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USE OF GEOMETER'S SKETCHPAD (GSP) IN TEACHING "PLAN & ELEVATION"

Kor Liew Kee

Dept. of Mathematical Sciences, UiTM <[email protected]>

Tan Khan Aun

S.M. Sains Tun Syed Sheh Shahabudin <[email protected]>

Lim Chap Sam

School of Educational Studies, USM <[email protected]>

Abstract Review of literatures shows that collaborative practice among teachers enhances their morale and provides them with a support network to pursue innovative teaching. This paper reports a case study that aimed to motivate mathematics teachers to integrate innovative use of GSP in the classroom through teacher collaboration. A total of five teachers and a group of 24 students participated in this case study. Qualitative data were collected from the teachers through open-ended questionnaires and individual interviews. A Likert-scale questionnaire was also developed to examine quantitatively students perceptions of the new teaching approach. Throughout the study, the participating group was mentored by a senior mathematics teacher who was more knowledgeable in GSP and acted as the leader of the group. Teachers who were initially novice in GSP received constant training and support from the leader. The teaching topic chosen was Plan & Elevation. Result shows that the participating teachers managed to master the adoption, adaptation and appropriation of technology integration in teaching the topic within a period of less than four months amidst their hectic teaching schedule. The teacher collaboration effort has developed a content template for the topic and several other templates with modified diagrams resembling the past year examination questions were also created alongside for reinforcement and revision purposes. The individual interviews with teachers revealed that these teachers were motivated and excited to participate in the next round of teacher collaboration. Meanwhile students agreed and perceived positively towards the GSP learning environment. Introduction Background Over the years most school mathematics teachers in Malaysia have placed a profound emphasis on examination performance in pursuing excellent result in the public exam. The ,,finish-syllabus syndrome is rampant and the emphasis of "drill-and-practice" or "lecture-and-drill" (Shafer, 2008, p.40) is also common in the mathematics classroom. However, this kind of chalk and talk teaching approach may have lost much of its appeal to the technology savvy students. Evidence has shown that technology has the capability to facilitate students mathematical understanding of mathematical ideas through dynamic multiple representations of graphs, table and equations simultaneously (Ainsworth, 1999). The Geometer's Sketchpad (GSP) is a powerful software which affords access to visualize 3-D objects for the teaching and learning of geometry (Jackiw, 2001). Hannafin, Burruss and Little (2001) claimed that student and teachers visualization as well as exploration of mathematics concepts were significantly reinforced by GSPs dynamic features. Although GSP has well been promoted in the curriculum specifications for secondary school mathematics in Malaysia (Ministry of Education Malaysia, 2001) and has been widely studied by a number of local researchers (Kasmawati, 2006; Nurul Hidayah Lucy Bt Abdullah, 2005; Ng & Teong, 2003 ; Teoh & Fong , 2005), its implementation is unconvincing. In her study on 151 teachers, Kasmawati (2006) found two reasons why teachers who had undergone GSP training courses but were reluctant to use the technology. They were (i) lack of time to prepare a GSP lesson; and (ii) lack of skill and confidence to use GSP to teach mathematics in class. Dwyer, Ringstaff, and Sandholtz (1991) examined teachers practices in technology-rich classrooms observed that there are five evolutionary stages associated with the integration of technology in the classroom teaching. It begins with the entry stage whereby teachers familiarize themselves with the fundamental basics of the hardware and software. This is then followed by adoption, adaptation and appropriation stages where teachers integrate and develop new approaches into the existing classroom activities. In the final innovation stage teachers reflect as well as adjust their fundamental perceptions of instruction. The shift of teaching approach normally occurs at this stage. Dwyer et al. (1991) as well as Means and Olsons (1994) concurred that the process of educating teachers to teach with technology is indeed very time demanding and requires continuous professional support to develop teachers confidence and competence in using technology. They

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contended that teachers normally need to take three to five years to become competent and feel confident enough to teach with the new technology (see Juersivich, Garofalo & Fraser, 2008). Further, Rana (2007) concurred with Galbraith (2002) that learning to use technology inevitably adds workload and increases teaching demands besides creating stress for the teachers. Teacher collaboration such as Lesson Study (Shimahara, 1998) is a collegial effort that provides continuous training and peer-tutoring for teachers along with their ongoing teaching. It is presumed to have the potential to redress situation whereby time constrain is the major hindrance towards implementation of new technology. Under such presumption this study was conducted to examine the effect of embracing teacher collaboration through lesson study group to promote innovative use of GSP among secondary school mathematics teachers. The research was guided by three research questions: (i) What kind of innovative teaching materials can the teachers contribute to teach a geometry topic such as Plan & Elevation using the GSP through teacher collaboration? (ii) What are teachers reflections on the use of GSP? (iii) How do students react to the use of GSP in geometry class? Research Methodology Context and Respondents This case study was conducted in 2008 to examine the possibility of employing teacher collaboration such as Lesson study to promote secondary school mathematics teachers to teach geometry with the GSP. The researchers began by approaching the school principal and his mathematics teachers of a residential school in Penang to consent as participants. Subsequently five mathematics teachers agreed to participate with a senior expert mathematics teacher as their group leader. In fact, the participant teachers were members of an existing Lesson Study group. A class of Form Five students (11 boys and 13 girls, aged 15-16 years) were selected to participate in the special designed Plan & Elevation lessons with the use of GSP. All the participant teachers were beginners in GSP except their group leader who had gone for training in GSP and had used GSP before in his former school teaching. No student had any GSP knowledge or skills prior to the study. Methods Collaborative work among the participant teachers began from March to July 2008. The participant teachers collaboratively planned the lesson, conducted peer observation of the lesson, discussed and reflected on the teaching. The topic chosen was Plan & Elevation. After several discussions and planning, the first research lesson was conducted in April 2008. The group leader taught the lesson while the other group members observed. After the teaching observation, the participants reflected and revised the lesson. The second teaching was then carried out in July 2008 using the improved version of the lesson and the teaching materials. This time, the teachings were conducted in the computer laboratory whereby students were allowed to use computers for their group activities and revision exercises (see Table 1 for a detailed list of activities reported). Immediately after the completion of the second teaching, students were asked to respond to a survey questionnaire with items adapted from the Programme for International Student Assessment Student Questionnaire (PISA, 2003). The questionnaire was administered to examine the students perception of the topic taught with GSP. The four areas covered were: general perception about the topic (10 items; reliability coefficient = .8977), affection about the topic (13 items; reliability coefficient = .9202), cognition or knowledge about the topic (18 items; reliability coefficient = .8559), and perceived classroom atmosphere or classroom control during the lesson (12 items; reliability coefficient = .8810). The score was rated on a fourpoint Likert scale ranging from 1 (strongly disagree) to 4 (strongly agree). The participant teachers were interviewed after the second teaching. Results and Discussions Establishing a Practicable Work Schedule Despite the hectic teaching schedule and time constraint, the collaboration group managed to meet to plan, discuss, prepare the teaching materials and taught the research lesson as planned. Table 1 outlines the details of the collaborative activities that were carried out from March to August 2008 led by the senior mathematics teacher as group leader. Table 1 Report of Teacher Collaboration Activities (March-July 2008) Meetings Task Participants Activities 03/03/08 Plan research Research lesson Topic for research lesson: Plan & Elevation. lesson planning group Outlined the unit and planned the research lesson. Instructional/lesson plan was prepared. 04-20/03/08 Preparing the Research lesson One member drafted the lesson plan and discussed with lesson plans planning group the rest until completion.

