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THE USE OF GEOGEBRA IN

COLLABORATIVE LEARNING IN

MATHEMATICS

WONG LIT MAY

UNIVERSITI TEKNOLOGI MALAYSIA

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THE USE OF GEOGEBRA IN COLLABORATIVE LEARNING IN

MATHEMATICS

WONG LIT MAY

thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Education (Mathematics)

Faculty of Education

Universiti Teknologi Malaysia

JANUARI 2013

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“I hereby declare that I have read this thesis and in my opinion this thesis is

sufficient in terms of scope and quality for the award of the degree of Master of

Education (Mathematics)”

Signature : __________________________

Name of Supervisor : ASSOC. PROF. DR. MOHINI BINTI MOHAMED

Date : 31ST JANUARY____________

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I declare that this thesis entitled “The Use Of Geogebra In Collaborative

Learning In Mathematics” is the result of my own research except as cited in the

references. The thesis has not been accepted for any degree and is not concurrently

submitted in candidature of any other degree.

Signature : __________________________

Name : WONG LIT MAY___________

Date : 31ST JANUARY_____________

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Forever Love

For

Parents, Brothers, Sister, Friends and Fiance

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ACKNOWLEDGEMENT

At first, I would like to express my sincere appreciation to my thesis

supervisor, Associate Professor Dr. Mohaini Binti Mohamed who provided me ideas,

guidance and continually support in my research. Her comments, suggestion and

criticisms during the whole progress of this research are gratefully praised. Without

her encouragement, motivation and persistent helps, this research would not have

been possible.

Besides my supervisor, I would like to thanks several government authorities

such as Faculty of Education University Technology Malaysia, Jabatan Pelajaran

Johor Bahagian Pendaftaran Pendidikan dan Guru and Bahagian Kementerian

Perancangan dan Penyelidikan Dasar Pendidikan, Kementerian Pendidikan Malaysia

for their assistances in approving my request to carry on my research in secondary

school.

I would like to extend my appreciation to Puan Hj Habibah Binti Dol, Miss

Soh Jiun Yi and Cik Ismah Azilah Binti Mat Isa for listing the respondents, preparing

the ICT facilities and cooperation to smoothen my research. Without them, it would

be impossible for me to complete my thesis in time.

I thank my fellow course mate Kuek Meng Lie and Irene Tiong for updating

the information and assisting me throughout the whole research.

Last but not least, I would like to thank my family and friends: my parents,

Wong Yen May, Leng Mun Thong and Teo Wan Key. They supported me in

mentally and helped enormously through all the difficulties I encountered.

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ABSTRACT

This research aims to find out the level of the students’ cognitive skills via

using GeoGebra and investigate whether GeoGebra as a tool helps in learning

process. It has more specifically sought to obtain an understanding of the students’

cognitive skills according to Bloom Taxonomy via GeoGebra in Mathematics

classroom. Students’ interest to learn mathematics is also being tested. GeoGebra is a

dynamic mathematics software which consists of algebra, geometry, spreadsheet and

calculus to help students in learning process. The sample in this research consists of

7 Form 4 secondary school students in Johor Bahru. During this research, GeoGebra

and the concept of geometry and algebra were introduced to students. After that,

students had to answer some geometry and algebraic questions via social networking.

Through this social networking, students solve problems, give comments and

conduct discussion among themselves. Students’ level of cognitive skills was

obtained from this session. At the end, students were required to have an individual

interview and a questionnaire session with the researcher. These helped researcher to

find out whether GeoGebra as a tool helps students in learning process. The results

showed that 6 students were able to reach higher order thinking skill in Bloom

Taxonomy cognitive level during the discussion in social net working. Collaborative

learning helps students to think in a new open-minded way and may begin to change

students’ view of mathematics. Students like to use GeoGebra. They found that

GeoGebra is a user-friendly and significant in motivating their learning.

