

receive treatment and experimental group that received treatment in terms of

principles, which are understand the problem, make a plan, utilize the plan and

reviewing the solution, of problem solving skills?”

A repeated measure analysis of variance (ANOVA) was conducted on students by

group, (control group vs. experimental group) and time (pre-study vs. post-study) to

82

find out if one group made more progress than the other group at the conclusion of

the study, and to measure each group's scores about understanding problem, making

plan, implementation of plan and review their solutions from the pre- to the posttest.

Means and standard deviations on students by group and test are presented in Table

4.10.


understanding problem, making plan, implementation of plan and review their

solutions in terms of pretest and posttest

Dependent Variable Treatment

taken or not

Mean Std.

Deviation

N

Understanding_pre No 29.63 1.32 27

yes 33.24 1.07 34

Understanding_Post No 22.22 0.93 27

yes 27.06 1.14 34

Plan_pre No 27.04 1.07 27

yes 24.12 1.13 34

PlanPost No 23.70 1.24 27

yes 28.24 1.11 34

Implement_pre No 18.89 1.50 27

yes 14.12 1.23 34

Implement_Post No 14.82 0.85 27

yes 22.35 0.89 34

Review_pre No 14.82 0.89 27

yes 20.29 1.24 34

Review_Post No 19.26 1.24 27

yes 25.29 0.90 34

Firstly, after examining central tendency and distribution, it was seen that the

assumption of independence was met by having all students complete their tests

individually. The distribution of scores was analyzed to ensure that the

assumption of normality for the repeated measured ANOVA model was not

violated. Levene’s test of homogeneity of variances was used to ensure that the

assumption of equal variances was not violated for all depended variables which

83

are understand_pr, understandPost, Plan_pr, PlanPost, implement_pr,

implementPost, review_pr, reviewPost. The descriptive statistics indicate that the

assumption of normality was not violated. Descriptive statistics for ANOVA is

presenting in Table 4.10.

Table 4.11. The results of ANOVA test for problem solving skills scale in terms

of pretest and posttest score experiment groups and control groups.

Source F Sig. η2

Between Subjects treatment 3.38 0.02 0.19

Within Subjects test 5.93 0.00 0.30

test * treatment 3.71 0.01 0.21

The results of ANOVA test in terms of pretest and posttest score between

experiment groups and control groups show that there was a statistically

significant difference in interaction about levels of problem solving skills between

experimental and control groups (Table 4.11).

84

Table 4.12. The results of ANOVA test for levels of problem solving skills scale

in terms of pretest and posttest score experiment groups and control groups.

Source Measure Type III

Sum of

Squares

df Mean

Square

F Sig. η2

Test Understand 13.88 1.00 13.88 10.56 0.00 0.15

Making_plan 0.05 1.00 0.05 0.03 0.85 0.00

Implement 1.30 1.00 1.30 0.99 0.32 0.02

Reviewing 6.71 1.00 6.71 4.80 0.03 0.08

test *

treatment

Understand 0.11 1.00 0.11 0.09 0.77 0.00

Making_plan 4.18 1.00 4.18 3.16 0.08 0.05

Implement 11.40 1.00 11.40 8.65 0.00 0.13

Reviewing 0.02 1.00 0.02 0.02 0.90 0.00

Error

(test)

Understand 77.61 59.00 1.32

Making_plan 78.12 59.00 1.32

Implement 77.73 59.00 1.32

Reviewing 82.58 59.00 1.40

According to results, level of understanding the problem has a significant

difference between pretest and posttest in the control group. As indicated by the

above data, there was a main effect of understanding the problem, F (1,59) =

10.56, p < .05. After follow up tests, a significant decrease can be seen between

pretest and posttest. Other two levels, which are making a plan and implementing

the plan, have no significant difference between pretest and posttest in control

group (F (1,59) = 0.03, p > .05 and F (1,59) = 0.99, p > .05).There was only a

positive significant difference in level of reviewing in control group F (1,59) =

4.80, p < .05 see table 4.12).

However, after analyzing data for experimental group, it was indicated that there

was only positive significant difference in level of implementation between

pretest and posttest (F (1,59) = 8.65, p > .05). The other levels which are

understand the problem, making a plan and review the solution, have no

significant difference between pretest and posttest in experimental group (F (1,59)

= 0.09, p > .05, F (1,59) = 3.16, p > .05 and F (1,59) = 0.02, p > .05) .

85

Table 4.13. The results of ANOVA analysis concerning the level of

“understanding the problem”

Sum of

Squares df

Mean

Square F Sig.

Between

Groups 3.769 1 3.769 3.535 .063

Within Groups 93.831 88 1.066

Total 97.600 89

According to the results of ANOVA indicated in table, the test was not

significant, F(1.88)= 3.54, p= .063. Although there was not a statistically

significant difference between the control groups that did not receive treatment

and experimental group that received treatment in terms of understand the

problem (p<0.05), it can be seen a positive difference between group that received

the treatment and group that did not receive the treatment. Table 4.13 shows

scores of understand the problem between group that received the treatment and

group that did not receive the treatment.

Figure 4.3. Changes in the mean difference scores of level of understand the

problem

86

In addition, relationship with between group that received the treatment and group

that did not receive the treatment can be seen in Figure 4.3 in terms of

understanding the problem.

Table 4.14. The results of ANOVA analysis concerning level of make a plan

Sum of

Squares df

Mean

Square F Sig.

Between

Groups 8.372 1 8.372 11.165 .018


Total 134.622 89

According to the results of ANOVA indicated in table, the test was significant,

F(1.88)= 11.165, p= .018 (see Table 4.14). There was a statistically significant

difference between the control groups that did not receive treatment and

experimental group that received treatment in terms of understanding the problem

(p<0.05). In other words, a positive difference can be seen between the group that

received the treatment and the group that did not receive the treatment. Figure 4.4

shows scores of making a plan between group that received the treatment and

group that did not receive the treatment.

Figure 4.4. Changes in the mean difference scores of level of making a plan

87

The mean difference scores of level of making a plan between group that received

the treatment and group that did not receive the treatment was presented in Figure

4.4.

Table 4.15. The results of ANOVA analysis concerning level of utilize the plan

Sum of

Squares df

Mean

Square F Sig.

Between

Groups 10.035 1 10.035 11.165 .001


Total 89.122 89

According to the results of ANOVA indicated in table, the test was significant,

F(1.88)= 11.165, p= .001 (see Table 4.15). There was a statistically significant

difference between the control groups that did not receive treatment and

experimental group that received treatment in terms of making a plan (p<0.05).

Positive difference can also be seen between group that received the treatment and

group that not received the treatment. Figure 4.5 shows scores of utilizing the plan

between group that received the treatment and group that not received the

treatment.

Figure 4.5. Changes in the mean difference scores of level of utilize the plan

88

According to the results of ANOVA indicated in Table 4.16, the test was

significant, F(1.88)= 7.63, p= .007. This means, there was a statistically

significant difference between the control groups that did not receive treatment

and experimental group that received treatment in terms of understanding the

problem (p<0.05).

Table 4.16. The results of ANOVA analysis concerning level of making a revision

Sum of

Squares df

Mean

Square F Sig.

Between

Groups 9.106 1 9.106 7.633 .007


Total 114.100 89

Figure 4.6 shows scores of making a revision between group that received the

treatment and group that did not receive the treatment.

Figure 4.6. Changes in the mean difference scores of level of making a revision

89

4. Is there a difference between experimental and control groups in terms of

students’ attitudes towards the mathematics scores and the students’ problem

solving skill scores?

A 2 (Pretest: taken, not taken) X 2 (Treatment: utilized, not utilized) between-

subjects multivariate analysis of variance (MANOVA) was performed on two

dependent variables: problem solving skills and attitude towards mathematics.

Although there were few outliers that were not influential points and since

MANOVA can tolerate few outliers they were included in the analysis (Pallant,

2007, p. 279). Using an alpha level of .05 to evaluate homogeneity assumptions,

Box's M test of homogeneity of covariance was not significant (p = .135). This

means, the result of the Box`s M Test of Equality of Covariance Matrices showed

that all significant values were larger than 0.05 so this assumption was not

violated for all MANOVA analyses (Table 4.17).

Table 4.17. Box's Test of Equality of Covariance Matrices

Box's M 14.296

F 1.508

df1 9

df2 20110.844

Sig. 0.138

For the equality of the error variances, Levene`s test revealed that all variables

satisfy this assumption (see Table 4.18).

Table 4.18. Levene's Test of Equality of Error Variances

F df1 df2 Sig.

TotalPost_PSS 0.776 3 86 0.511

ToatalPost_Attitude 0.761 3 86 0.519

After the verification of the assumptions, two-way MANOVA was conducted to

test the null hypothesis regarding research question four at significance level of

0.05. Wilks’ Lambda (Λ) was considered for testing multivariate null hypotheses.

The result was shown in the Table 4.19.

90

Table 4.19. Multivariate Tests

Effect Wilks'

Lambda

Value

F Hypothesis

df

Error df Sig0. Partial

Eta

Squared

Observed

Power

Intercept 0.010 41790.515 20.000 850.000 0.000 00.990 10.000

Pretest 0.931 30.141 20.000 850.000 0.048 0.069 0.589

Treatment 0.807 100.193 20.000 850.000 0.000 0.193 0.984

Pretest * treatment 0.966 10.512 20.000 850.000 0.226 0.034 0.314

* p<0.05

Significant differences were found among the dependent variables with respect to

pretest and treatment separately at the alpha (α) level of significance 0.05.

However, there exists no significant interaction between pretest and treatment on

the combined dependent variables.

