Chapter 1

Introduction

1.0Introduction

The integration of technology in education is no longer a new idea. Becausetechnology has become such an integral part of society, it is necessary to integrateits use in education in a variety of ways. The use of computer technology hasmoved beyond computer assisted instruction in the form of tutorials or drill andpractice. Today's technology can provide teachers and students with opportunitiesfor teaching and learning that were impossible in the past. Computers can be usedas devices for communicating with people literally a world apart. They can be usedas tools to create instructional materials or as presentation devices to provideinformation in ways never before possible.

In the field of mathematics education, it is generally agreed upon that Higher order thinking skills or HOTs is a teaching methodology that educates students to evaluate information and develop solutions to problems. Schools that capitalize on the relationship between technology and education reform will help students to develop higher order skills and to function effectively in the world beyond the classroom. In the recent surveys, it also indicates that technology can enhance student engagement and productivity. More specifically, technology increases the complexity of the tasks that students can perform successfully, raises student motivation, and leads to changes in classroom roles and organization (Baker, Gearhart, & Herman, 1994; Dwyer, Ringstaff, & Sandholtz, 1990; Means & Olson, 1995).

The integration of technology into the teaching and learning of mathematics has not escaped the attention of educators. As a discipline, mathematics too is very much influenced by the rapid development of information and communication technology (ICT) and mathematics educators have been looking at ways to integrate ICT into the curriculum over the last decade. The principle of integrating ICT in mathematics teaching and learning is no longer controversial but on the contrary it has come to be embedded in the mathematics curricula of most countries in the world. Increasingly the use of technology is now seen as essential in the teaching and learning of mathematics in schools.

1.1 Significance of the study

In a study by Mullis et al. (2008), approximately 20% of Malaysian students failed to achieve the geometry, equations minimum benchmarks in mathematics. Students fail to give accurate answers, especially in geometry. In addition, students do not understand mathematical concepts and lack necessary skills in problem solving. Students have problems understandingbasic mathematics and fundamental geometry concepts (Azlina and Suhaila, 2008). Thus, it is important for teachers to find the best way to teach mathematics. One software program that is currently available free of charge is GeoGebra.

Technology is not only for those professionals who work in science or industry anymore. Now we have decent level of facilities with technology in elementary and secondary schools, but it is questionable whether we take advantage of the technology that is available to us. It is time to build up more substantial and practical foundations for the use of technology in mathematics classroom so that technology can contribute to students' better understanding.

Besides affecting many areas, in our age, the rapid development of science and technology also affects the field of education in many aspects. Technology plays an important role in enriching the educational process. In the subject of new Technologies in education, one of the electronic tools recently worked on intensively is computer. With the development of computer technology, in mathematics education, the computer is taken as the basic element in almost every environment where the subject is reform movements.

The intent of the appropriate use of the computer in mathematics education must be computers helping providing students develop high-level skills and encouraging the students to establish their own mathematics by letting them gain his or her mathematician's experience. Dynamic geometry software, the reflections of the rapid development in computer technology, show promise to achieve these goals (Gven & Karata, 2003). Lessons involving higher order thinking skills require particular clarity of communication to reduce ambiguity and confusion and improve student attitudes about thinking tasks.

1.2 Statement of problem

Student acquisition of problem solving and higher order thinking skills has long been a goal of schools in general and of mathematics educators specifically. Thus, it is imperative that the tools we use to teach those skills be equal to the challenge of this goal. Geometry is a basic and important subject area of school mathematics and conceptually, the basis. In geometry class, students learn characteristic features and the relations among them with geometric shapes and structures. Spatial visualization, thinking of two or three dimensions of a geometric shape in space and looking at various aspects is the most important part of geometric thinking (NTCM, 2000).

Expression of dynamic geometry softwares, is common name of very special geometry softwares developed for geometry such as Cabri Geometry, Geometers Sketchpad, Cinderella. DGS, entering the education field, has allowed students to hypothesize, explore the theorems and relations, and test them by rescuing the geometry from paper-pen process being static structure and making it dynamic on the computer screen (Gven ve Karata, 2003).

National Council of Teachers of Mathematics (2000) stated that in school mathematics principles and standards, concrete materials, drawings and dynamic geometry softwares are necessary to learn geometry. Because, dynamic geometry softwares such as Cabri, Geometry Inventor, Cinderalla, Geometer's Sketchpad facilitate student's establishing relationship between geometrical shapes and making inferences. Students will be able to analyze a problem by studying a multitude of examples, and then make conjectures by observing recurring patterns.

