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
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.
i
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
vi
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
vii
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
viii
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
ix
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
x
38
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
methods
xi
50
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
(Students’ Efficacy)
xii
69
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
xiii
73
LIST OF FIGURES
Figure 1.1
Research Framework
8
Figure 2.1
Maslow’s hierarchy of needs
24
xiv
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
ii
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 selfefficacy 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.
iii
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 kuasieksperimental 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
iv
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. Pelajarpelajar 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.
v
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
1
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
2
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
3
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
4
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.
5
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?
6
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.
7
There were no differences in students’ preferences for the traditional
H07:
instructional method and collaborative learning.
1.6
Research Framework
The diagram below shows the research framework of this study.
Independent Variables
Dependent Variables

Students’ Mathematics
Achievement

Students’ Interest in the subject
Traditional
Instructional Method

Students’ Perceptions of the
teaching method
Students’ Gender

Students’ Efficacy in the subject

Male Students


Female Students
Students’ Preferences of the
teaching method
Instructional Method


Collaborative
Learning

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.
8