Table 4.20. Tests of Between-Subjects Effects for MANOVA

Source Dependent

Variable

Type III

Sum of

Squares

df Mean

Square

F Sig0. Partial

Eta

Squared

Observed

Power(a)

Pretest TotalPostPSS 180.250 1 180.250 30.727 0.057 0.042 0.480

Post_Attitude 770.942 1 770.942 10.615 0.207 0.018 0.242

Treatme

nt

TotalPostPSS 940.034 1 940.034 190.204 0.000 0.183 0.991

Post_Attitude 90.009 1 90.009 0.187 0.667 0.002 0.071

Pretest *

treatment TotalPostPSS 0.172 1 0.172 0.035 0.852 0.000 0.054

Post_Attitude 1470.123 1 1470.123 30.048 0.084 0.034 0.408

Significant differences were found in dependent variables with respect to

independent variables of pretest and treatment. The alpha (α) level was significant

(0.05). Using Wilk's criterion (Λ) as the omnibus test statistic, the combined

dependent variables resulted in significant main effects for both pretest. Wilk`s Λ

= 0.931. F (2. 85) = 3.124 p = 0.048. partial 2 = 0. 069. and treatment. Wilk`s Λ

91

= 0.807. F (2. 85) = 10.193. p = 0.00 partial 2 = 0.193. The pretest X treatment

interaction was not statistically significant F(2. 85) = 1.512. p = 0.226. partial 2

= 0.034 (see Table 4.19).

Effect Size

The effect size degree indicates the degree of the relationship among variables.

That is to says, it is an indicator of the association between two or more variables

(Stevens. 2002). To evaluate the questions regarding group comparisons eta-

square is considered: the effect size classification for eta-square (η2) values less

than 0.01 may indicate small whereas values around 0.06 show medium and

values 0.14 and above indicate large effect size. In the present study, standardized

path coefficients(R), squared multiple correlation (R2) and eta-square (η2)

coefficients were taken into consideration as effect sizes (Cohen. 1988. p.2;

Pallant. 2007. p. 208).

Table 4.21. Multivariate Tests

Effect Wilks'

Lambda

F Hypothesis

df

Error

df

Sig. Partial

Eta

Squared

Observed

Power

Pretest 0.93 3.14 2.00 85.00 0.05 0.07 0.59

treatment 0.81 10.19 2.00 85.00 0.00 0.19 0.98

Pretest *

treatment

0.97 1.51 2.00 85.00 0.23 0.03 0.31

For all effects, the eta-squared η2 has medium effect that is only 6.9% and 19.3%

of the variance are explained by small sample size and only two depended

variables (See Table 4.19). The follow up test are shown in the table 4.20. To

92

probe the statistically significant multivariate effects, univariate 2 X 2 ANOVAs

were conducted on each individual dependent variables.

The partial eta-squared η2 which is a measure of the strength of the relationship

between two variables has medium effect size for pretest and for treatment by

pretest interaction that are 6,9% and 3% of the variances are explained by two

dependent variables respectively. On the other hand, the partial eta-squared η2 has

large effect size for treatment on students’ problem solving skills and their attitude

towards mathematics. That is 19% of the variance is explained by the two

dependent variables regarding Cohen’s (1988) classification of η2 effect size

where 0.01 is small, 0.06 is medium, and 0.14 or greater is considered as large.

Table 4.22Tests of Between-Subjects Effects for ANOVA

Source Dependent

Variable

Type III

Sum of

Squares

df Mean

Square

F Sig. Partial

Eta

Squared

Observed

Power(a)

Pretest TotalPostPSS 18.250 1 18.250 3.727 0.057 0.042 0.781

treatment 94.034 1 94.034 19.204 0.000 0.183 0.999

Pretest *

treatment

147.123 1 0.172 0.035 0.850 0.000 0.408

Pretest Post_Attitude 77.942 1 77.942 1.615 0.207 0.018 0.242

treatment 9.009 1 9.009 0.187 0.667 0.002 0.071

Pretest *

treatment

147.123 1 147.123 3.048 0.084 0.034 0.408

* p<0.05

For problem solving skills as a depended variables, the main effect of pretest

yielded an F ratio of F(1, 86) = 3.72, p = 0.057, η2 = 0.042 indicating that the

mean problem solving achievement score was not significantly greater for pretest

taken groups than for pretest not taken groups(see Table 4.22).. The main effect

of treatment yielded an F ratio of F (1, 86) = 19.204, p < 0.05, η2 = 0.183

indicating that the mean change score was significantly different in the group that

received the treatment and the group that did not. The interaction effect was also

non-significant, F(1, 86) = 0.035, p >0 .05, η2 = 0.034 see Table 4.22) .

http://en.wikiversity.org/wiki/Variable

93

Table 4.23Pairwise Comparisons across pretest and treatment

Dependent

Variable

(I) Pretest

taken or not

(J) Pretest

taken or not

Mean Difference

(I-J)

Std. Error Sig.

TotalPostPSS No yes -0.97 0.50 0.06 yes No 0.97 0.50 0.06 Post_Attitude No yes -2.00 1.58 0.21 yes No 2.00 1.58 0.21 (I)

Treatment

taken or not

(J) Treatment

taken or not

Mean Difference

(I-J)

Std. Error Sig.

TotalPostPSS No yes -2.20 0.50 0.00 yes No 2.20 0.50 0.00 Post_Attitude No yes -0.68 1.58 0.67

yes No 0.68 1.58 0.67

* p<0.05

For the attitude toward mathematics as a dependent variable, there was not any

significant main effect for pretest, F(1, 86) = 1.615, p = 0.207, η2 = 0.018. Neither

the main effect for treatment, F(1, 86) = 0.187, p = 0.667, η2 = 0.02, nor the

interaction effect of Pretest * treatment was non-significant, F(1, 86) = 3.048, p >

0.05, η2 = 0.034 (see Table 4.22)..

For the independent variables pretest and treatment, pairwise comparisons were

taken into account (see Table 4.23). It was revealed that students taken pretest

have reported higher scores than students not taken (MD=0.97, SD= 0.50) in

terms of problem solving skills. However, this difference is not significant

between them. In addition, there was a significant mean difference between

students taken treatment and students not taken treatment (MD=2.20, SD= 0.50)

in terms of problem solving skills. It can also be seen in Figure 4.7.

94

Figure 4.7. Treatment*Pretest with respect to problem solving skills

For the independent variables pretest and treatment, pairwise comparisons were

taken into account for attitude towards mathematics (see Table 4.18). It was

revealed that students taken pretest have reported higher scores than students not

taken (MD=2.00, SD= 1.58) in terms of attitude towards mathematics. However,

this is not significant difference between them. In addition, there was a

significant mean difference between students taken treatment and students not

taken treatment (MD=0.68, SD= 1.58) in terms of attitude towards mathematics. It

can also be seen in Figure 4.7.

95

Figure 4.8. Treatment*Pretest with respect to attitude towards mathematics

4.3. Qualitative results

In the second phase of the mixed methods research of this study, in order to

deeply understand students’ attitudes and problem solving skills in mathematics

that are affected with these variables, qualitative data were collected through

interviews, and document analysis. Structured interviews which are most

frequently used in qualitative researches (Briggs, 1986; Patton, 1990; Guba &

Lincoln 1989, 1994; Marshal & Rossman, 1999; Yıldırım & Şimşek 2005) were

done with participants. Structured interview questions and products that students

prepared were utilized in order to understand about process of students` problem

solving and attitude towards mathematics. The transcripts of the interviewed

students’ verbal explanations for their problem solving processes were compared

96

to the stages of problem-solving skills by which results of problem solving

achievement test had been classified.

4.3.1. Summary of qualitative results of problem solving achievement

test

Seventy five students took the test for problem solving achievement. In order to

analyze students’ problem solving achievement test scores, the rubric developed

by Charles, Lester, and O’Daffer (1987) was used. The questionnaire mean scores

were converted to the same three levels of agreement used in the interview rating

to be able make comparison with the interview data. This scale has three phases or


and getting an answer. For each of these problem-solving categories, 0, 1, or 2

points were assigned. A separate score was recorded by researcher and co-scorer

that was a mathematics education professional with extensive experience in

elementary mathematics content and pedagogy for each section: understanding,

planning, solution, and presentation in order to triangulate the data analyzes. The

aim of this was to determine the specific strengths and weaknesses of student’s

problem solving skills in this research. Therefore, this allows the researchers to

guide for improvement for further studies. Numbers of students’ means and

standard deviation among groups for each question according to categories of


answer were coded by rubric are following; (see Table 4.24).

97

Table 4.24. Mean scores and standard deviation among groups according to


and getting an answer

Total Post A Total Post B Total Post C

N Mea

n

Std.

Deviatio

n

N Mea

n

Std.

Deviatio

n

N Mea

n

Std.

Deviatio

n

6/A

Pasakoy

1

8

7.94 2.89 1

8

6.44 2.31 1

8

3.94 3.17

6/B

Pasakoy

1

5

5.46 3.60 1

6

2.50 3.50 1

8

1.38 2.87

6/A Milli

Egemenli

k

1

7

6.35 3.04 1

7

5.41 3.68 1

7

3.35 3.57

6/A Milli

Egemenli

k

2

4

6.54 3.59 2

4

5.42 3.51 2

4

4.08 2.86

Their answers were assessed according to the rubric used in this study and the

means as well as the standard deviations of the scores were calculated for each

problem-solving phase. The mean scores about problem-solving categories which

are the understanding problem, planning a solution, and getting an answer for first

phase are 0.28, 0.15 and 0.05 in Table 4.26.

98

Figure 4.9. Total Scores means and standard deviation according to categories of


answer

As it can be seen from figure 4.9, the answers to the given questions

to each question in the test were scored. A pattern decreasing from understanding

the problem to getting an answer was detected.