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ABSTRAK

Kajian ini bertujuan untuk menceburi tahap kemahiran kognitif pelajar

melalui penggunakan GeoGebra dan menyiasat sama ada GeoGebra sebagai suatu

alat untuk membantu dalam proses pembelajaran. Ia adalah lebih khusus untuk

mendapatkan pemahaman kemahiran kognitif pelajar menurut Taksonomi Bloom

melalui GeoGebra di dalam kelas Matematik. Minat pelajar untuk belajar matematik

melalui juga diuji. GeoGebra adalah perisian matematik dinamik yang terdiri

daripada algebra, geometri, spreadsheet, dan kalkulus untuk membantu pelajar dalam

proses pembelajaran. Sampel dalam kajian ini terdiri daripada 7 pelajar sekolah

menengah tingkatan 4 di Johor Bahru. Semasa kajian ini, GeoGebra dan konsep

geometri dan algebra telah diperkenalkan kepada para pelajar. Selepas itu, pelajar

diminta menjawab beberapa soalan geometri dan algebra melalui rangkaian sosial.

Melalui rangkaian sosial ini, pelajar menyelesaikan masalah, memberi komen dan

menjalankan perbincangan di kalangan mereka. Tahap kemahiran kognitif pelajar

diperolehi daripada sesi ini. Pada sesi akhir, pelajar dikehendaki bertemuramah

dengan penyelidik secara individu dan menjawab soal selidik yang disediakan. Ini

membantu penyelidik untuk mengetahui sama ada GeoGebra sebagai alat utuk

membantu pelajar dalam proses pembelajaran. Hasil kajian menunjukkan bahawa 6

orang pelajar dapat mencapai peringkat berfikir keterampilan tinggi dalam tahap

kognitif Taksonomi Bloom semasa perbincangan dalam rangkaian sosial.

Pembelajaran berkumpulan membantu pelajar berfikir secara terbuka dan mengubah

pandangan pelajar terhadap matematik. Pelajar suka untuk menggunakan GeoGebra.

Mereka mendapati bahawa GeoGebra adalah mesra diguna dan penting dalam

memotivasi pembelajaran mereka.

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TABLE OF CONTENTS DEDICATION ………………………………………………………………… iii

ACKNOWLEDGEMENT …………………………………………………… iv

ABSTRACT…………………………………………………………………… v

ABSTRAK…………………………………………………………………….. vi

TABLE OF CONTENTS……………………………………………………… vii

CHAPTER 1: INTRODUCTION

1.1 Introduction………………………………………………………….. 1

1.2 Background of Study………………………………………………… 2

1.3 Problem Statement…………………………………………………... 4

1.4 Rationale of Study…………………………………………………… 6

1.5 Objective of Study…………………………………………………... 7

1.6 Research Question…………………………………………………… 7

1.7 Limitations…………………………………………………………... 7

1.8 Definition of the Term………………………………………………. 9

CHAPTER 2: LITERATURE REVIEW

2.1 Introduction…………………………………………………………. 11

2.2 Collaborative learning (CL) and Computer-Supported Collaborative

Learning (CSCL) in Mathematics Education………………………. 11

2.3 Role of Technology in Mathematics Education ………………………. 13

2.4 Social Networking

2.4.1 Facebook……………………………………………………… 14

2.4.2 Why is Facebook?..................................................................... 15

2.5 GeoGebra

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2.5.1 What is GeoGebra?................................................................... 16