1.3 Objective of the study

The main aim of this study is to investigate the effect of GeoGebra in secondary school mathematics teaching towards enhancing the higher order thinking skills. Specifically, the objectives of the study isa) to investigate the effectiveness of using GeoGebra on the students achievement in geometryb) to examine the GeoGebra usage in mathematics classroom on the students attitude towards geometry topicc) to obtain the perception of students on the use of GeoGebra in geometry topic1.4 Research QuestionsThis study attempts to answer the following questions:1) Is there any significant differene in the students achievement in geometry topic between the experimental and control group?2) In what way GeoGebra can be used as a tool in order to enhance the higher order thinking skills?3) How do students react to the use of GeoGebra in geometry class?4) What are the effects of GeoGebra towards students attitudes in mathematics?

1.5Definition of termsThis study indicates few definitions:I.GeometryGeometry is the branch of mathematics that involves properties, measurements, and relationships of points, lines, angles, surfaces, and solids.

II. SoftwareSoftware is the set of step by step instructions that tell a computer how to do a job for you. These instructions are known as a program.

III.GeoGebraGeoGebra is dynamic mathematics software for education in secondary schools that joins geometry, algebra, and calculus.

IV.Higher Order Thinking Skills (HOTS)Higher order thinking skills include critical, logical, reflective, metacognitive, and creative thinking. They are activated when individuals encounter unfamiliar problems, uncertainties, questions, or dilemmas. Successful applications of the skills result in explanations, decisions, performances, and products that are valid within the context of available knowledge and experience and that promote continued growth in these and other intellectual skills.

1.6 Limitation of the study

The following limitations may provide obstacles to the study. First, it was a disadvantage that classes were not randomly chosen. The other limitation was time taken to complete the lesson. The constraint of time leaves student with no opportunity to further explore GeoGebra. Students with partial computer skills or first-time user of GeoGebra may face problems as they might spent longer time to familiarise themselves with GeoGebra. Thus, their concentration during lesson may be distracted.

Chapter 2

Literature Review

2.0Introduction

In the world of information technology, rapid changes have taken place in education. Intense competition and efforts toward the formation of a world-class education system have also emerged. There has been an increase in the use of multimedia technology, especially computers and special software, in the teaching of science and mathematics. Integrating technology in teaching provides greater learning opportunities for students (Roberts, 2012) and the use of technology can enhance the student abilities (Al- Aali, 2008). In addition, integrating technology in the classroom helps to produce students who are visionary and have the potential and expertise in both technology and academics.

Technological advances in mathematics education have paved the way for teachers to use technology to improve the quality of teaching and learning. As a result of the implementation of policies that emphasize the importance of using technology in education, all parties involved in education are faced with the important task of reforming methods of teaching and learning. The field of mathematics education has changed greatly due to technology. Educational technology can facilitate simple computation and the visualization of mathematics situations and relationships, allowing students to better comprehend mathematical concepts in practice. The use of technology can be a tool for students to model mathematical relationships in real-world situations.

Research completed over the last decade has confirmed the potential benefits of education technology applied to the teaching and learning of mathematics. Education technology, when used effectively, can enhance student understanding of mathematical concepts, bolster student engagement, and strengthen problem-solving skills. The last two decades of the twentieth century were marked by the advancement of technological aids in mathematics education. Graphing calculators, computer algebra systems, the World Wide Web, and more recently dynamical software paved the way for radical change in the way mathematics is taught. The variety of resources available and the lack of readiness of instructors to utilize these resources prompted many national and international organizations to set standards for the use of technology as a teaching tool in mathematics classrooms.

Since then, much research has been published on the effect of technology on the learning process of the recipients (i.e. the students) assessing both its benefits and its limitations (Abboud & Habre, 2006; Habre, 2000; Laborde, 2001; Quesada & Maxwell, 1994).

A. GeoGebra: Dynamic Mathematics Software GeoGebra was designed by Mark Hohenwarter. This software is dynamic and includes geometry, algebra and calculus. GeoGebra is designed for use in mathematics education in secondary schools and higher educational institutions (Hohenwarter, 2004). GeoGebra software comes with basic object of object points, vectors, segments, polygons, straight lines, which are all part of a cone shape and function (Antohe, 2009; Hohenwarter, 2004) and the ability to offer various types of instruction. In addition, GeoGebra is able to perform online, interactive teaching, which allows more opportunities for teachers to upload resources for online learning (Hohenwarter et al., 2008). This software is open source, or free, to be downloaded by all users and is not subject to any license fee. In addition, GeoGebra software is designed for use in schools and educational institutions (Hohenwarter, 2004). GeoGebra is a versatile software, able to generate a picture or graphic visualization of mathematical ideas or concepts (Hohenwarter and Jones, 2007) and to display a picture or graphic on the simultaneous visualization of the window graphics, algebra and geometry (Arranz et al., 2009).