0

2

4

6

8

10

6/APasakoy

6/BPasakoy

6/A MilliEgemenlik

6/A MilliEgemenlik

Total Post A

Total Post B

Total Post C

99

Table 4.25. Table for Total Scores means and standard deviation for each group



6/A Pasakoy 6/B Pasakoy

Total Pre A N 14 18

Mean 6.50 3.94

Std. Deviation 3.67 2.98

Total Pre B N 14 18

Mean 5.36 3.89


Total Pre C N 14 18

Mean 4.64 2.67


Total Post A N 15 18

Mean 7.94 5.47


Total Post B N 16 18

Mean 6.44 2.50


Total Post C N 16 18

Mean 3.94 1.37


100

Table 4.25 shows the means and the standard deviations of students’ scores in

phases of problem solving; understanding the problem, planning a solution, and

getting an answer at the school where they took the pretest and posttest.

Figure 4.10. Figure for total Scores means and standard deviation for each group



As can be realized from the Figure 4.10, although the scores obtained from each

phase increased, the correlation between all the phases remained similar.

0

2

4

6

8

TotalPre A

TotalPre B

TotalPre C

TotalPost A

TotalPost B

TotalPost C

6/A Pasakoy

6/B Pasakoy

101

Table 4.26. Frequency table for each question concerning categories of problem

solving; understanding the problem, planning a solution, and getting an answer

according to problem solving achievement test.

0 1 2

Frequency Percent Frequency Percent Frequency Percent Mean Std.

Dev.

ss1a 59 78.7 11 14.7 5 6.7 0.28 0.58

ss1b 66 88 7 9.3 2 2.7 0.15 0.43

ss1c 73 97.3 0 0 2 2.7 0.05 0.32

ss2a 35 46.7 17 22.7 23 30.7 0.84 0.87

ss2b 44 58.7 16 21.3 15 20 0.61 0.80

ss2c 58 77.3 4 5.3 13 17.3 0.40 0.77

ss3a 31 41.3 16 21.3 28 37.3 0.96 0.89

ss3b 44 58.7 11 14.7 20 26.7 0.68 0.87

ss3c 53 70.7 5 6.7 17 22.7 0.52 0.84

ss4a 39 52.7 19 25.7 16 21.6 0.69 0.81

ss4b 49 65.3 13 17.3 13 17.3 0.52 0.78

ss4c 57 76 7 9.3 11 14.7 0.39 0.73

ss5a 14 18.7 11 14.7 50 66.7 1.48 0.79

ss5b 20 26.7 11 14.7 44 58.7 1.32 0.87

ss5c 30 40 5 6.7 40 53.3 1.13 0.96

ss6a 15 20 30 40 30 40 1.20 0.75

ss6b 35 46.7 19 25.3 21 28 0.81 0.85

ss6c 51 68 19 25.3 5 6.7 0.39 0.61

ss7a 18 24 30 40 27 36 1.12 0.77

ss7b 26 34.7 27 36 22 29.3 0.95 0.80

ss7c 50 66.7 18 24 7 9.3 0.43 0.66

From the output shown below it is understood that 73 participants (%97.3) had 0

point for understanding the problem in first question (see Table 4.25). According

to frequencies, lowest frequency of planning a solution was first problem. This is

not a conflict. If a problem was not understood, people could not make a plan to

solve it.

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4.3.2. Summary of qualitative results of students` interviewed about

problem solving and attitude towards mathematics

In the current study, it was inferred from students’ responses that they feel

successful in math and that practice is a factor in learning how to solve

mathematics problems and attitude towards mathematics (see Table 4.27).

Table 4.27. Codes/themes after interview analysis.

Understanding Solving Reviewing Attitude Expression

Stu

den

t

What was the

first thing you

did when you

saw the math

problem?

Please describe

strategies that you

used to help you

solved the

math problem.

How did you

know when you

get the problem

right?

What words do

you use to

describe your

feelings when

you see the math

problems?

Level of

student`s

expression

about solving

what he did.

1 read Solve the problem I don’t I hate this low

2 freeze Identify key words Check it Don’t Like low

3 check the

options

Solve the problem I don’t Neutral low

4 Highlight Solve the problem Check it Neutral high

5 Put a label Write down facts Check it Neutral medium

4.3.2.1. What was the first thing you did when you saw the math

problem?

In the interview, firstly, “What was the first thing you did when you saw the math

problem?” was asked in order to reveal their attitudes towards mathematics.

Students’ responses were coded and five typical responses were found: read,

freeze, check the options, highlight, and put a label. In this part of the data

collection procedure, the structured interview questions were asked to the

participants and some of their responses could be summarized as follows: “When

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I first saw the mathematics problem, I read it”, “I need to understand what is

asked in the problem first”.

Figure 4.11. Result of “What was the first thing you did when you saw the math

problem?”

According to the results as illustrated in Figure 4.11, 33% of the students read the

problem again to find more information in order to look for information that will

help them solve the problem.16% of the student stated that they do nothing when

they see mathematics problem in order to solve the problem

4.3.2.2. Describing strategies that you used to help you solved

the math problem.

The second question, “Please describe strategies that you used to help you solved

the

math problem” coded three typical responses: solve the problem, identify key

words, and write down facts. Typical participant responses were as follows:

“First, I try to understand the question. Then, I try to find a solution”. This can be

regarded as an example of Polya’s (1946) second stage of making a plan for the

solution.

33%

16% 17%

17%

17%

What was the first thing you did when you saw the math

problem?

read

freeze

check the options

Highlight

put a label

104

Figure 4.12. Result of strategies that students’ used to help them solve the

mathematics problem.

As can be interpreted from Figure 4.12, 17% of the students try to identify the key

words of the question and use this information to solve the problem whereas 50%

of the students stated that “I solve the problem.”

4.3.2.3. How did you know when you solved the problem, right?

The third question, “How did you know when you solved the problem, right?”

coded two typical responses: I check it and I don’t check it.

50%

17%

33%

Please describe strategies that you used to help you

solved the …

Solve the problem

Identify key words

Write down facts

105

Figure 4.13. The result of “How did you know when you solved the problem,

right?”

According to the results presented in Figure 4.13, 67% of the students stated that

they check their answer to verify if it is correct, and 33% of the students do not do

anything if their answer is correct. While interviewing, students were hesitating to

talk about correctness of the problem which they already solved.

4.3.2.4. What words do you use to describe your feelings when

you see the math problems?

The fourth question, “What words do you use to describe your feelings when you

see the math problems?” coded three typical responses: I hate this, Don’t like it

and neutral.

33%

67%

How did you know when you solved the problem, right?

I don’t

Check it

106

Figure 4.14. The result of “What words do you use to describe your feelings when

you see the math problems?”

As can be interpreted from Figure 4.14, this question shows that 67% of the

students neutral towards word problems. 16% of students hate these kinds of math

problems and the other 17% don’t like.

4.3.2.5. Level of student`s expression about how to solve their

math problems.

The fifth question, “Please can tell me about how to solve your math problem?”

coded three typical responses: low, medium, high.

16%

17%

67%

What words do you use to describe your feelings when you

see the math problems?

I hate this

Don’t Like

Neutral

107

Figure 4.15. The result of the student`s expression levels about how to solve their

math problems.

This question indicates that 50% of the students could not talk about their problem

solutions properly. 17% of students speak about their problem solutions. The

other 33% were telling on medium level (see Figure 4.15).

4.4. Summary

On the whole, both positive and negative results were found in this study about

the effects of technology enrichment instruction on the sixth grade public school

students’ attitudes and problem solving skills in mathematics. One of the results is

that there is a positive improvement of the students’ problem solving skills in the

groups which received technology enrichment mathematics instruction. The other

results were related to students’ attitude towards mathematics. According to the

findings, there was no significant difference between experimental group that

received technology enrichment instruction and those received traditional

instruction in terms of attitudes towards mathematics.

Participants were 88 six grade school students enrolled in four mathematics

classrooms at two public primary schools. Approximately half (N = 43) of the

50%

33%

17%

Level of student`s expression about how to solve their math

problems.

low

medium

high

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students took the traditional mathematics instruction throughout the study while

the rest of the students (N = 45) took technology enrichment instruction.

Instruments used in the study are problem solving skill scale, problem solving

achievement test and attitude toward mathematics scale and a rubric for content

analysis of students’ responses through other data collection tools like interviews

and observations. Only the students in two classes completed the PSS, PSA test

and MAS twice, once at the beginning of the study (i.e., pretest) and again at the

end of the study (i.e., posttest). Students in the remaining two classes completed

all instruments at the end of the study as a post test.

4.4.1. Problem Solving Skills

First of all, the effects of technology enrichment instruction on sixth grade public

school students’ problem solving skills in mathematics were investigated in this

study. The supporting evidence was used in order to understand the differences

among the students with pretest and without pretest in terms of problem solving

skills in technology enrichment instruction, to show the impact of the instruction

in terms of problem solving skills and to find the answers to five sub questions for

the first research question. With the sub questions, it was aimed to show whether

there is a relationship between pretest and treatment of problem solving skills in

technology enrichment instruction in elementary schools.

Students’ problem solving achievement scores were significantly greater for the

groups taking the pretest (M = 8.07, SD = 2.27) than the group who did not take

the test (M = 9.34, SD = 2.55) for the first sub research question (F (1, 84) = 4.51,

p < .05). In the second sub research question, an F ratio of F (1, 84) = 21.16, p <

.05 was found that the mean change score was significantly higher in the

treatment taken (M = 10.11, SD = 2.35) than treatment not taken (M = 7.67, SD =

2.05). In the third sub question, there was not an interaction effect between pretest

and treatment as an independent variable (F (1, 84) = 0.13, p > .05).