2.5.2 Why is GeoGebra?.................................................................... 16

2.5.3 What is Algebra and Geometry?.............................................. 17

2.6 Problem Solving and Cognitive Skills……………………………... 20

2.7 Conclusion…………………………………………………………. 22

CHAPTER 3: RESEARCH METHODOLOGY

3.1 Introduction…………………………………………………………. 23

3.2 Research Design…………………………………………………….. 23

3.3 Research Location…………………………………………………... 25

3.4 Respondents of study……………………………………………….. 25

3.5 Research Instrument………………………………………………… 25

3.6 Data Collection……………………………………………………… 27

3.7 Procedure of the Study……………………………………………… 28

CHAPTER 4: DATA ANALYSIS

4.1 Introduction…………………………………………………………. 30

4.2 Analysis of the Respondents’ Cognitive Skills According to

Taxonomy Bloom via Facebook……..……………………………... 30

4.3 Analysis the Respondents’ Cognitive Skills and Interest of GeoGebra

via Interview………………………………………………………… 48

4.3.1 Finding from Respondent 1…………………………………… 54

4.3.2 Finding from Respondent 2…………………………………… 55

4.3.3 Finding from Respondent 3…………………………………… 56

4.3.4 Finding from Respondent 4…………………………………… 57

4.3.5 Finding from Respondent 5…………………………………… 58

4.3.6 Finding from Respondent 6…………………………………… 59

4.3.7 Finding from Respondent 7…………………………………… 62

4.4 Analysis respondents’ feedback whether GeoGebra as a tool helps in

learning process via questionnaire…………………………………… 63

CHAPTER 5: DISCUSSION, CONCLUSION AND RECOMMENDATION

5.1 Introduction…………………………………………………………. 67

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5.2 Discussion – The Level of the students’ Cognitive skills according to

Bloom Taxonomy via social net working and interview……………. 67

5.3 Discussion- GeoGebra as a tool helps in learning process via Interview and

questionnaires ……………………………………………………….. 70

5.4 Conclusion…………………………………………………………… 71

5.5 Recommendation……………………………………………………. 73

REFERRENCES…………………………………………………………….. 74

APPENDIX

Appendix A: Module…………………………………………………… 86

Appendix B: Questions would be discussed via social net working….... 101

Appendix C: Questionnaire……………………………………..………. 110

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CHAPTER 1

INTRODUCTION 1.1 Introduction

Malaysia’s education is not focus only on results of the test score but still

have some teachers are not willing to integrate technology into their mathematics

classroom. (Cheah, 2008). Perhaps one of the reasons is their perception where using

technology will not improve the achievement of test scores. Actually, learning is not

only for exams, teachers have to create a better environment to let students enjoy

their learning. To integrate technology into education need a systematic evaluation of

all activities of ICT in the classroom (Otieno, 2008).

Students are given opportunity to learn in various teaching method. The

mathematics activities should also be designed to give students opportunities to apply

mathematics in different context and to see the relevance of mathematics in daily life.

One of the better choices to learn mathematics is to use computer/software. With this

facility, learning process will shift from being teacher-centered to student-centered

and supported by a flexible and open-ended learning environment.

Mathematics is regarded as a way of thinking because of the abstraction of

mathematics. We cannot see the process that is happening in the mind and cannot see

the thinking process that is involved while doing mathematics. Learning mathematics

is not about providing practice on rote skills and memorization. It is looking at

students’ thinking ability and abilities to apply what they comprehend to solve a

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problem. Mathematics is a way of thinking that it requires students to provide good

reasoning and proof. Learning mathematics with computer/software also helps

students in learning process and actively control over students’ thinking process

when trying to solve the problems.

To make this shift, the education system must undergo a radical

transformation. The schooling culture must be transformed from one that is memory-

based to one that is informed, thinking, creative and caring, through leading-edge

technology. This helps students to prepare and make a successful transition to the

modern and more global environment.

In short, this study provides a view of students’ cognitive skills level after

learning geometry and algebraic by using GeoGebra. Students’ cognitive skills level

would be classified according to Bloom Taxonomy. Besides, this study also reflects

whether or not the GeoGebra as a tool helps in learning process in collaborative

learning.

1.2 Background of Study

Nowadays, mathematics teachers are facing challenges in using Information

and Communication Technologies (ICT). It is important to identify teacher

preparation and professional development programs that lead towards the

development of technology pedagogical content knowledge (TPCK) (Niess, 2006).

Koschmann (1996) introduced computer-supported collaborative learning

(CSCL) as an emerging paradigm of educational technology. In the past decade,

online education has grown rapidly but some studies have revealed students’

resistance to computer-supported collaborative learning (CSCL) programs. (Litz,

2007). However, contrary to the above research findings found that students'

attitudes towards mathematics were generally favorable (Etheris and Tan, 2004). The

result showed that students who solve the problem in scaffolded communication

environment (one of the application in Knowledge Forum, a CSCL program) tend to

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perform better than those students who did not use the scaffolded communication

environment.

