THE EFFECTIVENESS OF USING COLLABORATIVE LEARNING IN THE

TEACHING OF FORM FOUR MATHEMATICAL REASONING

GEORGE TAN GEOK SHIM

This project is submitted in partial fulfillment of the requirements for a

Bachelor of Education (Mathematics)

with Honours

Faculty of Cognitive Sciences and Human Development

UNIVERSITI MALAYSIA SARAWAK

2008

The project entitled ‘The Effectiveness of using Collaborative learning in the

teaching of form four Mathematical Reasoning’ was prepared by George Tan

Geok Shim and submitted to the Faculty Cognitive Sciences and Human

Development in partial fulfillment of the requirements for a Bachelor of Education

(Mathematics) with Honours.

Received for examination by:

----------------------------------------

(Associate Professor Dr. Hong Kian Sam)

Date:

-------------------------------------

Grade

i

ACKNOWLEDGEMENT

I am glad and indeed fortunate to manage to finish this thesis report before the actual

due date. There are a number of people that I would like to acknowledge for their

assistance in carrying of the research. Without their help, I doubt I would have been

able to complete this thesis successfully.

Firstly, I would like to express my appreciation to my supervisor, Associate Professor

Dr. Hong Kian Sam for all his guidance and advices throughout the whole research

process. Without his help, it will definitely be hard for me to finish this thesis report

in time.

Secondly, I would like to say thank you to my course mates; Gan Siew Ling, Kueh Su

Li, Hii Yung Ing, Lau Siew Bey, Ting Jack Yew and Ting Sing Siong for their

cooperation and support.

Thirdly, I would like to express my appreciation to the principal, Mr. Tilai Bala

Udan, and all the teachers of SMK Siburan, Kuching for their cooperation. I would

also like to say thank you to all the students who were the sample of this study.

Finally, I would like to express my gratitude to my parents, lecturers and friends for

all their support throughout the research process.