109

As the Solomon four groups research design requires, the same pretest procedures

were utilized in the class 1 and class 2 because these classes were located in the

same school and the students were at the same grade level. The students in two of

these classes were taught by the same teacher and their maturation level did not

differ much. External validity was also considered. The effects of the pretest

sensitizing the groups to the posttest were also considered because group 3 and

group 4 did not take the pretests, and were thus not sensitized to the information

that was on the posttest. In order to validate the findings, with pretest and without

pretest groups were compared.

On the other hand, the Mann-Whitney U test revealed a significant difference

between the experimental and the control group. The problem solving

achievements post-test scores were greater for experimental group than for control

group with pretest, U = 245.50, z = -3.18, p = .001. Experimental group had an

average rank of 37.83 while control group had an average rank of 23.47. The

result of the test without pretest was U = 49.00, z = -2.43, p = 0.015, p < 0.05.

Experimental group had an average rank of 11.56 while control group had an

average rank of 19.23 3 (see Table 4.28. Mann-Whitney U test scores in terms of

problem solving achievements post-test scores with / without pretest.Table 4.28).

Table 4.28. Mann-Whitney U test scores in terms of problem solving

achievements post-test scores with / without pretest.

U z p Rank

Pretest Experimental 245.50 -3.18 .001 37.83

Control 23.47

Without

pretest

Experimental 49.00 -2.43 0.015 11.56

Control 19.23

110

In order to determine the specific strengths and weaknesses of students’ problem

solving skills in this research, students’ problem solving achievement test scores

were assessed based on the rubric used in this study. The means as well as the

standard deviations of the scores were calculated for each problem-solving phase.

The mean scores about problem-solving categories which are the understanding

problem, planning a solution, and getting an answer for first phase were found to

be 0.28, 0.15 and 0.05. According to the results of students’ problem solving

achievement test scores, planning a solution was the first problematic point. This

should not be regarded as a conflict because if a problem was not understood,

people could not make a plan to solve it. Lastly, the relationship between all the

phases remained similar although the scores obtained from each phase increased. The

observation and questioning students were also employed during a problem-

solving session. The structured interview involving six students was used as one

of the data collection tools in this study to evaluate a number of important

problem-solving performance and attitude goals.

For the third research question, a repeated measure analysis of variance

(ANOVA) was conducted on students by group, (control group vs. experimental

group) and test (pre-study vs. post-study) to find out if one group made more

progress than the other group at the end of the study and to measure each group's

scores about understanding problem, making plan, implementation of plan and

review their solutions from the pre- to the posttest. After analyzing the data, the

level of understanding the problem has a significant difference between pretest

and posttest in the control group. As indicated by the above data, there was

significant difference on understanding the problem phase, F (1, 59) = 10.56, p <

.05. On the other two levels, which are making a plan and implementing the plan,

no significant difference between pretest and posttest in control group were found

(F (1,59) = 0.03, p > .05 and F (1,59) = 0.99, p > .05). There was also a significant

difference in level of reviewing in control group F (1,59) = 4.80, p < .05.

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4.4.1. Attitude towards Mathematics

In this chapter, the effects of technology enriched instruction on the sixth grade

public school students’ attitudes towards mathematics were investigated. The

supporting evidence was looked into so as to understand the differences among the

students with pretest and without pretest in terms of attitudes towards

mathematics, to show the influence of the instruction in terms of attitudes towards

mathematics and to find the answers to five sub questions for the second research

question.

Students’ attitudes towards mathematics were subjected to a two-way analysis of

variance having two levels of pretest (taken, not taken) and two levels of

treatment (taken, not taken). All main effects were statistically significant at the

0.05 significance level. Students’ attitudes towards mathematics score were not

significantly greater for the group with the pre-test (M = 62.42, SD = 6.09) than

for the group without the pretest (M = 60.41, SD = 8.61) for the first sub research

question of the second research question F (1, 84) = 1.74, p > 0.05. In the second

sub research question, an F ratio of F (1, 84) = 0.47, p > 0.05 was found that the

mean change score was not significantly higher in the treatment group (M =

61.91, SD = 5.72) than control group (M = 61.86, SD = 8.30). In the third sub

question, there was not an interaction effect between pretest and treatment as an

independent variable, F (1, 84) = 2.79, p > 0.05).

On the other hand, the Mann-Whitney U test revealed a significant difference

between the experimental and the control group. The Mann-Whitney U test

showed a significant difference in that attitudes towards mathematics post-test

scores was not greater for experimental group than for control group with pretest,

U = 424.50, z = -0.57, p = 0.57, p > .05. Experimental group had an average rank

of 32.36 while control group had an average rank of 29.77. The result of the test

without pretest were U = 71.50, z = -1.43, p = 0.153, p > .0. Experimental group

112

had an average rank of 12.97 while control group had an average rank of 17.50

(see Table 4.29).

Table 4.29. Mann-Whitney U test scores in terms of attitude towards mathematics

post-test scores with / without pretest.

U z p Rank

Pretest Experimental 424.50 -0.57 0.568 32.36

Control 29.77

Without

pretest

Experimental 71.50, -1.43 0.153 12.97

Control 17.50

For the last research question, the 2 (Pretest: taken, not taken) X 2 (Treatment:

utilized, not utilized) between-subjects multivariate analysis of variance

(MANOVA) was performed on two dependent variables: problem solving skills

and attitudes towards mathematics. Significant differences were found among the

dependent variables with respect to pretest and treatment separately at the alpha

(α) level of significance 0.05. However, there exists no significant interaction

between pretest and treatment on the combined dependent variables. After using

Wilk's criterion (Λ) as the omnibus test statistic, the combined dependent

variables resulted in significant main effects for both pretest. Wilk`s Λ = 0.931. F

(2. 85) = 3.124 p = 0.048. partial 2 = 0. 069. and treatment. Wilk`s Λ = 0.807.

F(2. 85) = 10.193. p = 0.00 partial 2= 0.193. The pretest X treatment interaction

was not statistically significant F(2.85) = 1.512. p = 0.226. partial 2 = 0.034.

113

CHAPTER 5

DISCUSSION AND CONCLUSION

5.1. Introduction

This study investigated the technology integration to education and classrooms,

students’ problem solving skills and students’ attitude towards mathematics in

elementary schools.

Data were collected through both qualitative and quantitative methods. The major

findings and conclusions related to the research questions were presented in this

chapter. Instruments which used in the study are Problem Solving Skill Scale,

Problem solving achievement test and Attitude toward Mathematic Scale and a

rubric for content analysis of students’ responses through such other data

collection tools as interviews and observations. Structured interviews were

conducted with the participants for understanding how they solve the

mathematical problems, and how they feel about it. In previous chapter, whether

or not pretest and treatment have an effect on problem solving skills in enhancing

instruction with technology in the elementary schools were analyzed.

Also, descriptive statistics were reported upon the participants’ size in the groups,

standard deviations and means in regard to problem solving and attitude towards

mathematics. Parametric and non-parametric statistical test which were factorial

Anova, Manova, Mann Whitney-u test were utilized to examine the statistical data

gathered by questionnaires and scales. The participants’ views were investigated,

which generally revealed complementary results to the statistical results. In the

following chapter, these major points were discussed based on the related

114

literatures. At the end of the chapter, the implications and the recommendations

for further research were declared.

5.2. Discussion of Findings

The discussion of the findings is presented in two sections. First one is the effects

of Technology Enrichment Instruction on students’ problem solving skill. Second

one is also students’ attitudes towards mathematics.

5.2.1. Problem Solving Skills

The objective of this study is to understand the difference among the students with

pretest and without pretest in terms of problem solving skills in enhancing

instruction with technology, to show the impact of enhancing instruction with

technology in terms of problem solving skills. Besides, it was aimed to investigate

whether there is a relationship between pretest and treatment of problem solving

skills in enhancing instruction with technology in elementary schools.

Combining text and animated graphics make the information more memorable by

helping learners convert this information in both visual and verbal forms and

integrate these forms in long-term memory (Mayer, 2003). Therefore, computers,

projectors, recording devices and video devices represent a few of the tools which

have resulted from technology and have been incorporated into education as a

media for information exchange, which makes the delivery of information

possible in ways other than traditional lectures and text formats (Roblyer,

Edwards, & Havriluk, 1997).

In order to understand the impact of enhancing instruction with technology in

terms of problem solving skills, PSS was designed according to George Polya’s

principles (i.e., understanding the problem, making a plan, utilizing the plan,

looking back on the work). This scale includes mathematics problems including

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the practice of multiplication, addition, subtraction and division in order to

evaluate students’ problem solving achievement. There are twenty multiple-choice

items in this scale that has five items for each principle; understanding, making

plan, solution, and revision.

After a two-way analysis of variance having two levels of pretest (taken, not

taken) and two levels of treatment (taken, not taken), all main effects were found

to be statistically significant. The data analyses showed that main effect of pretest

on problem solving achievement was significantly different. This means, the mean

of problem solving achievement score was significantly greater for pretest taken

groups (M = 8.07, SD = 2.27) than for pretest not taken groups (M = 9.34, SD =

2.55). Another result of the study was that the impact of enhancing instruction

with technology (M = 10.11, SD = 2.35) in terms of students’ problem solving

skills was significantly higher than the traditional instruction (M = 10.11, SD =

2.35). This means, average success of problem solving skills’ levels which are

understand the problem, make a plan, utilize the plan, look back on your work (i.e,

expressing what they did). When considered to interaction effects of treatment and

pretest issues, data analyses results showed no significant interaction between

them. These results are also similar with Hartweg and Heisler’s studies. In their

research study, Hartweg and Heisler (2007) investigated the professional

development of teacher about how to integrate problem solving into third grade

mathematics curriculum. At the end of the research, students’ mathematical

understanding and mathematical writing skills improved. In addition, their

confidence in problem solving and their writing of mathematical explanation

improved according to teacher surveys and student attitude surveys.

