INSTITUTE FOR MATHEMATICAL RESEARCH UNIVERSITY PUTRA MALAYSIA MALAYSIA www.inform.upm.edu.my

1. INSTITUTE FOR MATHEMATICAL RESEARCH UNIVERSITY PUTRA MALAYSIA MALAYSIA www.inform.upm.edu.my

2. LEARNING MATHEMATICS THROUGH UTILIZATION OF TECHNOLOGY STUDY 1 Rohani Ahmad Tarmizi (rohaniat@gmail.com) Ahmad Fauzi Mohd Ayub Kamariah Abu Bakar Royati Saha

3. BACKGROUND • Technology in education had vast impact on learners worldwide. • When technology and appropriate teaching methods are integrated in teaching and learning, positive impact maybe observe on both cognitive and affective domain of learning. • Technology as a tool or a support for communicating with others, allows learners to play active role in the classrooms.

4. BACKGROUND • In mathematics, many technological softwares and hardwares can be used as a tool in teaching and learning in the classrooms. • With technology students become more active in thinking about information, making choices, and executing skills than is typically in a teacher-led lessons. • In mathematics classrooms, tools such as Graphing calculators, Autograph, Geometer’s Sketchpad, e-transformation, Geogebra, Mathematica, Matlab, Derive, Cabri have been widely used both at secondary and tertiary level.

5. BACKGROUND • In this study, several technological tools were explored in its efficiency and utilization at the secondary level- Graphing calculators, Autograph

6. Graphing Calculator Group • Graphing Calculator is a hand-held mathematics calculator that can • Draw and analyses graphs, • Computes the values of mathematical expression, • Solve equations, • Perform symbolic manipulation, • Perform statistical analyses

7. ZOOM To adjust the windows to a predefined setting. TRACE To move the cursor along the graph function using ◄ and ► WINDOW To set the viewing windows GRAPH Displays the graph you have defined. Y= Display Y=Editor,where you can enter functions. ▲ ► ▼ ◄ Let you move the cursor in four directions. 2ND Provides access to the secondary function. CLEAR Erases the last entry; erases the Home screen. ALPHA To access the green letters above the keys. X,T,Θ,n Pastes the variable into the definition of a function ENTER Executes commands and evaluates expressions. Graphing Calculator

8. Graphing Calculator Group

9. Graphing Calculator Group GRAPHING CALCULATOR • GC is considerably a versatile tool for teaching or learning mathematics. • GC is not only a teaching tool in the hands of the teacher, it is also a learning tool in the hands of students when used during classroom investigations, concept development and guided discovery exercises, explorations, open-ended homework exercises, and extended modeling projects. • The use of GC in classroom transforms the class to that of a laboratory. • Students could work in small groups where they can investigate patterns, analyze results and solve problems, thereby constructing their own mathematical understanding.

10. Autograph Group

11. Autograph Group

12. Conventional Group

13. METHODOLOGY Design of The Study • Experimental design was used for this study. • Students were selected at random and assigned to groups. • The experimental groups underwent learning using graphing calculator and Autograph technology while the control group underwent learning using conventional instructional strategy. • Four phases were conducted: • Introduction to software • Introduction to topic • Integrated teaching and learning using software • Testing using achievement test and The Paas Mental Effort Rating Scale.

14. Design of the Study Experimental, non-equivalent control group pretest-posttest design Students were assigned to three groups randomly. Similar questions as in the posttest.

15. Learning to use the GC or Autograph or the traditional learning Beginning of a lesson - to induce in students an appropriate set of behavior and to spur students to attack their work enthusiastically and diligently. EXPERIMENTAL GROUPS: Students were required to solve the given problems using paper-pencil CONTROL GROUP: Students were given problems to solve using paper-pencil • Introduction to the technological tools • Induction set phase • Learning and assessment phase • Test phase • Concept development - important concepts learnt were emphasized

16. INSTRUMENTS OF THE STUDY • 1. Mathematics Achievement Test (MAT) • 2. Paas Mental Effort Rating Scale The MAT was designed by the researchers to measure students’ understanding of the Quadratic Function topic. It comprised of three questions based on the learning outcomes covered in the learning phase. The time allocated to do the test is 30 minutes.