vi

TABLE OF CONTENTS

ACKNOWLEDGEMENT i

ABSTRACT ii

ABSTRAK iv

TABLE OF CONTENTS vi

LIST OF TABLES x

LIST OF FIGURES xiv

CHAPTER 1: INTRODUCTION

1.0 Introduction 1

1.1 Background of the study 1

1.2 Problem Statement 4

1.3 Research Objectives 5

1.4 Research Questions 6

1.5 Research Hypotheses 7

1.6 Research Framework 8

1.7 Definitions of Terms 9

1.7.1 Collaborative Learning 9

1.7.2 Effectiveness 10

1.7.3 Mathematics Reasoning 10

1.7.4 Traditional Instructional Method 11

1.8 Significant of the research 11

1.9 Limitation of the research 12

vii

CHAPTER 2: LITERATURE REVIEW

2.0 Introduction 13

2.1 Collaborative Learning 13

2.2 Learning Theories related to Collaborative Learning 16

2.2.1 Constructivist Theory 16

2.2.2 Sociocultural Theory 16

2.3 The differences between Collaborative Learning and Cooperative 17

Learning

2.4 Characteristics of Collaborative Learning 19

2.5 The benefits of Collaborative Learning 21

2.5.1 Build Self-Esteem 23

2.5.2 Creates an environment of active, involved and 24

exploratory learning

2.5.3 Develops higher level thinking skills 25

2.6 Gender differences in Mathematics 25

2.7 Empirical finding on Collaborative Learning 27

2.7.1 General studies-based finding 27

2.7.2 Mathematics 28

2.8 Summary 29

CHAPTER 3: METHODOLOGY

3.0 Introduction 30

3.1 Research Design 30

3.2 Research Participants 31

3.3 Research Instruments 31

3.3.1 Pretest and Posttest 31

3.3.2 Questionnaire 32

viii

3.4 Research Procedures 32

3.5 Data Analysis 33

3.6 Summary 34

CHAPTER 4: FINDINGS

4.0 Introduction 35

4.1 Demographics of the samples 35

4.2 Reliability test 38

4.2.1 Pretest and Posttest 38

4.2.2 Questionnaire 39

4.3 Results of the study 40

4.3.1 Effectiveness of using Collaborative Learning for the 40

topic of Mathematical Reasoning and the effects of

gender on the findings

4.3.2 Students’ interest in the subject 42

4.3.3 Students’ perceptions on the teaching approaches based on 51

gender and teaching method

4.3.4 Students’ efficacy in mathematics 64

4.3.5 Preferred instructional method 74

4.4 Summary 74

CHAPTER 5: DISCUSSIONS AND SUMMARY

5.0 Introduction 75

5.1 Summary of the study 75

5.2 Summary of the results 76

5.3 Discussions of findings 77

5.3.1 Effectiveness of Collaborative Learning 77

ix

5.3.2 Gender issue in Collaborative Learning 78

5.3.3 Interaction effects between teaching method and gender 79

5.3.4 Interests in mathematics 80

5.3.5 Perceptions of the teaching method 80

5.3.6 Efficacy in learning mathematics 81

5.3.7 Preferences of the teaching method 81

5.4 Implications of the study 83

5.5 Suggestions for future studies 83

5.6 Conclusion 84

REFERENCES 85

APPENDICES

Appendix A: Work Schedule 90

Appendix B: Test Blueprint 91

Appendix C: Pretest 92

Appendix D: Posttest 99

Appendix E: Lesson plan (Traditional Instruction) 106

Appendix F: Lesson plan (Collaborative Learning) 110

Appendix G: Worksheet (Collaborative Learning) 115

Appendix H: Research Questionnaire 118

x

LIST OF TABLES

Table 2.1

Differences between Cooperative Learning and Collaborative Learning 18

Table 2.2

Characteristics of Collaborative Learning 20

Table 2.3

Summary of characteristics of Collaborative Learning 21

Table 2.4

Forty four benefits of Collaborative Learning 21

Table 3.1

Statistical analysis of the research 33

Table 4.1

Summary of the samples’ demographics 37

Table 4.2

Reliability values for the Pretest and Posttest 38

xi

Table 4.3

Reliability values for the questionnaire 39

Table 4.4

Two Way Analysis of Variables (ANOVA) results 41

Table 4.5

Means and standard deviations 42

Table 4.6

Analysis (Frequency and Percentage) of responses to Section B 47

(Students’ Interest)

Table 4.7

Analysis (Mean and Standard Deviation) of responses to Section B 49

(Students’ Interest)

Table 4.8

Independent t-test results for students’ interest in the subject based on teaching 50

methods

xii

Table 4.9

Independent t-test results for students’ interest in the subject based on gender 50

Table 4.10

Analysis (Frequency and Percentage) of responses to Section C 57

(Students’ Perception)

Table 4.11

Analysis (Mean and Standard Deviation) of responses to Section C 61

(Students’ Perception)

Table 4.12

Independent t-test results for students’ perceptions based on the 63

teaching methods

Table 4.13

Independent t-test results for students’ perceptions on the teaching methods 63

based on gender

Table 4.14

Analysis (Frequency and Percentage) of responses to Section D 69

(Students’ Efficacy)

xiii

Table 4.15

Analysis (Mean and Standard Deviation) of responses to Section D 72

(Students’ Efficacy)

Table 4.16

Independent t-test results for students’ efficacy in the subject based on 73

teaching methods

Table 4.17

Independent t-test results for students’ efficacy in the subject based on gender 73

xiv

LIST OF FIGURES

Figure 1.1

Research Framework 8

Figure 2.1

Maslow’s hierarchy of needs 24

ii

ABSTRACT

THE EFFECTIVENESS OF USING COLLABORATIVE LEARNING IN THE

TEACHING OF FORM FOUR MATHEMATICAL REASONING

George Tan Geok Shim

The year 2020 is just 12 years away and the time is getting shorter to achieve our

dream of becoming a fully developed and industrialized nation. Hence, all efforts

should be fully channeled by the government and all interested parties to establish a

scientific and progressive society as envisioned by the sixth challenge in Malaysian’s

Vision 2020 (Shahar Banun Jaafar, 2005). In order to attain this vision, our education

system needs to produce knowledge workers with a sufficiently high literacy in

mathematics. Fong (1993) regarded mathematics as an indispensable tool, a much

needed subject in this age of modern technology. Collaborative learning refers to the

form of classroom organization in which students work together, in small groups, on

a shared activity and with a common goal and is noticeable in most problem solving

subjects such as mathematics (Barnes, 1998). This study focused on looking at the

effectiveness of collaborative learning in the teaching of form four mathematical

reasoning compared to traditional instructional, and the possible effects of gender on

the instructional methods. This study also looked at the gender effects on interest

toward the subject, perceptions of the teaching methods and students’ efficacy in the

subject. The study was carried out using a pretest-posttest quasi-experiment design

with one treatment group and one control group. The study used two classes:

treatment (Collaborative learning) and control (Traditional instructional) groups

where each class consisted of 34 samples. The instruments of the study consisted of

the pretest, posttest and questionnaires. The result showed that the collaborative

learning group outperformed the traditional instructional group. This result supported