Moreover, in order to triangulate the data analyses, another statistical test utilized

to get evidence whether or not there is a difference between the control group that

did not receive treatment and the experimental group that received treatment in

both schools in terms of problem solving. At the end of the analysis, the data for

both schools, similar results were obtained. For example, experimental group had

an average rank of 37.83, while control group had an average rank of 23.47 in

116

Milli Egemenlik Primary School. Beside this, in Pasakoy Primary School, the

group which had treatment had an average rank of 11.56, while control group had

an average rank of 19.23. Problem solving achievements post-test scores were

greater for experimental group than for control groups in both schools.

In addition to inferential statistic’ result, seventy five students took the test for

problem solving achievement and evaluated by a rubric which was developed by

Charles (1987). It was used for grading students` responds. This rubric has three

phases or categories of problem solving; understanding the problem, planning a

solution, and getting an answer. For each of these problem-solving categories, 0,

1, or 2 points would be assigned by researcher and co-evaluator. After data coding

of the open-ended test by the problem solving skills rubric, the common aspects of

these codes were gathered together. In this sample, qualitative data types were

converted into numerical codes that can be statistically analyzed. The total scores,

means and standard deviations for each of question related to these categories

were calculated.

In addition to the answers for the original research questions, it was observed that

all levels’ scores of problem solving process is getting lover gradually while

moving forward to. Same pattern of outcome presented even if group took pretest

or treatment. The posttest’s means of understanding the problem, planning a

solution, and getting an answer were presented by all groups. For example, the

mean scores were 7.94, 6.44 and 3.94 in the experimental class of Pasakoy

primary school. However, the comparison of the pretest and post means in terms

of treatment taken or not has an interesting result. While all levels of problem

solving score rose in experimental classes, there was not a raise in control group

except for understanding level.

In conclusion, use of technology for many educators has significant effect on

mathematics problem solving. Kitchens (1996) also expressed over the years

technology has been employed most often to furnish ways in which information

could be presented and exchanged. During the past decade, developments in

117

information technology have influenced the several areas such as communication,

nature of work, structure of organizations, daily life and also education. The “new

media” which are computers and Internet has allowed or facilitated the provision

of the important feature interactivity in educational applications in order to

enhance learning potential (Rice 1984, as cited in Chou, 2003).

In mathematics problem solving process, the importance of technology should be

as a tool according to this view. Students should use the technology as mid tool to

get more benefit from “computer applications that, when used by learners to

represent what they know, necessarily engage them in critical thinking about the

content they are studying (Jonassen, 2000)”.Mathematical problem solving is not

a simple process that involves simple calculation. On the contrary, this process

involves much more complex stages. For everybody, solving a problem starting

with reading and understanding the problem situation, consider what the problem

is asking; make a plan for what mathematical procedure(s) need to be used to

solve the problem. The rest of following steps are complete the plan, assess the

correctness of the answer, and then express the results.

The study findings were in agreement with other studies in the literature. The

whole process of problem solving depends on how well students can understand

the problem what they read, whether their mathematical knowledge provides them

with the necessary tools to solve the problem. The results are consistent with the

results of Özsoy’s (2002) study which concludes that there is a positive significant

relationship between students’ mathematics achievement scores and scores

obtained from Polya’s problem solving steps in problem solving ability test.

Students’ confidence and ability to evaluate their own work also give them a

substantial effect to solve the problem. Thus, they are able to communicate to

their peers or teachers what they have done. Thomas (1990) also validated that the

use of computer graphic problem solving activities helped students to better

understand function concepts and improved student attitudes also have positive

118

effects on the academic achievement of students in the USA (Bangert-Drowns et

al., 1991; Kulik et al., 1987).

The result of the problem solving skill scale and achievement test showed us

positive effects of technology enhanced mathematics instruction on students’

problem solving skills. Integrating technology into mathematics curriculum, the

computers provided relatively unstructured exercises of various types, such as

games, simulations, tutoring, web searching, calculating etc. to enrich the

classroom experience, stimulate and motivate students in this study. The results

from this study advised that the effects of technology enrichment instruction are

positive over traditional Instruction on sixth grade public school students’

problem solving skills in mathematics. Many educators give remarkable efforts

with great expectation that technology will dramatically increase students’ critical

thinking ability such as problem solving skills and academic achievement.

However, Clark’s mentioned that there is no learning benefit of the media. In

addition, he says that, “media are mere vehicles that deliver instruction but do not

influence student achievement any more than the truck that delivers our groceries

causes changes in our nutrition. Basically, the choice of vehicle might influence

the cost or extent of distributing instruction, but only the content of the vehicle

can influence achievement” (p. 446). However, according to this research, there

are evidences to prove that using technology for enhancing traditional instruction

has evidence students’ learning about how to solve mathematical problems.

Moreover, the results suggest that classroom teachers need to review research-

based evidence that accumulated for positive outcomes by using technology in

instruction.

5.2.2. Attitude towards Mathematics

The purpose of this research study was to determine whether there a difference in

students’ attitude towards mathematics between control groups and experimental

119

groups. In the literature, there are so many studies and opinions about correlation

among achievement, interest, and motivation such as John Dewey (1913), Ainely

(2001). Because of the research design, four groups were employed, which were

two control groups and two experimental groups in two different schools in the

same. Two groups of them took a technology enrich instruction in math class;

however the other groups did not use any technical media in the mathematics

class. Groups received 4-week instruction and 16 lectures each of which was 40

minutes. At the beginning of the study, mathematics attitude scale which is about

their feelings and attitudes on learning mathematics was given both experimental

and control groups, just in one school as a pre-test to measure subject attitude

toward mathematics because of the research design properties. At the end of the

study, all four groups took the same questionnaire for the purpose of comparing

the pre- and post-study results on students' attitudes about learning mathematics.

Result of the research was showed that the means of attitude towards the

mathematics score was not significantly greater for pretest taken groups (M =

62.42, SD = 6.09) than for pretest not taken groups (M = 60.41, SD = 8.61). This

means, the analysis of the total scores on students' attitudes on learning

mathematics indicated that the experimental and control groups were equivalent.

The other follow up analyses also indicated same kind of results. The results were

similar to the study conducted by White’s study (1998) and Fielder’ study (1989).

According to White (1998), the control group exhibited a significant increase in

students’ attitude toward mathematics. However, Kulik, Bangert and Williams

(1983) found that computer assisted instruction methods tended to moderately

raise mathematics achievement and foster more positive attitudes towards

mathematics

Although there was no improvement in attitude of the treatment, groups were too

small to be statistically significant in this current study improvement. In addition,

changing attitudes towards something needs more time. The duration of study was

only four weeks which is not enough time to improve attitude toward

mathematics. A much longer study may be achieved the different outcomes in

120

attitudes of students who participate technology enhanced instruction. Moreover,

students who were in experimental groups had to deal with more new stuff about

computer, software related to study, etc. Students’ level of experience using the

computer and Internet may have contributed to the negative attitudes in the

treatment group. Because they need to get used to this new context in a short time,

their attitude toward the mathematics may also be lower. Mathematics anxiety

combined with computer anxiety may have an effect on attitudes in the

technology enhanced mathematics courses.

In this study, it was tried to identify significant issue in need of investigate and

development. Beside this, variety of new technologies was observed how to

facilitate the mathematical problem solving skills and attitudes towards

mathematics of all students.

5.3. Implications and Recommendation

According to instructional principles of MoTNE, the new technology supports

learners to have a chance to explore and model a diversity of mathematical gains

at highly complicated situations and, at the end, create a holistic mathematics

opinion. Second, the new computer technologies have the amplifiers and

organizers roles on cognitive domain (Heid, 1997) as well as support

mathematical problem solving for all students. With the multiple involvements

comprising self- reflections and a real world scenario involving all kind of

technological devices in classroom, computers, spreadsheets etc., students

reflected to a many characteristics of teaching with technology. In this experience,

the computer technology assisted as a tool or stimulator for mathematics

instructions.

For this study, first the implication is the need for the reconsideration of the

instruction strategies that can be implemented in other levels of students to

121

improve problem solving skills. Instruction strategies emphasizing collaborative

studies (Johnson and Johnson, 1996) as well as cooperative studies (Heller et al.,

1992) should be incorporated into the technology in the classrooms.

As consistent with the literature, technology enhanced instruction here has a

reasonable effect, it is supposed to be among factors for mathematics problem

solving skills. Consequently, teachers and instructors should be aware of this

situation and be able to find ways to integrate technology to their instructions.

Another implication for practitioners is that inquiry-based learning, problem-

based learning, project-based learning, case-based learning, active learning and

discovery learning (Froyd, 2003) should be employed facilitating the development

of problem solving skills through technology enriched classroom environments.

In the current educational settings, students do not involve so often in real-life

problems and they have to cope with these problems on the basis of their learning

process at school. In other words, when they encounter with ill-structured items,

their performance mainly depends on what they have learned so far by means of

the curriculum. Therefore, situations that require the improvement of

mathematical problem solving ability should be supported by the instructors.

Large-scale projects should be implemented for more effective technology

integration into instruction. In this study, there were only 88 students in the study;

further studies might include more students. In the context of these projects, more

efficient use of technology in mathematics instruction should be investigated

through the cooperation of the MoTNE, schools. In addition, more activities about

problem solving should be prepared for teachers. Therefore, mathematics teachers

may eliminate learning difficulties and save their time.