CSCL offer a wide range of formal and informal learning opportunities to

individuals and groups worldwide (Hurme and Jarvela, 2005). The results of their

study showed that the students co-regulate their thinking while solving mathematics

problems. Besides, they found that when the students carried out activities in

networked discussions, the technology created an environment to stimulate students’

thinking through their mathematics knowledge. Higher order thinking skills (HOTs)

occurred among the students.

Besides CSCL, collaborative learning also helps students in learning process.

Collaborative learning provides group learning and significantly outperformed but

individual learning help group on content understanding only (Chen, 2008). She

stated that collaborative learning structure increases students’ academic achievement

compared to the individual help group. Students got better understanding during the

discussion by using collaborative learning. It helped students in teamwork skills and

problem strategies. It enhanced students’ ability to build up their self-regulation.

Students with collaborative learning would have better achievement than others.

Collaborative leaning allows students to learn mathematic and understand the

concepts of mathematics in cooperative way. Using computer/software (such as

GeoGebra and Geometry Sketch pad) helps teachers in teaching and learning process

and enables them to achieve teaching goal easily. Various ability and characteristic

of students would achieve different cognitive skills level. There is a need to know

that how far for the collaborative learning would develop the cognitive skills level of

students.

Technology plays as a tool to support teachers and students in their problem

solving skill, communication, collaboration, thinking skills, and knowledge creation

(McGhee and Kozma, 2000). Thus, teachers can transform this tool between

instructional roles, curricula, and practices in the classroom. There is a need to

persistent urge to align school education with the fast changing needs of the society

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and the world. So, using collaborative learning in teaching process would be one of

the methods to achieve teaching goal and enhance students’ learning ability.

Generally, positive attitude of teachers towards ICT adoption was held in

Malaysia secondary school (Lau and Sim, 2008). The integration of the ICT has been

widely practiced in the classroom especially in mathematics subject (Abu, 2010).

Some examples of the dynamic mathematical softwares are Geometer’s Sketchpad,

GeoGebra, Autograph and the Graphing Calculator which are powerful symbolic and

numerical calculations. Abu (2010) found that these dynamic mathematical softwares

enable students to produce quick calculations and assist them in abstracting

mathematical concepts. GeoGebra is a dynamic mathematical software which is easy

to learn and it leads students to reproduce “centuries of mathematical advances”

(Stahl, Rose and Goggins, 2010). In this study, GeoGebra has been chosen as a

teaching tool in the classroom in order to identify students’ cognitive skills level after

using GeoGebra in learning process.

In short, there are many positive impacts after using computer/ software in

learning process. Thus, there is a need to know whether by using computer/ software

in Malaysia education environment, students would increase their interest of learning

and understanding in learning process base on their significant cognitive skills level.

1.3 Problem Statement

Most of the teachers still prefer teacher-centered learning method. Thus, the

implementation of ICT in school helps teacher to build a better teaching and learning

environment. Students-centered is always needed. One of the aim in mathematics

curriculum for secondary schools is to face the challenges in everyday life brought

about by the advancement of science and technology. Therefore the use of

technology in our teaching and learning process should be emphasized to fulfill our

curriculum aim (Ministry of education, 2004).

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Educators need to incorporate new technologies into their classroom teaching

practice in order to improve students’ outcomes and exploit the potential of ICT

(McGehee and Griffith, 2004). The occurrence of positive impact of ICT only

depends on how teachers use ICT in their teaching and learning programs (Kozma,

2003). Teachers’ teaching method combine with using technology in the classroom

would be succeed and make substantial changes in their teaching life (Roschelle,

2000).

Technology in education is a widely-used and very broad term (Reis and

Ozdemir, 2010). Teachers have to be a balance between using technology and

traditional methods of teaching and learning in the classroom (Janet, 1999).