Wilczenski, Bontrager, Ventrone and Correia’s (1999) findings that more students

iii

from the collaborative learning group obtained accurate answer in the posttest when

compared to students who worked without group collaboration. In addition, the

results of the study showed that female students obtained better results in the posttest

compared to male students. These findings contradicted Anastasi’s (1958; cited in

Hyde, Fennema & Lamon, 1990) findings where differences did not appear until well

into the elementary school year. The study also found that students’ preferred

collaborative learning compared to traditional instructional. Students in the

collaborative learning group also showed higher interest in the subject and better self-

efficacy in the subject. This result was supported by Pietsch (2005) study where there

was greater participation among students in the collaborative learning classes,

suggesting that students’ levels of critical thinking, self-regulation and help-seeking

increased. However, gender did not appear to have an effect on students’ interest in

the subject, preference for teaching method and self-efficacy in the subject.

iv

ABSTRAK

KEBERKESANAN PEMBELAJARAN KOLABORATIF DALAM

PEMBELAJARAN PENAAKULAN MATEMATIK TINGKATAN EMPAT

George Tan Geok Shim

Tahun 2020 hanya tinggal 12 tahun lagi dan ini bererti hanya tinggal sedikit masa lagi

untuk mencapai impian kita menjadi sebuah negara industri dan membangun. Oleh

itu, segala usaha perlu dilakukan oleh kerajaan dan badan-badan berkenaan untuk

membina sebuah suatu masyarakat sainstifik dan progresif sepertimana yang

termaktub dalam cabaran ke-enam Wawasan 2020 (Shahar Banun Jaafar, 2005). Bagi

mencapai wawasan tersebut, sistem pendidikan kita perlu menghasilkan K- pekerja

(pekerja ilmuan) yang mempunyai pengetahuan matematik yang tinggi. Fong (1993)

mengatakan bahawa matematik adalah alat yang berguna dan suatu mata pelajaran

yang amat diperlukan dalam abad teknologi moden ini. Pembelajaran kolaboratif

bermaksud sejenis organisasi bilik darjah di mana pelajar bekerjasama, dalam

kumpulan yang kecil, dalam berkongsi aktiviti dan mempunyai sasaran yang sama

dan wujud dalam semua subjek berbentuk penyelesaian masalah seperti matematik

(Barnes, 1998). Kajian ini berfokus kepada mengkaji keberkesanan pembelajaran

kolaboratif dalam mengajar topik “Penaakulan Matematik” tingkatan empat jika

dibandingkan dengan pengajaran tradisional dan kesan jantina kepada keberkesanan

kaedah pengajaran. Kajian ini juga melihat kesan jantina ke atas minat pelajar

terhadap subjek, persepsi kepada kaedah pengajaran dan efikasi diri pelajar dalam

subjek tersebut. Kajian ini dijalankan menggunakan kajian ujian pra-pasca kuasi-

eksperimental dengan satu kumpulan kajian dan satu kumpulan kawalan. Kajian ini

menggunakan dua kelas: kumpulan kajian (Pembelajaran kolaboratif) dan kumpulan

kawalan (Pengajaran tradisional) di mana setiap kelas mempunyai 34 sampel. Alat

ukur kajian adalah ujian pra, ujian pasca dan borang soal selidik. Keputusan

v

menunjukkan bahawa kumpulan pembelajaran kolaboratif mengatasi kumpulan

tradisional. Keputusan ini menyokong dapatan kajian oleh Wilczenski, Bontrager,

Ventrone dan Correia (1999) di mana mereka mendapati bahawa lebih ramai pelajar

daripada kumpulan kolaboratif mendapat jawapan yang tepat dalam ujian pasca jika

dibandingkan dengan kumpulan yang tidak bekerja dalam kumpulan kolaboratif.

Selain daripada itu, keputusan juga menunjukkan bahawa pelajar perempuan

mendapat keputusan yang lebih baik jika dibandingkan dengan pelajar lelaki. Dapatan

ini adalah bertentangan dengan keputusan kajian Anastasi (1958; dalam Hyde,

Fennema & Lamon, 1990) di mana tidak wujud perbezaan sehingga di penghujung

sekolah rendah. Kajian ini juga mendapati bahawa pelajar lebih memilih

pembelajaran kolaboratif jika dibandingkan dengan pengajaran tradisional. Pelajar-

pelajar dalam kumpulan pembelajaran kolaboratif juga menunjukkan minat yang

lebih tinggi terhadap mata pelajaran dan efikasi diri yang lebih tinggi. Keputusan ini

disokong oleh Pietsch (2005) di mana terdapat banyak penglibatan pelajar dalam

kelas pembelajaran kolaboratif dan berpendapat bahawa terdapat peningkatan dalam

pemikiran kritikal pelajar, sikap berdikari dan sikap untuk mencari pertolongan.