GeoGebra provides three different views of mathematical objects: a Graphics View (available in two different windows), a numeric Algebra View, and a Spreadsheet View.

Fig. 1: GeoGebra interface

Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards. Elements can be entered and modified directly on screen, or through the Input Bar. GeoGebra has the ability to use variables for numbers, vectors and points, find derivatives and integrals of functions and has a full complement of commands like Root or Extremum. Teachers and students can use GeoGebra to make conjectures and to understand how to prove geometric theorems.

B. HOTS: Higher Order Thinking Skills

Higher-order thinking, also known as higher order thinking skills (HOTS), is a concept of Education reform based on learning taxonomies such as Bloom's Taxonomy. The idea is that some types of learning require more cognitive processing than others, but also have more generalized benefits. In Bloom's taxonomy, for example, skills involving analysis, evaluation and synthesis (creation of new knowledge) are thought to be of a higher order, requiring different learning and teaching methods, than the learning of facts and concepts. Higher order thinking involves the learning of complex judgmental skills such as critical thinking and problem solving. Higher order thinking is more difficult to learn or teach but also more valuable because such skills are more likely to be usable in novel situations.

Higher order thinking skills are grounded in lower order skills such as discriminations, simple application and analysis, and cognitive strategies and are linked to prior knowledge of subject matter content. Appropriate teaching strategies and learning environments facilitate their growth as do student persistence, self-monitoring, and open-minded, flexible attitudes. This definition is consistent with current theories related to how higher order thinking skills are learned and developed. Although different theoreticians and researchers use different frameworks to describe higher order skills and how they are acquired, all frameworks are in general agreement concerning the conditions under which they prosper.

Fig. 2: Categories in the cognitive domain of Bloom's Taxonomy

Questioning should be used purposefully to achieve well-defines goals. Typically a teacher would vary the level of questions within a single lesson.

Usually questions at the lower levels are appropriate for: evaluating students' preparation and comprehension. diagnosing students' strengths and weaknesses. reviewing and/or summarizing content.Questions at higher levels of the taxonomy are usually most appropriate for: encouraging students to think more deeply and critically. problem solving, encouraging discussions. stimulating students to seek information on their own.

2.1Research LiteratureMany recent literatures show that new developments and considerations are highly appreciated all over the world. Mathematics education authors both in teaching and learning mathematics connect the issue with pedagogical considerations (Galbraith and Haines, 1998; Murphy and Greenwood, 1998; Garofalo et. al. 2000; Kadijevich and Haapasalo, 2001; McAlister et. al., 2005). These considerations usually focus on cognitive dimensions of mathematics education and effective computer (and educational software) use in action (Monaghan, 1993, 2004) and highlight their effects on students learning, achievements and affective dimensions. For example, an acceptable level of computer use has positive effect on students views, performance and confidence about the context.

Computer algebra systems (e.g. Derive, Maple) and dynamic geometry software (e.g. Cabri Geometry, Geometers Sketchpad) started to attract more attention along with new developments in technology all around the world. Consequently, new software packages are developed and tried to be integrated into teaching and learning environments. The use of computers as a mathematics teaching aid can improve student motivation and increase their confidence (Sivin-Kachala & Bialo, 2000). Nowadays, many software programs can be used to help students be more responsible for their own learning through creative and interesting exploration. Teaching and learning software are now increasingly important, especially in the subject of calculus (Ahmad Fauzi et al., 2009).

Mathematical software, such as MathCAD, Maple, Autographs, and the like, has been widely used in the teaching and learning mathematics. Many studies have been conducted on the effects of using various software packages on teaching and learning of mathematics. However, the existing studies show inconsistent results.

When teaching mathematics, teachers use traditional methods that are commonly used to explain mathematical concepts and procedures. Teachers should also consider using technology that is useful and beneficial to students. Teaching should be planned so that the process of teaching and learning will run smoothly and effectively. Positive approach will produce a positive and effective result (Ager, 2000). Teachers must be willing to accept change and make technology a reality in the classroom. Teachers who are entrusted to educate the nation's future leaders should give serious attention to the use of technology in teaching and learning. Educators should strive to ensure that mathematics is interesting for students to learn while focusing on important concepts in mathematics.