17. PROCEDURE OF THE STUDY Randomized assignment of students to the experimental and control groups and were placed in three different classrooms. A pretest on Quadratic Functions were then conducted a for all groups. INTRODUCTION Use of GC or Autograph followed by Induction Set for the topic ‘Quadratic Function’ Videotaped sessions INTERVENTION GC Strategy, Autograph Strategy & Conventional Strategy POSTTEST Mathematics Achievement & PAAS mental effort rating scale

18. METHODOLOGY Population and Sample • The target population of this study was Form Four students (grade 10) in National Secondary School in Malaysia. • The samples selected for this study were Form Four students from two schools. • The students were brought to the university (Universiti Putra Malaysia) to participate in the learning sessions. • The total number of students in the graphic calculator group was 41 students, groups two followed the Autograph learning mode was 39 and the conventional group was 47 students.

19. RESULTS Table 1: Comparison of Mathematics Achievement Test • Overall mean of MAT scores of GC group was significantly higher than the conventional group and Autograph group. • These findings indicated that the GC strategy group had performed better in test phase than the conventional • group and Autograph.

20. RESULTS Table 2: Comparison of Mental Effort

21. RESULTS Learning phase • ANOVA test results indicated that there was no significant differences in the mean mental effort between the three groups during learning phase. • Planned comparison test showed that mean mental effort during learning phase of GC group was significantly higher from those of conventional group. Test phase • Planned comparison test showed that mean mental effort during test phase of GC group was significantly lower from those of the Autograph group. • This finding indicated that the GC strategy group had benefited from the learning sessions hence their mental effort was lower compared to the Autograph group during the test phase.

22. RESULTS 2-D Instructional Efficiency • Table 3: Comparison on instructional efficiency index • planned comparison test showed that the mean for GC group was significantly higher than conventional group followed by Autograph group • This suggests that learning by integrating the use of GC was more efficient than using conventional strategy and Autograph group.

23. RESULTS • Table 4: Comparisons of selected variables

24. CONCLUSION • The results also showed that the higher performance of the GC strategy was achieved with a lower mean mental effort during test phase. • The eta squared indices were .34 and .13 respectively, a large and moderate effect based on Cohen (1988), implying that the GC strategy provides effective impact on cognitive load. • The results also suggested that the higher achievement was achieved with a reduction in cognitive load. This contention was supported by the significantly higher level of 3-D instructional condition efficiency index reported by the GC strategy as opposed to the other two strategy.

25. CONCLUSION • Graphing calculator is instructionally more efficient compared to conventional method and Autograph software. • Systematic planning of instructions and good learning package using graphing calculator and Autograph will give new views in mathematics teaching and learning. • This shows that dynamic technological tools, particularly graphing calculator provide positive impact upon learners thus becoming potential tools in teaching mathematics at Malaysian secondary school level.

26. CONCLUSION • In conclusion, graphing calculators are excellent tools which can foster students to explore and investigate during mathematical activities besides enhancing students understanding and performance. • However, there is a need to conduct further research on how to integrate graphing calculators in mathematics instruction so that students' mathematical understanding are enhanced and reinforced.

27. EXPLORING EFFECT OF UTILIZING GEOMETER SKETCHPAD ON PERFOMANCE AND MATHEMATICAL THINKING OF SECONDARY MATHEMATICS LEARNERS STUDY 2 Kamariah Abu Bakar (kamarab@educ.upm.edu.my) Rohani Ahmad Tarmizi Ahmad Fauzi Mohd Ayub Aida Suraya Mohd Yunus

28. BACKGROUND • The teaching and learning of geometry utilizing dynamic geometry softwares have been explicitly indicated in the Malaysian secondary school syllabus (Ministry of Education, 2003) • Teachers have been recommended to utilize such software and one such dynamic geometry software licensed to be used in the Malaysian schools is the Geometer’s Sketchpad (GSP) software.