Instead of short research study, long term studies which conduct to investigate

effect of technology enrichment instruction may be more helpful to observe

students’ attitude toward mathematics or towards technology and also students’

problem solving process.

122

Another implication of the study for the researchers is that researchers should

work closely with teachers and developers of new hardware and software in order

to conduct high-quality research. By this means, the researchers and the teachers

can see the effects of the new tools before the application of these tools into the

wide educational contexts.

Consequently, it is wished that this study will contribute to the literature through

providing clarification for the limitations declared in previous studies or support

new studies with the previous findings. The results of this study can assist the

designers of new technology enriched teaching or learning instructional design to

consider along with their instructional design. At the end, the design of effective

learning tasks utilizing technology integration should be incorporated.

123

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141

APPENDICIES

APPENDIX A

INTERVIEW PROTOCOL

Questions:

1. Örnek problem verilecek.

2. Problem çözerken ne düşünürsün ne yaparsın?

3. Anlama Aşaması

a. Soruyu ilk gördüğünde ne yaptın? Daha sonra ne yaptın?

b. Problemde sorulan nedir? İçinde önemli olan şeyler nelerdir?

c. Soruda anlaşılmayan bir şey var mı? Varsa nedir?

4. Çözüm aşaması

a. Problemi çözmek için hangi yolu düşündün? Bu yol bu problemi

çözer mi?

b. Problemde sana zor olan kısmı neresidir? Bu kısmın üstesinden

gelmek için ne yaptın?

5. Bulunan Sonucun kontrol edilmesi

a. Problemin cevabının doğruluğundan emin misin? Nasıl?

b. Cevabın doğruluğunu kontrol etmek önemli midir? Neden?

6. Anlatın

a. Problemin çözümünü anlatır mısın?

b. Sence baksa yolla çözülebilir mi? Mesela neler olabilir?

c. Problemi çözerken neler hissettin? Şimdi ne hissediyorsun?

142

APPENDIX B

MATHEMATICS ATTITUDE SCALE

Adınız Soyadınız:………………………………………….. Cinsiyetiniz:…………..

Okulunuzun ismi:…………………………………………. Sınıfınız:………………

MATEMATİK DERSİNE KARŞI TUTUM ÖLÇEĞİ

Genel Açıklama: Aşağıda öğrencilerin matematik dersine ilişkin tutum cümleleri

ile her cümlenin karşısında"Tamamen Uygundur", "Uygundur", "Kararsızım",

"Uygun Değildir" ve "Hiç Uygun Değildir" olmak üzere beş seçenek verilmiştir.

Lütfen cümleleri dikkatli okuduktan sonra her cümle için kendinize uygun olan

seçeneklerden birini işaretleyiniz.

T

amam

en

Uy

gu

ndu

r

Uy

gu

ndu

r

Kar

arsı

zım

Uy

gu

n

Değ

ild

ir

Hiç

Uy

gu

n

Değ

ild

ir

1. Matematik sevdiğim bir derstir.

2. Matematik dersine girerken büyük sıkıntı duyarım. 3. Matematik dersi olmasa öğrencilik hayatı daha zevkli olur. 4. Arkadaşlarımla matematik tartışmaktan zevk alırım.

5. Matematiğe ayrılan ders saatlerinin fazla olmasını dilerim. 6. Matematik dersi çalışırken canım sıkılır. 7. Matematik dersi benim için angaryadır. 8. Matematikten hoşlanırım. 9. Matematik dersinde zaman geçmez. 10. Matematik dersi sınavından çekinirim. 11. Matematik benim için ilgi çekicidir. 12. Matematik bütün dersler içinde en korktuğum derstir. 13. Yıllarca matematik okusam bıkmam. 14. Diğer derslere göre matematiği daha çok severek çalışırım. 15. Matematik beni huzursuz eder. 16. Matematik beni ürkütür. 17. Matematik dersi eğlenceli bir derstir. 18. Matematik dersinde neşe duyarım. 19. Derslerin içinde en sevimsizi matematiktir.

143

20. Çalışma zamanımın çoğunu matematiğe ayırmak isterim.

144

APPENDIX C

PROBLEM SOLVING SKILLS SCALES

Ad Soyad: Okulu:

Öğrenci No:

PROBLEM ÇÖZME BAŞARI TESTİ

1) Murat saat 08.30'da evden çıkarak berbere gitti. Berberde 30 dakika kalan Murat,

yürüyerek 10 dakikada markete gitti ve 15 dakika içinde alışverişini bitirdi. Eve

döndüğünde saat 09.45'i gösterdiğine göre Murat'ın dışarıda geçirdiği süre kaç

dakikadır?

Yukarıda problemi çözmek için, Murat'la ilgili verilen bilgilerden hangisi

gereksizdir?

a) Eve dönüş saati

b) Evden çıkış saati

c) Berberde kaldığı süre

d) Gereksiz bilgi yoktur.

2) Mehmet, evlerinin bahçe duvarını boyamak istiyor. Duvarın 3 metrekaresini boyamak

için 1 kutu boya gerekiyor. Duvarın boyanacak yüzeyi toplam 36 metrekare ise,

duvarın tamamını boyamak için kaç kutu boya alınmalıdır? Problemin özeti

aşağıdakilerden hangisidir?

a) 3 m2 duvara 1 kutu boya gittiğine göre 36 m

2 duvara kaç kutu boya

gerekir?

b) 36 kutu boya ile kaç m2 duvar boyanır?

c) 1 kutu boya ile 36 m2 duvar boyanıyorsa 3 kutu boya ile kaç m

2

boyanır?

d) 3 m2 duvar için 1 kutu boya gerekiyorsa 36 m

2 duvar kaç liraya

boyanır?

145

3) Bir satıcı tanesini 120 Kr'a aldığı 12 düzine bardağı dükkânına getirirken 12 tanesini

düşürüp kırıyor. Satıcının bardakların satışından 20 TL kar etmesi için bardakların

tanesini kaç liraya satmalıdır?

Aşağıdakilerden hangisi bu probleme benzerdir?

a) Elimizdeki para ile 15 tane gofret alırsak, 45 Kr. artmakta, 16 tane

gofret alırsak da 50 Kr. eksik kalmaktadır. Buna göre bir gofret kaç

liradır?

b) Bir manav kilogramı 1 TL'den 25 kg çilek almıştır. Çileklerin 3

kilosunu çürüdüğü için atmıştır. Manav, kalan çileğin kilogramını kaç

liradan satmalıdır ki 5 TL kar etsin?

c) Bir kırtasiyeci tanesi 50 Kr. olan 12 düzine kalemi satışa çıkartıyor.

Elinde 5 düzine kalem kaldığına göre, kırtasiyeci kaç lira kazanmıştır?

d) Bir kitapçı, ilk günkü satışından 300 TL, ikinci gün ise ilk günkü

satışının yarısından 18 TL fazla satış yapıyor. Kitapçı, iki günde toplam

kaç TL satış yapmıştır?

4) Farklı iki sayının toplamı 264'tür. Büyük sayı küçük sayının 5 katına eşitse, büyük

sayı kaçtır?

Aşağıdakilerden hangisi bu probleme benzerdir?

a) İki sayının farkı 1974'tür. Küçük sayıya 183 eklenir, büyük sayıdan

269 çıkarılırsa, yeni fark ne olur?

b) 80 m uzunluğundaki bir top kumaştan önce 12,25 m, daha sonra da 9,4

m kumaş satılırsa geriye kaç m kumaş kalır?

c) İstanbul ile Antalya arası 720 km'dir. İstanbul'dan kalkan bir otobüs,

yolda 2 defa yarımşar saatlik mola vererek 10,5 saat sonra Antalya'ya

varıyor. Otobüsün saatteki ortalama hızı kaç kilometredir?

d) Mehmet ile babasının yaşları toplamı 49'dur. Babasının yaşı,

Mehmet'in yaşının 6 katına eşitse, babası kaç yaşındadır?

146

5) Bir çuval nohudun önce 4/5 'i, sonra kalanın 1/3 'ü satıldı. Geriye 12 kg

nohutkaldığına göre çuvalda kaç kg nohut vardır?

Bu problemi anlatan şekil aşağıdakilerden hangisidir?

6) "235 TL'yi 522 TL'ye tamamlamak için kaç TL'ye daha ihtiyaç vardır?" problemini

gösteren matematik cümlesi aşağıdakilerden hangisidir?

a)235 + 522 = ? b)522 : 2 = ?

c) 235 + ? = 522 d) 235 x ?= 522

147

7) Bir atlet saatte 20 km hızla koşmaktadır. Saatteki hızı 50 km olan bir otomobille atlet,

aynı anda harekete başlarsa, 1,5 saat sonra atlet otomobilden kaç km geride olur?

Bu problemi çözmek için öncelikle aşağıdakilerden hangisi yapılmalıdır?

a) Atletle otomobilin hızlarının farkı bulunmalıdır.

b) Atletin iki saatte aldığı yol bulunmalıdır.

c) Atletle otomobilin hızları toplanmalıdır.

d) Atletle otomobilin hızları çarpılmalıdır.

8) Kare biçimindeki bir bahçenin bir kenarı 35 metredir. Bu bahçenin çevresine 5 metre

aralıklarla kavak fidanı dikilecektir. Kavak fidanının tanesi 2 TL olduğuna göre; bu iş

için kaç TL gereklidir?