In addition to building skills in mathematics, learning using technology can have a positive long-term effect on students. By giving them the opportunity to learn and understand mathematics through technology, students are provided with knowledge to compete and function in the high-tech world. It is the responsibility of educators to provide a bright future for students in the face of the world that depends on Mathematics, Science, and Technology (Furner & Marinas, 2007).

Currently, the inclusion of technology in the classroom has been widespread in rural and urban areas. Therefore, in order to help educators integrate technology in teaching and learning mathematics, teachers can use GeoGebra as one of the alternatives. This software can be downloaded from the official website of GeoGebra free of charge and is able to work across various platforms, including Windows, Macintosh, Linux, and Unix (www.geogebra.org). The most interesting aspect of GeoGebra is a virtual community of users who frequently contribute to the free teaching materials produced. GeoGebra can be used to teach Geometry, Algebra, and Calculus (Antohe, 2009; Hutkemri & Effandi, 2010; Rincon, 2009).

GeoGebra effectively disseminates knowledge that includes planning, delivery, guidance, and evaluation that aims to spread the knowledge or skills to students (Hutkemri & Effandi, 2010). GeoGebra software has the potential to help teachers implement teaching test conjecture on geometry, algebra, and calculus.

Chapter 3

Methodology

3.0Introduction

This is quasi experimental study that involves two groups of students, i.e. experimental group and control group. In this study, the experimental group used GeoGebra based on instructional activities while the control group used conventional method. Both group took the same pre test and post test.

3.1 Sampling

A total of 22 Form Two students were involved in this quasi-experiment study. They consisted of 11 students in the treatment group, who are those learning the Form Twos Geometry topic by implementing the activities developed with the assistance of the GeoGebra and 11 students in the control group who learned the same topic conventionally. Both group took the same pre-test and post-test. The detailed information is shown in Table 1.

Table 1: Sample Data

GroupSampleMethod

Control11Conventional

Experiment11GeoGebra software

3.2InstrumentationThis research were using two instruments which the first instruments was the achievement test while the second was the perception test.

a) The Geometry Achievement Test

The instrument used in this study was designed by the researcher. This test was prepared to investigate form 2 students performance on geometry and consist 5 questions based on Taxonomy Blooms Higher Level.

The contents of the test are shown in Table 2

Taxonomy Blooms LevelQuestion number

Application1

Application2

Synthesis3

Evaluation4

Evaluation5

Table 2

b) The GeoGebra Perception Test

This test consists of 14 questions on a 5 point Likert Scale with a range of strongly agree to strongly disagree. A total score is calculated by assigning a value of 1 (strongly disagree) to 5 (strongly agree) to each item and then adding the values shown in Table 3. It is a formal and systematic test that used paper and pencil procedure for gathering information on students perception. ScaleStatement

1Strongly Disagree

2Not Agree

3Not Sure

4Agree

5Strongly Agree

Table 3: 5 point Likert Scale

This test is divided into 4 categories namely:i) Section A: Respondents Backgroundii) Section B: Students perception on the usage of the GeoGebraiii) Section C: Students perception on how GeoGebra helps the understanding of geometrical constructions.iv) Section D: Student perception on their self-confidence in problem solving and their affection to communicate when using the GeoGebra

Please tick ( /) in the box below with suitable answers.

Section A : Background

23

1. JantinaLelaki

Perempuan

2. Bangsa Melayu

Cina

India

Lain-lain

3. Kategori sekolahBandar

Luar Bandar

4. Pekerjaan Ibu BapaKerajaan

Swasta

Lain-lain (Sila Nyatakan )

5. Pendapatan Ibu Bapa / PenjagaKurang RM500

RM501 RM1000

RM1001 RM1500

RM1501 RM2000

Lebih daripada RM2000

NoStatementStrongly DisagreeNot AgreeNot SureAgreeStrongly Agree

12345

(B) Students perception on the usage of the GeoGebra

1The GeoGebra is easy to use.12345

2The GeoGebra can give accurate answers.12345

3The GeoGebra helps to visualize12345

4I can draw and construct geometry shapes easily with GeoGebra12345

(C) Students perception on how GeoGebra helps the understanding of geometrical constructions.

5GeoGebra helps me to understand the topics more easily 12345

6I did not find the topic difficult to learn12345

7I understand my lessons better when using GeoGebra compared to just using the textbook12345

8The Geometry concept is easy to understand with GeoGebra12345

(D) Student perception on their self-confidence in problem solving and their affection to communicate when using the GeoGebra

9I look forward to my mathematics class.12345

10I enjoyed learning this topic.12345

11I am interested in the things I learned in this topic12345

12I made real effort in learning this topic because I wanted to be one of the best.