29. BACKGROUND • Geometer’s Sketcpad (GSP) is a software programme that revolutionized the teaching and studying of mathematics especially in geometry. • It is a computer software for creating, exploring and analyzing a wide range of mathematics concepts in the field of algebra, geometry, trigonometry, calculus, and other areas (Geometer’s Sketchpad, Reference Manual, 2001).

30. BACKGROUND • Almeqdadi(2000) in his study had investigated the effect of using the GSP on students’ understanding of some of the geometrical concepts. • The sample consisted of 52 students from the Model School, Yarmouk University, Jordan. • The result of the study indicated that there was a significant difference between the means of students on the posttest and more gain in the scores from the pretest to the posttest in the case of the experimental group.

31. BACKGROUND • There are also some studies that showed negative results. • Teoh Boon Tat & Fong Soon Fook (2005) in their study to examine the effects of using the GSP and the graphic calculator (GC) in the learning of the vertex form of quadratic functions among field dependent (FD) and field independent (FI) cognitive style students. • They found that the students performed as well when using GSP or the GC in the learning of quadratic function by way of visualization of graphs.

32. BACKGROUND • A similar research was conducted by Ling (2004) which compared the use of the GSP software, the GC and the traditional method to learn on the cross-section of a cone. • Reslts of the study showed that the GSP software and the GC did not show a significant effect on the achievement of the students. • From all the findings, it may be concluded that the utilization of the GSP software has obtained mixed reviews on its effectiveness.

33. OBJECTIVES The purpose of this study is to investigate the effectiveness of integrating a mathematical software which is Geometer’s Sketchpad compared to the traditional approach in teaching and learning of form four Additional Mathematics subject on the topic of ‘Quadratic Functions’. Specifically, the objectives are: • To compare students mathematical perfomance utilizing GSP and conventional instruction in mathematics teaching and learning at the Malaysian secondary level. • To compare instructional efficiency of learning conditions utilizing GSP and conventional instruction in mathematics teaching and learning at the Malaysian secondary level. • To investigate the attitude of students towards learning GSP and conventional instruction in mathematics teaching and learning at the Malaysian secondary level.

34. METHODOLOGY Design of The Study • A true experimental design randomized posttest only control group design was used for this study with students randomly assigned into two groups. • The experimental group underwent learning using GSP technology while the control group underwent learning using a conventional instructional strategy. • This study used four phases: • Introduction to Geometer Sketchpad • Introduction to Quadratic functions • Integrated teaching and learning using Geometer Sketchpad • Testing using set of Quadratic Equation Test

35. Design of The Study Experimental, non-equivalent control group pretest-posttest design Students were assigned to two groups randomly. Similar questions as in the posttest.

36. Learning to use the GC or Autograph or the traditional learning Beginning of a lesson - to induce in students an appropriate set of behavior and to spur students to attack their work enthusiastically and diligently. EXPERIMENTAL GROUPS: Students were required to solve the given problems using Geometer Sketchpad software CONTROL GROUP: Students were given problems to solve using paper-pencil • Introduction to the technological tools • Induction set phase • Learning and assessment phase • Test phase • Concept development - important concepts learnt were emphasized

37. INSTRUMENTS OF THE STUDY • Mathematics Achievement Test (MAT) • Pass Mental Effort Rating Scale • Questionnaire on Perceived Efficacy of the technological tools The MAT was designed by the researchers to measure students’ understanding of the Quadratic Function topic. It comprised of three questions based on the learning outcomes covered in the learning phase. The time allocated to do the test is 30 minutes. A set of Questionnaire was adapted from previous studies measuring perceived efficacy of the instructional strategy followed by the students namely the use of Geometer Sketchpad and traditional learning.