Bu problemin çözümü için sırasıyla hangi işlemler yapılmalıdır?

a) çarpma, çarpma, çarpma

b) çarpma, bölme

c) çarpma, bölme, çarpma

d) çarpma, toplama, bölme

9) 20 kişi bir otobüs kiralamak istiyor. Bunlardan 5 kişi vazgeçtiği için, diğerleri 30'ar

TL fazla ödemek zorunda kalıyor. Buna göre otobüsün kirası kaç TL'dir?

Problemi çözmek için aşağıdaki seçeneklerden hangisi yapılmalıdır?

a) 20-5 = 15 b) 20-5 = 15

15:5 = 3 15x30 = 450

30 x 3 = 90 450 : 5 = 90

90x15 = 1350 20x90=1800

c) 20-5 = 15 d) 20-5 = 15

15:5 = 3 15x30 = 450

30 x 3 = 90 450 x 5 = 2250

90 x 3 = 270

10) 50 yolcusu bulunan bir otobüsten 5 erkek, 5 kadın inince geriye kalanlar arasında

erkeklerin sayısı bayanların sayısının 3 katı oluyor. Buna göre ilk halde otobüste kaç

erkek vardı?

a) 25 b)30 c) 34 d) 35

148

11) Düzinesini 300 Kr.'a aldığı tokaların tanesini 40 Kr.'a satan bir kırtasiyeci, 3 düzine

toka satınca kaç TL kar eder? Bu problemi çözmek için sırasıyla hangi işlemler

yapılmalıdır?

a) toplama, çıkarma, çarpma, çarpma, bölme

b) bölme, çıkarma, çarpma, çarpma, bölme

c) bölme, çarpma, toplama, bölme

d) çarpma, çıkarma, çarpma, bölme

12) Mehmet'in babası kendisine takım elbise diktirmek için metresi 19 TL'den 6 m kumaş

alıyor. Mehmet'in babası işçilik ücreti olarak terziye 280 TL ödediğine göre,

aşağıdakilerden hangileri yanlıştır?

I) Elbise 280 TL'ye mal olmuştur.

II) İşçilik ücreti kumaştan pahalıdır.

III) Elbisede kullanılan kumaşın tutarı 114 TL'dir.

IV) Hepsi yanlıştır.

a) I – II b) I -IV c) III –IV d) II –

IV

13) 9 kişinin yaş ortalaması 30 dur. İçlerinden biri ayrılınca, kalanların yaş ortalaması 28

oluyor. Ayrılan kişi kaç yaşındadır?

a) 46 b)44 c)45 d)43

14) 160 m uzunluğundaki bir yolcu treni, uzunluğu 215 m olan köprüden geçecektir.

Lokomotifin köprüye girişi ile son vagonun köprüden çıkışı 15 saniyede olmaktadır.

Buna göre trenin saatteki hızı kaç km'dir?

a) 85 b) 90 c) 95 d) 100

15) Bir uçak, benzin deposu dolu olarak İstanbul Atatürk Hava Limanı' ndan kalkıyor.

izmir'e geldiğinde, deposunun 10

9'u boşalıyor, izmir'den 480 litre benzin alarak

deposunu yarıya kadar dolduruyor. Bu uçağın deposu kaç litreliktir?

a) 900 b)1000 c) 1100 d) 1200

149

16) Mustafa'nın parası, Yeşim'in parasının 7 katıdır. İkisinin paraları toplamı 988 TL

olduğuna göre; Mustafa'nın ne kadar parası vardır?

Problemin Çözümü:

Mustafa'nın parası = 7 x Yeşim'in parası

Mustafa'nın parası + Yeşim'in parası = 988 TL

8 x Yeşim'in parası = 988 TL

988:8 = 123,5 (Yeşim'in parası)

7 x 123,5 = 864,5 TL

864,5 TL (Mustafa'nın parası)

Yukarıda çözümüyle birlikte verilen problemin sağlamasını ifade eden işlem

aşağıdakilerden hangisidir?

a) 864,5 + 123,5 = 988 c) 864,5 - 123,5 = 741

b) 988 - 864,.5 = 123,5 d) 988 + 123,5= 1111,5

17) Bir sinemadaki kadın ve erkek seyircilerin toplam sayısı 180'dir. Erkeklerin 7 katı,

kadınların 5 katına eşit olduğuna göre; bu sinemada kaç kadın ve kaç erkek seyirci

vardır?


7 kat + 5 kat = 12 kat

180: 12 = 15

7 x 15 = 105

5 x 15 = 75

18) Yukarıda çözümüyle birlikte verilen problemin sağlaması yapılmak istendiğinde,

aşağıdakilerden hangisi doğru olur?

a)5 x 75 = 375 b) 7 x 75 = 525

7 x 105 = 735 5 x 15 = 75

c) 7 x 75 = 525 d) 7 x 15 = 105

5 x 105 =525 5 x 75 = 375

150

19) Bir satıcı, 6 kasa kiraza 138 TL ödemiştir. Kirazları dükkânına getirmek için 42 TL

masraf yapmıştır. Satıcı bir kasa kirazdan 15 TL kazanmak isterse; kirazın kasasını

kaç TL'den satmalıdır?

Problemin Çözümü :

I) 138 + 42 =

II) 30 + 15 =

III) 180:6 =

Bu problemin çözümü için verilen işlemlerin doğru sıralanışı aşağıdaki

seçeneklerin hangisinde verilmiştir?

a) III - II -1b) III -1 - II

c) I - II - IIId) I - III – II

20) Serkan Bey'in arabası 8 litre benzinle 100 km gitmektedir. Arabasının deposunda ise

48 litre benzin vardır. Hafta sonu gezisine çıkan Serkan Bey, 800 km yol yaptığına

göre; kaç litre benzin almıştır?

Problemin Çözümü :

I) 8 x 100 = 800

II) 800 : 100 = 8

III) 8 x 8 =64

IV) 64-48 = 16

Kaç numaralı işlem bu problemin çözümü için gereksizdir?

a) I b)II c)III d) IV

151

21) Turist olarak Ankara'ya gelen Mary, 355 Avro'sunu TL'ye çevirmek için bankaya

gidiyor. 1 Avro =180 Kr ve banka da 3 TL ücret aldığına göre, Mary kaç TL

almalıdır?


355x180 = 63900 Kr

63900 : 100 = 639 TL

639 - 3 = 636 TL

Yukarıda çözümü verilen problemin sağlaması yapılmak istendiğinde hangi işlemler

yapılmalıdır?

a) 636 - 3 = b) 63900 : 100 =

633x100= 639x180 =

63300: 180 =

c) 636 + 3= d) 639+180 =

639x100= 819x100 =

63900:180= 63600:180 =

Test Bitti.

Katkılarınızdan dolayı teşekkür ederim.

152

APPENDIX D

ACTIVITIES

Senaryo 1:

Okulunuza bir basketbol sahası yapılacaktır. Sizin bunun için bir maliyet

çıkarmanız gerekmektedir.

Yol gösterme. Maliyeti çıkarırken şunları düşünmeniz işinizi kolaylaştırabilir.

a. Ne büyüklükte bir alana ihtiyacımız var?

b. Ne gibi malzemeler almalıyız? (Boya, fırça, file, yer döşemesi v.b)

c. Malzemeleri en ucuz nereden alabiliriz? (İnternetten araştırma)

d. Ne kadar bir maliyeti olacağı hesaplaması yapılacaktır.

Senaryo 2:

Okul idaresi dönem sonu kutlaması planlamaktadır. Bu plan içinde 200 davetliye

yemek ikram edilmesi de planlanmaktadır. Ancak idare yemek menüsünde neler

olacağı ve maliyetinin ne kadar olacağına karar verememiştir. Sizden bu durum

için sağlıklı ve hesaplı bir menü önermeniz istenmektedir. Menünüzdeki yemek

çeşitlerinizin yağ, kadronhidrat, protein ve besin değerlerini (kalori) ve

menünüzün toplam maliyeni bir rapor halinde idareye iletmeniz gerekmektedir.

Kaynaklar

http://www.afiyetle.com/index.php

http://www.european-vegetarian.org/lang/tr/info/kit/kit.php

http://www.kedimveben.com/vegkalori.htm

http://www.kedimveben.com/vegdenge.htm

http://www.afiyetle.com/index.php

http://www.european-vegetarian.org/lang/tr/info/kit/kit.php

http://www.kedimveben.com/vegkalori.htm

http://www.kedimveben.com/vegdenge.htm

153

Senaryo 3:

Anne babanız eve gelen su faturasının yüksekliğinden şikayet etmektedir. Bunun

için sizden evde aylık ortalama kaç litre su kullanıldığını ve buna göre yaklaşık su

faturanızın ne kadar olduğunu hesaplamanız isteniyor. Bu hesaplama sonunda

evde su kullanılan her işin toplam su kullanımın yüzde kaçı olduğunu grafikle

göstermeniz istenmektedir.

http://www.wwf.org.tr/su/

www.suyunubosaharcama.org

Projenin amacı:

Çalışmanın sonunda öğrenciler;

İnterneti kullanarak besinleri sınıflandırarak çeşitli besinlerin yağ, kolesterol,

protein, karbonhidrat değerlerini toplayabilecek,

Sağlıklı beslenmenin nasıl olduğunu öğrenecek,

Oran orantı ve ölçme kavramlarını gerçek yaşamdaki problemi çözmede nasıl

kullanıldığını anlayacaklar.

Miktarlar arasında ilişkileri anlayabilecek

http://www.wwf.org.tr/su/

http://www.suyunubosaharcama.org/

154

APPENDIX E

LESSON PLANS

BİLİŞİM SINIFI MATEMATİK DERSİ UYGULAMASI

Konu: Oturma odanızın yeniden tasarlanması (Mükemmel bir oturma odası sizce

nasıldır.)