12345

13I scored high marks for this topic 1234 5

14I get to interact with both my teachers and friends when I use GeoGebra

12345

3.3 Instructional ActivitiesThis research used instructional activities based on GeoGebra to help the students in understanding the geometrical concept better. In the instructional activities, the students are exposed on using GeoGebra in geometrical construction topic. The students used the instructional activities for 2 weeks. The activities allowed the students to explore, discover, and investigate the concept of triangles. Besides that, these activities also helped students to enhance their thinking and mathematical problem solving.

Examples of instructional activities using GeoGebra softwarei) Construct equilateral triangle

ii) construct right triangle

3.4 Research Procedure

The study started with two groups were learning geometrical construction topic by conventional method, where the teacher taught them in the classroom. After that, the experimental group and the control group were given a pre test with regard to the topic that they have learned. Pre test is essential to measure the prior knowldege they on the topic. Each student's scores were recorded. Students who were in the experimental group is exposed to the use of GeoGebra software. They were given opportunity to use GeoGebra software to learn geometrical construction topics. Students in the experimental group was exposed to the instructional activities that was prepared by the researcher. Also, the students were given time to explore the GeoGebra on their own after the basic use of it was taught.

This study used several phases for the experimental group, namely: 1) Introduction to Geometrical Construction2) Pre test3) Introduction to GeoGebra4) Integrated teaching and learning using GeoGebra with exercises (instructional activities)5) Assessment using a set of Geometrical Construction Test as the posttest.6) Perception of GeoGebra Test

The conventional (control group) on the other hand, underwent only:1) Introduction to Geometrical Construction topic2) Pre test3) A session on teaching and learning with further exercises4) Assessment using a set of Geometrical Construction Test as the posttest.

Fig. 4: General flow chart of research process

Chapter 4

Result and Discussion

4.0 Introduction

Descriptive statistics was used to compute mean of both the control group and experimental group using SPSS. The mean and standard deviation for the scores in the beginning and the end of the research for both control and experimental group were compared whether the scores at the beginning and the end of research is significantly different.

4.1The Achievement TestTable 1 : Mean, Standard Deviation for both groups.

GroupNMeanStd. DeviationStd. Error Mean

pretestcontrol group1153.455.781.74

experimental group1154.544.691.41

posttestcontrol group1153.905.351.61

experimental group1160.003.461.04

p < 0.05

The result shows that the experimental group has a pre test mean score of 54.54 (standard deviation of 4.69) compared to the control group that has a pre test mean score of 53.45 (standard deviation of 5.78). The results showed that there was no significant mean difference between the experimental group and the control group with respect to the pre- test.

In the post test the experimental group has mean score of 60.00 (standard deviation of 3.46) compared to the control group that has a post test mean score of 53.90 (standard deviation of 5.35). The results showed that there was significant mean difference between the experimental group and the control group with respect to the post- test.

4.2The GeoGebra Perception Testi) SD- Strongly Disagree ii) D-Disagree iii) NS- Not Sure iv) A- Agree v) SA- Strongly Agree

Table 2; Section B: Students perception on the usage of the GeoGebra (Frequency, Percentage)NoStatementSDDNSASA

1The GeoGebra is easy to use.1(9.1%)1(9.1%)6(54.5%)2(18.2%)1(9.1%)

2The GeoGebra can give accurate answers.1(9.1%)1(9.1%)3(27.3%)5(45.5%)1(9.1%)

3The GeoGebra helps to visualize2(18.3%)0(0%)1(9.1%)6(54.5%)2(18.2%)

4I can draw and construct geometry shapes easily with GeoGebra1(9.1%)1(9.1%)4(36.4%)4(36.4%)1(9.1%)

In the section B, there are four questions (Question 1, 2, 3 and 4) that required the students evaluation on the usage of GeoGebra. In the area of GeoGebra usage, 54.5% of the respondents not sure whether the GeoGebra is easy to use and, 18.2 % agreed that GeoGebra is easy to use. However, 9.1 % respectively strongly did not agree and did not agree that GeoGebra can give accurate answers. 54.5% respectively agreed that GeoGebra helps to visualize and 18.2 % also agreed that GeoGebra helps to visualize. Furthermore, 36.4% of respondents agreed and 36.4% also not sure if they can draw and construct geometry shapes easily with the help of GeoGebra.

The next category was based on the whether using GeoGebra could help in the understanding of Geometrical Constructions topics.