38. PROCEDURE OF THE STUDY Randomized assignment of students to the experimental and control groups and were placed in three different rooms. A pretest on Quadratic Functions were then conducted a for all groups. Videotapes sessions Introduction to the Intervention Mode followed by Induction Set for the topic ‘Quadratic Function’ INTERVENTION GSP Strategy & Conventional Strategy POSTTEST Mathematics Achievement & Survey of Perceived Efficacy of GSP Strategy or Conventional Strategy

39. METHODOLOGY Population and Sample • The target population of this study was Form Four students (grade 10) in National Secondary School in Malaysia. • The samples selected for this study were Form Four students from two schools. • The students were brought to the university (Universiti Putra Malaysia) to participate in the learning sessions. • The total number of students in the GSP group was 45 students whilst the conventional group was 47 students

40. RESULTS • Table 1: Comparison of Mathematics Achievements • Overall mean of MAT scores showed that there was no significant difference between mean perfomance scores of the control group compared to scores for the GSP group. • In fact, the mean score of the control group is higher than the result of the experimental group.

41. …RESULTS • Table 2: Comparisons of selected variables

42. …RESULTS • Table 2 (con’t): Comparisons of selected variables

43. …RESULTS • There was no significant difference between procedural steps when performing each activity like plotting the graphs, were analyzed. • There was also no significant difference between conceptual skills obtained by the control group as compared to the experimental group.

44. …RESULTS Table 3: Mean and SD of students’ attitutes towards the teaching and learning approaches.

45. …RESULTS • The attitudes of students towards the respective teaching approaches used was measured according to the four dimensions of students attitudes. • Level of enthuasiasm refers to the extent students were enthused to continue learning using the respective approaches. • Level of enjoyment refers to extent students had enjoyed the approached used to teach the respective group. • Level of anxiety refers to the extent the approach had imposed and created anxiety during learning. • Level of avoidance refers to students perceptions that the respective approaches were a waste of time and a fruitless effort.

46. CONCLUSION • It is crucial to note that the respondents are form four students selected from a nearby school. • Within six hours, students need to undersatnd the contents and to familirize with GSP. • For them, GSP is a new and exciting experince as observed from the attitudinal measures, but they do not have enough time to explore the GSP and benefited from its utilization during teaching and learning. • Time’s constraint thus might be one of the factors why this study came out with negative impact on the use of technology.

47. CONCLUSION • Further studies need to be done, especially on time needed for students to explore and learning using GSP in learning mathematics. • Furthermore, research also need to be conducted in normal classroom settings in Malaysian school in order to explore further in utilizing GSP in mathematics learning. • However, findings from this study can elicit ideas to teachers and researchers on the needs using ICT technology in teaching and learning mathematics.

48. Exploring the effectiveness of using GeoGebra ande-transformation in teaching and learning Mathematics STUDY 3 Kamariah Abu Bakara Ahmad Fauzi Mohd Ayubc Rohani Ahmad Tarmizi b a,b,cInstitute of Mathematical Research, Universiti Putra Malaysia, Malaysia

49. Introduction • Many studies have been conducted to determine the suitability or effectiveness of the use of computer software in teaching and learning mathematics. • Research by Rohani Ahmad Tarmizi, Ahmad Fauzi Md. Ayub, Kamariah, Abu Bakar, Aida Suraya Md. Yunus (2008) showed that teaching and learning mathematics utilizing the graphing calculator was found to be instructionally efficient significantly, compared to the conventional and Autograph software.

50. Findings by Kamariah, Abu Bakar, Rohani Ahmad Tarmizi, Ahmad Fauzi Mohd. Ayub, Aida Suraya Md. Yunus (2009). indicated that the use of Gemeters Sketchpad (GSP) induced higher mathematical thinking process amongst the GSP group. These findings showed that the use of GSP had an impact on both mathematical thinking process and performance. • Norris (1995) and Penkow (1995) reported that there was no significant differential effect between conventional teaching and the use of graphing calculator.