Bagaimanapun, tidak ada kesan jantina terhadap mata pelajaran, perspesi terhadap

kaedah pengajaran dan sikap pelajar terhadap pengajaran.

1

CHAPTER 1

INTRODUCTION

1.0 Introduction

This chapter is divided into nine main sections. Section 1.1 provides the background

of the study. Section 1.2 discusses the problem statement of this study. Section 1.3

provides the reasons and objectives of the study. This is then followed by Section 1.4,

which discusses the research questions of the study. Section 1.5 provides the research

hypotheses of the study. Section 1.6 gives an overall view of the research through the

research framework of the study. The next section (Section 1.7) gives the meanings

and definitions of various terms used in this study. Section 1.8 discusses the

importance and significance of the study. This is followed by Section 1.9 which lists

the limitations of this study.

1.1 Background of the study

The continuous development of a country is very important as it will determine the

survival of the nation. China and India are examples of countries that are emerging

2

and progressing rapidly towards becoming a developed nation to be able to compete

with other nations in the global world (Saran & Guo, 2004). Malaysia also strives to

become a fully developed nation by the year 2020 as envisaged by our former Prime

Minister, Tun Dr. Mahathir Mohammad (The Government of Malaysia, 2007).

The year 2020 is just 12 years away and the time is getting shorter to achieve our

dream of becoming a fully developed and industrialized nation. Hence, all efforts

should be fully channelled by the government and all interested parties to establish a

scientific and progressive society as envisioned by the sixth challenge in Malaysian’s

Vision 2020 (Shahar Banun Jaafar, 2005). According to Theaker (1997), the sixth

challenge in Vision 2020 is to develop a society which acts as a contributor to the

scientific and technological civilization of the future instead of a mere consumer or an

end-user of technology.

In order to attain this vision, changes to the educational system are inevitable and is

one of most crucial component of developing a country. Our education system needs

to produce knowledge workers with a sufficiently high literacy in mathematics.

According to Taylor (1998), knowledge workers are workers who create, modify and

synthesize knowledge. To become knowledge worker, the acquisitions of scientific

and technological literacy as thinking tool are essential. Literacy in mathematics is a

must in this context as it is the language of science and technology and the foundation

for the technological age. In a developed nation, those who are equipped with high

mathematics competency are able to carry out complex tasks effectively and

efficiently, especially in management and administration (Mok, 1993). Fong (1993)

regarded mathematics as an indispensable tool, a much needed subject in this age of

modern of technology.

No major technological nation can afford to let its mathematical base erode away.

This is because mathematics underpins all of the sciences and is critical to the

3

development of new areas of technological expertise and their commercial

exploitation (Millennium Mathematical Project, 1999). Mathematics is essential in

computing, biotechnology, telecommunications, aircraft design, medical imaging,

genetic research and many others. The examples above are just a handful of the

applications which translate complex mathematics theories into tangible practical

benefits (Millennium Mathematics Project, 1999).

To have a sufficiently high literacy in mathematics, students need to have good

mathematics performance and high mathematics achievement. Hence, school

administrators and other stakeholders are beginning to recognize that the educational

system needs fundamental changes to keep up with the pace of changes in the

knowledge and pedagogical fields. Some educational researchers and practitioners

have called for a change from the traditional educational system to one that

emphasizes interconnectedness, active learning, and shared decision making, arguing

that the traditional classroom competition is not healthy (Kagan, 2003). How can

teachers avoid the problem associated with classroom competition and motivate

students to think analytically and creatively by themselves? One alternative method

that teachers can use is through collaborative learning.

Collaborative learning refers to the form of classroom organization in which students

work together, in small groups, on a shared activity and with a common goal and is

noticeable in most problem solving subjects such as mathematics (Barnes, 1998).

According to Edwards (2002; cited in Tiong & Yong, 2004), peer collaboration is

effective for mathematical tasks which require reasoning but not for tasks which

require rote learning. Some studies in cooperative mathematics learning in small

groups call for the direct teaching of collaborative skills or team building to enable

groups to work effectively (Edwards, 2002; cited in Tiong & Yong, 2004).

Determining the effectiveness of using collaborative learning in mathematics can lead

to the adoption of this teaching approach of mathematics which could improve the

4

mathematics achievement among students. This can help Malaysia towards achieving

its goal of becoming a develop nation by the year 2020.