Table 3; Section C: Students perception on how GeoGebra helps the understanding Geometrical Constructions (Frequency, Percentage)

NoStatementSDDNSASA

5GeoGebra helps me to understand the topics more easily 1(9.1%)1(9.1%)2(18.2%)5(45.5%)2(18.2%)

6I did not find the topic difficult to learn3(27.3%)1(9.1%)2(18.2%)4(36.4%)1(9.1%)

7I understand my lessons better when using GeoGebra compared to just using the textbook2(18.2%)1(9.1%)4(36.4%)3(27.3%)1(9.1%)

8The Geometry concept is easy to understand with GeoGebra2(18.2%)1(9.1%)3(27.3%)4(36.4%)1(9.1%)

In the section C, there are four questions (Question 5, 6, 7 and 8) that required the students evaluation on how GeoGebra helps the understanding of geometrical constructions topic. 45.5% of the respondents agreed that GeoGebra help them to understand the topics more easily, 18.2 % were not sure and strongly agreed, also 9.1% of the respondents were strongly did not agree and agree. Besides that, 36.4% were agreed, 27.3% were did not agree that they did not find the topic difficult to learn. However, 36.4% were not sure if they understand the lessons better when using GeoGebra compared to just using the text book. In addition, 36.4% of the respondents were agreed that the Geometry concept is easy to understand with GeoGebra.

The next category was based on the whether using GeoGebra could enhance their self confidence in problem solving and their affection to communicate when using the GeoGebra. In the section D, there are 6 questions ( Questions 9, 10, 11, 12, 13 and 14).

Table 4; Section C: Students perception on their self confidence in problem solving and their affection to communicate when using the GeoGebra (Frequency, Percentage)

NoStatementSDDNSASA

9I look forward to my mathematics class.2(18.2%)0(0%)1(9.1%)7(63.6%)1(9.1%)

10I enjoyed learning this topic.1(9.1%)1(9.1%)2(18.2%)4(36.4%)3(27.3%)

11I am interested in the things I learned in this topic2(18.2%)1(9.1%)2(18.2%)5(45.5%)1(9.1%)

12I made real effort in learning this topic because I wanted to be one of the best.

1

(9.1%)1

(9.1%)3

(27.3%)5

(45.5%)1

(9.1%)

13I scored high marks for this topic1(9.1%)

1(9.1%)3(27.3%)4(36.4%)2(18.2%)

14I get to interact with both my teachers and friends when I use GeoGebra

2(18.2%)1(9.1%)0(0%)5(45.5%)3(27.3%)

For Question 9, 63.6% agreed that they look forward to their mathematics class, however 18.2% of the respondents were strongly disagreed that they look forward to their mathematics class. In addition for the Question 10, they were asking if they were enjoying to learn about this topic. 36.4% of them agreed, 27.3% strongly agreed and only 9.1% strongly disagreed and agreed. For the Question 11 inquired if they were interested in the things that they learned in this topic. Therefore, 45.5% agreed and 18.2% not sure and strongly disagreed. Responses to Question 12, 45.5% agreed that they made real effort in learning this topic because they wanted to be the best and 27.3% of them did not sure. Question 13 were asking if they scored high marks for this topic, so 36.4% agreed and 27.3% were not sure about it. For the last question, 45.5% agreed and 27.3% strongly agreed that they get to interact with both teacher and friends while using GeoGebra.

In the summary, the study concludes that most of students who used the GeoGebra found that learning geometrical constructions had become more exciting. In addition, their understanding of the geometrical constructions also improved and will be more if they are giving more time to explore the software. Despite of lacking time while doing the research, researcher could see the positive attitude of the students toward learning geometrical constructions.

4.3Discussion

A comparison of the pre-and post-test means of the students indicates that the treatment resulted in marked improvement in their performance in geometrical contructions topic for the experimental group. Similarly, the significant differences in the results of the post-test indicated that overall the students in the experimental group performed better than the students in the control group. Also when the two classes of students answers and their written explanations in the achievement test were deeply analyzed, it is seen that the students in the experimental group acquired conceptualisation of geometrical constructions better than control group.

From the results obtained, GeoGebra has the potential to create learning need, by stimulating situations in which current knowledge is inadequate in solving a problem. The significant differences in the results of the post-test indicated that GeoGebra affords generality of concepts and reveal mathematical structures with efficiency, unlike paper and pencil scenarios.