Ders: Matematik

Sınıf: 6

Problem: Öğrencilerden kendi oturma odalarını yeniden tasarlamaları

istenmektedir. Ancak ailelerini ikna edebilmeleri için bunun için gerekli işlerin

oda planının geliştirilmesi ve mobilyaların fiyatlarının araştırılıp ve

düzenlendikten sonra bir liste hazırlamaları istenmektedir.

Kazanımlar:

Öğrenciler teknolojiyi, ölçme, araştırma ve problem çözme becerini matematik

dersine entegre ederek gerçek hayatla ilgili bir problemi tamamlar.

Etkinlikler:

1. Excel Hesap tablolarının kullanımının gösterilmesi

2. Hücrelere formüllerin yazılmasının gösterilmesi

3. İnternette araştırma yollarını anlatılması gösterilmesi

4. Oturma odanızın her tarafının ölçülmesi. (duvarlar, pencereler, kapılar,

koltuklar vs.) (Ödev haftaya ve cizimi)

5. Bir Excel dosyası oluşturularak ölçülen değerlerin bir sayfaya girilmesi.

Bu sayfaya “ölçüler” isminin verilmesi. (Ödev)

6. Bir Word dosyası açılarak odanın yeni şeklinin çizilmesi.

7. Ölçüler kullanılarak yeni yerleşim planı tasarlanır.

8. Daha önce acılan Excel dosyasında yeni bir sayfa açılarak yeni odada

olacakların listesi, fiyatları girilir.

155

9. Ne kadar bir maliyeti olacağı ve katma değer vergisini ne kadar tutacağını

matematiksel formülleşmesin oluşturularak hesaplattırılır.

156

APPENDIX F

ACTIVITY SHEET

Odanızın Tasarlanması Projesi

Odanızın bir depremde hasar gördüğünü düşünelim. Sizde ailenizi yeni

tasarladığınız odanız konusunda ikna etmek istiyorsunuz. Microsoft Word,

PowerPoint, ve veya Excel programlarını kullanarak onları ikna edici bir sunum

hazırlamanız gerekiyor.

Temel soru:

Mükemmel bir oda neler gerekir:

Görevler:

1. Odanızdaki her şeyin ölçülmesi: duvarlar pencereler kapılar. Yatak ve

eşyalar

2. Odanın ölçülerini yazmak için bir Excel dosyası açın.Dosyanın adını

ölçüler olarak kaydedin. Daha sonra ölçülerinizi 1/20 oranında

küçülten bir formül girin.

3. Bir Word dosyasında odanızın yerleşimini gösteriniz.

4. Yeni odanızın ölçülerini sayfada gösteriniz.

5. Eşyaların fiyatlarını internet göz atıcısı ile sanal marketlerden alınız.

Odadaki eşyalarınızın isimlerini ve fiyatlarını bir Excel tablosunda

listeleyiniz. Bu dosyayı harcamalar olarak kaydedin.

.

157

APPENDIX G

SAMPLES OF STUDENT ACTIVITY NOTES

159

APPENDIX H

STUDENT SELF EVALUATION FORM

1. Bu bilişim teknolojileri dersinde en çok neden/nelerden hoşlandınız?

2. Problemi gördüğünde ne yaptın? Ne düşündün?

3. Problemi çözmek için hangi yolu kullandın?

4. Problemin sonucunu bulabildin mi? Sonunda nasıl hissettin?

5. Bilişim teknolojileri sınıfındaki bu derste eğlendin mi?

160

APPENDIX I

RUBRIC FOR MATH PROBLEM SOLVING

Scale I: Understanding the Problem

2 Complete understanding of the problem

1 Part of the problem misunderstood or misinterpreted

0 Complete misunderstanding of the problem

Scale II: Planning a Solution

2 Plan could have led to a correct solution if implemented properly

1 Partially correct plan based on part of the problem being

interpreted correctly

0 No attempt, or totally inappropriate plan

Scale III: Getting an Answer

2 Correct answer and correct label for the answer

1 Copying error; computational error; partial answer for a problem

with multiple answers

0 No answer, or wrong answer based on an inappropriate plan

161

APPENDIX J

PROBLEM SOLVING ACHIEVEMNT TEST

1.

2

15

7

53

16

= ? işleminin sonucu kaçtır?

2. Kemal amca evinin arkasındaki bahçeye menekşe ve karanfil fidesi

dikmek istiyor. Bahçesi dikdörtgen şeklide olup uzun kenarı 12m kısa

kenarı 8m’dir. Kemal amca her 1 m2 ye 6 tane menekşe ve 2 tane

karanfil dikmek istemektedir. Bu durumda Kemal amca bahçesi için kaç

tane menekşe ve kaç tane karanfil dikmesi gerekmektedir?

3. 523a sayısı 2 ve 3 e tam bölünebildiğine göre a kaç değişik değer

alabilir?

162

4. Şeker oranı %15 olan 120kg. şekerli suyun içinde kaç kg şeker vardır?

5. Sabit hızla giden bir araç 3 saatte 69 km yol alırsa,10 saatte kaç km yol

alır?

6. 8 – 36 : 6 + 6 . 2 =? İşleminin sonucu kaçtır?

7. Belediye aşağıdaki şekilde görülen oyun parkının boyalı olarak

gösterilen kısımlarına çimle döşemek istiyor. Çimen ile döşenmeyen

kısım ise kumla kaplanacaktır. Kumla kaplı bölgenin çevresi tel örgü ile

çevrilecektir. Acaba belediye kaç metre tel örgüye ihtiyaç duyacaktır?

5m

8m

20m

20m

20m

9m

25m

163

APPENDIX K

PERMISSION FORM from the MoTNE

164

CURRICULUM VITAE

PERSONAL INFORMATION

Surname, Name : Curaoğlu, Orhan

Nationality : Turkish (TC)

Date and Place of Birth : 16 March 19764, Bolu

Marital Status : Single

e-mail : [email protected]

EDUCATION

Degree Institution Year of

graduation

BS Ege University, 1997

Department of Mathematics

High School Bolu Ataturk High School 1993

WORK EXPERIENCE

Year Place Enrollment

2011-Present Abant Izzet Baysal

Universsity

Research Assistant

2002-2011 Middle East Technical

University

Research Assistant

1999-2001 Abant Izzet Baysal

Universsity

Research Assistant

1998-1999 Şıralık Vatan elementary

School, MofTNE

Mathematics Teacher

1998-1998 Doganli Primary School,

MofTNE

Classroom Teacher

FOREIGN LANGUAGES

English.

165

SELECTED PUBLICATIONS

Book chapter

Yukselturk, E., & Curaoglu, O. (2010). Blended Assessment Methods in Online Educational

Programs in Turkey: Issues and Strategies. In S. Mukerji, & P. Tripathi (Eds.), Cases on

Transnational Learning and Technologically Enabled Environments (pp. 327-343).

doi:10.4018/978-1-61520-749-7.ch018

Articles

Curaoğlu, O., Baturay, M. H. & Çakır, R. (2007). Posner Ders Tasarım Modeli Işığında

İngilizce Ders Tasarımının Geliştirilmesi. GÜ, Gazi Eğitim Fakültesi Dergisi, 28 (3), 37-50.

Congress (International or National)

Curaoglu, O., Bu, L., Dickey, L., Kim, H. & Cakir, R. (2010). A Case Study of Investigating Preservice Mathematics Teachers’ Initial Use of the Next-Generation TI-Nspire Graphing

Calculators with Regard to TPACK. In D. Gibson & B. Dodge (Eds.), Proceedings of Society

for Information Technology & Teacher Education International Conference 2010 (pp. 3803-

3810). Chesapeake, VA: AACE.

Curaoglu, O., Bu, L., Jakubowski, E., Dickey, L., Bayazit, N., Kim, H., Cakir, R. & Spector,

J.M. (2009). Prospective Mathematics Teachers’ Initial Reactions to Model-Centered

Instruction. In I. Gibson et al. (Eds.), Proceedings of Society for Information Technology &

Teacher Education International Conference 2009 (pp. 4025-4029). Chesapeake, VA: AACE.

Yiğit, E.Ö., Curaoglu, O. (2009). Using Technology in Social Studies Classrooms. 11th

Annual International conference in Education, Athens, Greece, 2009.

Curaoglu O., Kiraz E., Cakir R. & Baturay M. (2006). A technology supported method

course: Based on the revision of instructional design models. In Crawford, C., Willis, D.,

Carlsen, R., Gibson, I., McFerrin, K., Price, J., & Weber, R. (Eds.), Proceedings of Society for

Information Technology and Teacher Education International Conference 2006 (pp. 2798-

2803). Chesapeake, VA: AACE.

Curaoglu, O. A Framework for Technology Integrated Educational Model for Turkish

elementary school. In Crawford, C., Willis, D., Carlsen, R., Gibson, I., McFerrin, K., Price, J.,

& Weber, R. (Eds.), Proceedings of Society for Information Technology and Teacher

Education International Conference 2006 (pp. 2798-2803). Chesapeake, VA: AACE.

Curaoglu,O., Cakır, R., Yükseltürk E. A Proposal of Founding Instructional Technology

Center. New Information Technologies in Education, Izmir,Turkey, 2004.

Curaoglu,O., Cakır, R., Yukselturk E. General Instructional Message Design Principles in

Online Learning. New Information Technologies in Education, Izmir,Turkey, 2004

Projects

166

Researcher in the project “Investigating Pre-service Mathematics Teachers’ Initial Use of the

Next-Generation TI-Nspire Graphing Calculators: Case Study”, FCR-STEM TI Group,

Learning Systems Institute, Florida State University

the effects of technology enriched instruction on 6...

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