1.2 Problem Statement

Collaborative learning method is not a new teaching method as teachers have used it

for many years in various forms (Prendergast, 2004). Although some advanced

countries have implemented collaborative learning, this instructional approach has yet

to be implemented successfully in Malaysia. The present educational system in

Malaysia is still largely examination oriented where students mainly focused on

memorizing rather than understanding. Students who learned in an examination

oriented learning environment are likely to forget what they have learned in school as

it can best be metaphorized as “chew, spit and forget”. As learning is all about

understanding, the use of examination oriented instructional approach trains students

to memorize a certain facts and does not allow then to think in a creative matter. The

examination oriented classrooms are also less attractive and boring to the students as

there are fewer activities for the students and involved mainly passive learning.

In order to change this teacher-centred classroom, several improvements need to be

done and one of it is through the implementation of learners-centred teaching and

learning methods such as collaborative learning. With collaborative learning, students

will have the opportunity to experience more meaningful and motivating lessons in

the classroom. They will also able to develop inquiry skills which is essential for the

development of knowledge workers of the future. The use of group based approach

such as collaborative learning will enable students to learn the spirit of working

together as a team which is an essential skill in the real life situation.

However, the results of the studies definitely cannot be compared and used in the

Malaysia’s education setting because students in Malaysia behave differently, are

5

from different cultural background and may have different learning preferences

compared with students from of other countries. Other factors such as different school

environment and social expectation could also impact on the findings of similar

studies done in Malaysia. Hence, it is appropriate for a study to determine the

applicability of collaborative learning approach to be used in the local setting for

mathematics teaching.

1.3 Research Objectives

The main objective of this study was to determine whether collaborative learning

approach would produce higher test achievement among students than the traditional

form of instruction for the teaching of mathematical reasoning in form four.

Specifically, this study looked at the following research objectives.

1. To determine the differences in the mathematics achievement between the

groups of students taught using collaborative learning and traditional

instructional method for the topic of Mathematical Reasoning.

2. To determine the differences in the mathematics achievement based on

students’ gender.

3. To determine if there was an interaction effect between instructional

approach (collaborative learning and traditional instructional method) and

students’ gender on mathematics achievement.

4. To determine the differences in students’ interest in the subject based on

gender/ teaching methods.

6

5. To determine the differences in students’ perceptions on the teaching

method based on gender/ teaching methods.

6. To determine the differences in students’ efficacy in the subject based on

gender/ teaching methods.

7. To determine which instructional approach (collaborative learning and

traditional instructional method) the students preferred.

1.4 Research Questions

This study examines the following research questions:

1. Were there any differences in the mathematics achievement between the

groups of students taught using collaborative learning and traditional

instructional method for the topic of Mathematical Reasoning?

2. Were there any differences in mathematics achievement based on the

students’ gender?

3. Was there an interaction effect between instructional methods (collaborative

learning and traditional instructional method) and students’ gender on

mathematics achievement?

4. Were there any differences in students’ interest in the subject based on

gender/ teaching methods?

5. Were there any differences in students’ perceptions on the teaching method

based on gender/ teaching methods?

7

6. Were there any differences in students’ efficacy in the subject based on

gender/ teaching methods?

7. Which instructional approach (collaborative learning and traditional

instructional method) did the students prefer?

1.5 Research Hypotheses

This research has seven research hypotheses based on the research questions stated:

H01: There were no differences in the mathematics achievement between the

groups of students taught using collaborative learning and traditional

instructional method for the topic of Mathematical Reasoning.

H02: There were no differences in mathematics achievement based on students’

gender.

H03: There was no interaction effect between teaching methods (collaborative

learning and traditional instructional method) and students’ gender on

mathematics achievement.

H04: There were no differences in students’ gender in the subject based on gender/

teaching methods.

H05: There were no differences in students’ perceptions on the teaching method

based on gender/ teaching methods.

H06: There were no differences in students’ efficacy in the subject based on

gender/ teaching methods.

8

H07: There were no differences in students’ preferences for the traditional

instructional method and collaborative learning.

1.6 Research Framework

The diagram below shows the research framework of this study.

Figure 1.1. Research Framework

Based on the research framework, the independent variables of this study were

divided into two categories. The first category was the instructional used in this study

which were the collaborative learning and the traditional instructional methods.

The second category of the independent variable was the students’ gender where

students were categorized as male and female students.

Dependent Variables

Collaborative

Learning

Traditional

Instructional Method

Students’ Mathematics

Achievement

Students’ Interest in the subject

Students’ Perceptions of the

teaching method

Students’ Efficacy in the subject

Students’ Preferences of the

teaching method

Instructional Method

Students’ Gender

Male Students

Female Students

Independent Variables