Besides that, GeoGebra has facilitated to the students better understanding of the geometric concepts thought. Working in this environment helped students build increasingly sophisticated mental models for thinking about geometric concepts. Such work also encouraged and supported students development and understanding of the property-based conceptual system used in geometry. The dynamic instructional environment involved students as conceptualising participants, not massive spectators in the process of doing geometry. These findings support the findings of previous studies (Battista, 2002; Chazan, 1988; Choi-Koh, 1999; Dixon, 1997; Kakihana and Shimizu, 1994; Yusuf, 1991). These finding can support the question of how GeoGebra can be used as a tool in order to enhance the higher order thinking skills.

To answer the question on how do students react to the use of GeoGebra in geometry class and what are the effects of GeoGebra towards students attitudes in mathematics can be obtained from the GeoGebra Perception Test. GeoGebra provides a variety of representations and technical utilities that can be used to engage students to learn, organize, and remediate their knowledge of mathematics. It was showed that GeoGebra has many possibilities to help students to get an intuitive feeling and to visualize adequate math process. The use of this softwares tools allows students to explore a wider range of function types, and provides students to make the connections between symbolic and visual representations. However, the lack of time for the students to explore the software might be the main issues.

Technology is promoted and effective tool to teach and learn geometry. When technology is used appropriately, it can provide a rich environment in which students geometric understanding and intuition can be developed (NCTM, 1989). Calculators and computers with appropriate software transform the mathematics classroom into a laboratory much like the environment in many science classes, where students use technology to investigate, conjecture, and verify their findings (NTCM, 1989).

Geometry is one of the important areas of mathematics over the world. Geometry provides experiences that help students develop understanding of shapes and their properties. It enables students to solve relevant problems and to apply geometric properties to real-world situations. National Council of Supervisors of Mathematics endorsed that geometry was one of the ten proposed basis skill areas (NCSM, 1976) and is indeed a basic skill that should be taught to students of all ability levels (Sherard, 1981).

Chapter 5

Conclusion and Implications

5.0Conclusion

It is often said more about using interactive methods in teaching mathematics and about their implementation in the curriculum. However we appreciate that the first step must be done when the blackboard and chalk are replaced with dynamic image of mathematical phenomena, integrated in dynamic software like GeoGebra. There are no barriers to this and only the wish to use the system can produce the desired success. If the implementation conformity with the curriculum seems to be difficult, we accept that GeoGebra platform will be a challenge for beginning and maths teachers, if they will accept an innovative method to transmit information, they will encourage students, to spark interest to investigate, to discover the phenomenon mathematically and to justify the results found in rigorous mathematical sense in the end (Valerian N. Antohe, 2011).

A step by step construction, which represents the visual interpretation of the mathematical context, a problem of a geometric locus will follows the next steps: constructing geometric figures based on hypotheses, applying geometric transformation, (move the point, move the point along the line, move the line preserving the direction or modify the figure preserving the measure of some angles, etc.). Understanding the relationship between Euclidian construction and proof, we can create demonstration that involves animation and action button, find out geometrically and algebrically connections in a rigorous proof, [Gabriela-Simona Antohe, 2009].

GeoGebra provides good opportunity for students to work in pairs and talk through the project together. Attractive presentations prepared in advance, not only capture students attention but also may lessen the immediate cognitive load for educated and educators. In addition to what is traditionally recognized as benefits, a lot of teachers often use real world models.

In order to enhance the higher order thinking skills among the students, GeoGebra offers opportunities to bring the real world into the classroom, adding visualization, color and animation. This would not be possible in a traditional classroom. This GeoGebra thinking is expected in various topics of the curriculum but, if they are not found there, we shall connect the GeoGebra thinking with topics and other different experiences, in a model of more efficient curricula.

The task of education and training based on the new information and communication technologies is not to demonstrate that it has immediate results in a competition with other educational systems, but to replace some of the current structures with a new, probably higher spectrum performance, to meet the inherent changes that occur in culture and civilization. This is the purpose of using Geogebra software at class, to expand the boundaries of creativity in teaching-learning-assessment, to use the power of information technology to stimulate students imagination and facilitate the transfer of learning to everyday life. Surely the mere use of the software will not help us much if it is not combined with teaching techniques, with student-centered teaching methods, with active learning methods such as solvingproblems creatively, critical thinking, learning through discovery, through practice, learning through experiments ( Petre, 2011) .

5.1Implications

In response to the foreseeable change of global knowledge economy, it is imperative that the utilization of ICT in the teaching and learning process of Mathematics be practised since the use of dynamic geometry softwares have been explicitly indicated in the new Malaysian secondary school syllabus ( KPM, 2003). The findings of this study have raised implications to the way the teaching and learning processes are supposed to be carried out in the schools.