Continuous growth of technology provides a conducive learning environment for

teacher to teach. Thus, the integration of technology in teaching should be

implemented in learning environment. Students will pay more attention and have

better understanding to enjoy the learning process.

In Malaysia curriculum, using technology such as CD, computer, software,

projector... is not a common rutine in teaching process. Teachers used to teach

students with this facilities and helped students to achieve learning goal. Among

mathematics teachers in Malaysia, Geometry Sketch Pad is one of the mathematics

software for them to use in their mathematics class room. However, GeoGebra is a

new dynamic mathematical softwares which allows students to continue using it to

learn outside school hours (Reis and Gulsecen, 2010). It is free and can be used in

the mathematics classroom (Hohenwarter, 2010). The findings showed that

GeoGebra act as a supplement to traditional classroom instruction (Saha, Ayub, and

Tarmizi, 2010). Compare to traditional instruction alone, it creates a more effective

learning environment in mathematics classroom. Geogebra helps to furnish their

visual images of mathematical ideas and enable students to learn faster than non-

visual images (Saha, Ayub and Tarmizi, 2010). GeoGebra is free and easy to

integrate in the mathematics classroom (Hohenwarter, 2010).

In summary, technology in learning process is needed in order to achieve

teaching goal. Researcher beliefs that this is in strong connection with the

collaborative learning (computer/ software) towards cognitive skills. Does it develop

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any cognitive skills among the students after learning process from the GeoGebra?

Hence, this research aims to find out the students’ cognitive skills level after using

GeoGebra and defines whether GeoGebra suit as a tool in teaching and learning

process. In this research, GeoGebra is introduced to students as a teaching tool.

Students’ cognitive skills level would be obtained. Facebook is being selected as a

media for students to discuss online due to the offline of GeoGebra. Students do all

the mathematics questions by using GeoGebra and post their works and comments

into the discussion group(Facebook).

1.4 Rationale of Study

Collaborative learning requires teachers and students to adopt an educational

philosophy that focuses on “knowledge building” rather than “knowledge

reproduction” as main learning activity. Students would have better understanding in

practical learning process compare to memorizing. Classroom experiences can be

enhanced by using technology such as class website, blog assignments and mid-term

survey (Hoa, (2007). Using technology to teach mathematics can help in reducing

mathematics anxiety which it is due to failure of cognition or it is transferred from

others (Ye and Pyzdrowski, 2009). They found that before reducing the anxiety, it is

important to avoid the disadvantage situations which cause to the anxiety first. Thus,

using an appropriate technology/ software to target internal and external factors that

contribute to reduce mathematics anxiety is important.

Study of Ada (2009) concluded that there was a positive correlation between

the quality of collaborative process and the quality of cognitive skills fostered when

students use technology (computer/software). She claimed that when high levels of

social interaction and collaboration occur, the establishment of a community of

learning and fostering higher order thinking through co-creation of knowledge

processes would run together. Collaborative learning helps to enhance students’

interest in mathematics (Lin, 2008).

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This research is to investigate whether using GeoGebra as a teaching tool can

help students in applying their knowledge and explore their level of cognitive skills

in the discussions. The finding can provide guidance to the public whether by using

GeoGebra can help students in their learning and achieve the thinking goal.

1.5 Objective of Study

The aim of this study is to investigate student’s cognitive skill in

collaborative learning by using Geogebra. Specifically, the objectives of this study

are as below:

1. To find out the level of the students’ cognitive skills according to Bloom

Taxonomy via GeoGebra.

2. To find out whether GeoGebra as a tool helps in students’ learning

process.

1.6 Research Question

1. What are the levels of cognitive skills among the students?

2. Does GeoGebra as a tool helps in students’ learning process?

1.7 Limitations

This research is only based on the respondents in form four so it may not give

inferences to students in other forms. All samples are taken from a secondary school

and only involve 7 respondens due to the computer shortage in the school. Thus, the

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characteristic of these respondens may not give inferences to secondary students in

the whole of Malaysia.