5.2Recommandation

Further studies need to be done, especially on the time duration needed for students to learn and explore using GeoGebra in learning mathematics. Furthermore, more research also need to be conducted in normal classroom settings in Malaysian schools, in order to explore further the utilization of the GeoGebra in mathematics learning. However, findings from this study can elicit ideas to teachers and researchers on the needs to use ICT in teaching and learning mathematics.

Future research needs to ensure that the experimental group be: firstly, familiar and comfortable with the use of the computer per se; and secondly, familiar with whatever software that is supposed to be the treatment for the experimental group. Once the subjects are familiar and have the opportunity to explore the software, then the subjects will not be overly anxious into wanting to concentrate on too many new things at the same time. The subjects will then have to focus and concentrate on the content that is supposed to be learned. The time given for the experimental group and the control group to learn whatever content taught will be made the same.

REFERENCES:

1. A. Yousef, The Effect of the GSP on the attitude toward Geometry of High School students. Dissertation Abstract International, A 58105, Ohio University, 1997.2. Abd. Rahman Daud (1999). Teknologi Pendidikan : Edusystem Sdn.Bhd3. Abd. Razak Habib. 1994. Keperluan dan masalah dalam pendidikan matematik dan sains KBSM dan implikasinya terhadap kurikulum pendidikan guru. Kertas kerja Seminar Jawatan Kuasa Latihan Keguruan Antara Universiti. UKM : Bangi.4. Abd. Razak Habib, Abd. Rashid Johar, Abdullah Md. Noor & Puteh Mohd. 1996. Pelaksanaan KBSM dalam mata pelajaran matematik, sains dan sains sosial di sekolah. Kertas kerja Seminar Kebangsaan Penilaian KBSM. Kementerian Pendidikan Malaysia.5. Agness Voo. 1996. Kesepaduan dalam pengajaran dan pembelajaran matematik KBSM .Kertas kerja Seminar Kebangsaan Penilaian KBSM. KPM.6. Annie & Selden, J. 1997. Preservice teachers conceptions of mathematics and how to teach it. 7. Azlina, M.K. and A. Suhaila, 2008. Kesan kaedah pengajaranberbantukan Geometer Sketchpad terhadappencapaianpelajar dalam topik transformasi. Seminar Kebangsaan Pendidikan Sains dan Matematik.8. Best, J. W. & Kahn, J. V. 1998. Research in education. USA: Allyn & Bacon.9. Carpenter, T. P., Fennema, E., Peterson, P. L. & Carey, D. A. 1988. Teachers` pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal for Research in Mathematics Education .10. Edwards, J.A. and K. Jones, 2006. Linking geometry and algebra with GeoGebra. MicroMath, 194: 28- 30.11. Grossman, P.L. 1990. The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.12. Hassard, J. 2000. Pedagogical content knowledge concept map.13. Malaysian Ministry of Education. 1998. Huraian sukatan pelajaran matematik KBSM. Kuala Lumpur: Ministry of Education.14. Mathematics Teachers. 2000. Sharing Teaching Ideas. Posing Questions From Proposed Problems: Using Technology To Enhance Mathematical Problem Solving. Mathematics Teachers, Vol. 93, No. 7, October 2000.15. National Council of Teachers of Mathematics, NCTM Standards. Principles and Standards for School Mathematics. 2000.16. National Council of Teachers of Mathematics (NCTM). 1989. Curriculum and Evalution Standards for School Mathematics. Reston, VA: Author.17. National Council of Supervisors of Mathematics. 1980. The teaching of geometry. Washington, D.C.: National Academy Press.18. Noraini Idris. 1999. Linguistic aspects of mathematical education: How precise do teachers need to be? In M. A. Clemet (Ed), Cultural and language aspects of Science, Mathematics, and technical education (pp. 280-289). Brunei: Universiti Brunei Darussalam.19. Noraini Idris. 2006. Teaching and Learning of Mathematics: Making Sense and Developing Cognitive Abilities. Kuala Lumpur: Utusan Publication Sdn. Bhd.20. Tengku Zawawi Tengku Zainal. 1997. Matematik KBSM: Harapan dan Realiti. Jurnal Akademik MPKTBR. 21. Tengku Zawawi Tengku Zainal. 1999. Kefahaman Konsep Dalam Matematik. Jurnal Akademik MPKTBR. 22. Tengku Zawawi Tengku Zainal. 2000. Kurikulum matematik Sekolah Bestari Malaysia23. Tengku Zawawi Tengku Zainal. 2000. Isu pengajaran Matematik:Kepercayaan dan Pengetahuan Pedagogikal Kandungan Guru. Kuala Lumpur