GeoGebra is generally new to students even they have been taught about the

shapes, circle, algebraic and quadratic in form 2 and form 4 mathematics syllabuses.

As a result, teachers have to spend some time to introduce GeoGebra to students

before the lesson start. Other circumstance is the students who do not have Facebook

account, the researcher needs to help them to register. Facebook is a medium for

students to discuss and give opinion.

Most of the secondary school in Johor state has well wifi supported computer

facilities, but there are some unpredictable factors will affect the research progress.

The factors like:

1. Old version of hardware will limit the speed of networking.

2. Change of weather (raining/ storming) cause the internet connection.

3. Crowed Network connection will cause the delay/failure of data

transmission.

Beside that, respondent plays an important role in the research. Basically,

there are few limitations among the respondents will infect the smoothlyness of the

research, such as the interest of students, students’ participation and time limitation.

Due to the personal interest of each students, high workload in school, tuition class

after school hours and extracurricular activities, most of them are reluctant to spend

time for a new program.

Further more, the whole process of this research have to in good cooperation

with school authority without interrupting daily teaching and learning progress of

students in classes.

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1.8 Definision Of The Terms cocurriculum

A) Collaboration - Generally refers to individuals or organizations ‘working

together’ to address problems and deliver outcomes that are not easily or

effectively achieved by working alone (ARACY, 2009).

B) Collaborative learning – Two or more people learn something together.

Knowledge can be created within the population. The group members actively

interact by sharing their experiences and take park on asymmetry roles

(Wikipedia, 2013).

C) Critical thinking - Defined as a higher-order thinking skill which entails

evaluating arguments, and results in interpretation, analysis, evaluation and

inference (Astleitner, 2002).

D) CSCL - Online environment in which students are required to log on and

communicate and collaborate with each other in studying or solving a problem

(Litz, 2007).

E) Facebook – A social networking website which enables users to connect with

friends, family and relative.

F) Higher Order Thinking – It is a dynamic model of lifelong learning which

requires new knowledge and skills for successful adaptation to a changing world

such as comparing, evaluating, justifying and making inferences (Margaret F.,

2004). It is a concept of education reform based on learning taxonomies such as

Bloom's Taxonomy (Wekipedia, 2011).

G) ICT - Information And Communication Technology which includes any

communication device or application, encompassing: radio, television, cellular

phones, computer and network hardware and software, satellite systems and so

on.

H) GeoGebra - Free and multi-platform dynamic mathematics software for all

levels of education that joins geometry, algebra, tables, graphing, statistics and

calculus. It has received several educational software awards in Europe and the

USA (Hohenwarter, 2010).

I) Problem - A question / difficulty to be considered, solved, or answered.

J) Problem Solving Skills - Mourtos, Okamoto and Rhee (2004) stated the problem

solving skills is:

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1. Are willing to spend time reading, gathering information and defining the

problem.

2. Use a process, as well as a variety of tactics and heuristics to tackle

problems.

3. Monitor their problem-solving process and reflect upon its effectiveness.

4. Emphasize accuracy rather than speed.

5. Write down ideas and create charts / figures, while solving a problem.

6. Are organized and systematic.

7. Are flexible (keep options open, can view a situation from different

perspectives / points of view).

8. Draw on the pertinent subject knowledge and objectively and critically

assess the quality, accuracy, and pertinence of that knowledge / data.

9. Are willing to risk and cope with ambiguity, welcoming change and

managing stress.

10. Use an overall approach that emphasizes fundamentals rather than trying

to combine various memorized sample solutions.

K) Student – A person engaged in study, a learner, a pupil, a scholar, especially, one

who attends a school or who seeks knowledge from professional teachers or

from books.

L) Bloom Taxanomy – Consist six cognitive skills.

Lower order thinking skills- Knowledge, understanding, applying.

Higher order thinking skills - Analyzing, synthesis, valuation.

M) Teacher - A driver, guider, builder, counselor, creator, routine workers,

missionaries and monitors (Sharifah, 2004).