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18/04/08

Conduct research lessons

Discuss research lesson 2nd teaching of research lesson

08/07/08

Conduct teacher interview and collect questionnaires completed by the students.

Research lesson planning group, other invitees as desired Research lesson planning group, other invitees as desired Research lesson planning group, other invitees as desired Researchers, participant teachers and students.

Group leader taught the research lesson. Others observed.

Discussed immediately after the lesson was over.

Group leader re-taught research lesson; others observed and collect data.

Three teachers were interviewed by the research team. Twenty-two students managed to complete the questionnaires and returned them to the research team on the same day.

Producing Innovative Templates for "Plan & Elevation" Teacher collaboration effort indeed was very effective in helping the participant teachers to produce sets of well-designed templates for teaching Plan & Elevation. Even though the participant teachers were novice with GSP at the beginning, after some gruelling group discussions and knowledge sharing sessions they were able to improvise, modified and turned the basic sketch into attractive and colourful objects for teaching purposes. Figure 1 shows the basic template of a geometrical shape used in forming various geometrical objects. The template was adopted from Exploring Precalculus with Sketchpad (C) 2005 by Key Curriculum Press. Object 1 in Figure 2 was one of the 3-D models generated by the teachers and used in the classroom teaching. In the sketch area are four action buttons: plan, elevation X, and elevation Y and reset all which were pasted on the top right hand corner. On the top left hand corner are four other buttons namely the perspective, orthogonal, isometric and show axes buttons. Figures 3, 4 and 5 show the various images of Object 1 from plan to elevation. Figure 6 shows another angle of Object 1 after the perspective and show axes buttons were clicked on.

Figure 1. Basic template.

Figure 2. Object 1.

Figure 3. Plan from Z.

Figure 4. Elevation from X.

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Figure 5. Elevation from Y.

Figure 6. Object 1 from another perspective.

The participant teachers worked cooperatively to create rotating templates for all solids to improve the presentation of the content and to help students to visualize the object clearly from a wider angle. With some modifications and adaptations, the teachers manipulated the basic template and turned them into different objects that look similar to the past SPM examination questions on Plan & Elevation. The intention was to provide reinforcement exercises. Obviously at this stage, the participant teachers had demonstrated their capability of adoption, adaptation and appropriation of technology integration as held by Dwyer et al. (1991). Figure 7 below shows several of the objects used in the reinforcement exercises.

Figure 7. Improvised objects used in the reinforcement exercises. The result of improvising objects to suit the needs of the past year examination questions by the collaboration group has indicated that the participant teachers had successfully entered the final stage of innovation. Although the ideas of administering reinforcement exercise was not new but the ideas of delivering the reinforcement exercises on the screen using the dynamic GSP software was refreshing to the mathematics teachers as well as the students. Teachers' Reflection on the Use of GSP Due to lack of release time, only three teachers (Teacher X, Teacher Y, and Teacher Z) who had participated in the teacher collaboration were interviewed. Below is a summary of the conversation: Interview summary with teacher X. X had 30 years of teaching experience and had tried to use GSP to prepare the Plan & Elevation template. X commented that teacher collaboration has helped them to generate "a well-planned lesson". She said that in a GSP learning environment "every student did something" in their assigned "groups". She added that she preferred to use GSP than the actual "model" to teach Plan & Elevation because "it takes a longer time to build a model". She found that visualizing an object from different

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perspectives using GSP was more appealing and interesting than using the real model. emphasized that "facilities" play an important part in supporting technology in the classroom. Interview summary with teacher Y.

She

Y had 18 years of experience in teaching. She found that GSP made the task of teaching geometry "easier and faster". She was very attracted to the "animation features" of the GSP and stressed that "technical support on the software" is very important to the adoption of technology in the classroom. Interview summary with teacher Z. Z had 26 years of teaching experience. He believed that the "dynamic features in the GSP" can definitely "impact the learning". He found that using either GSP or model to teach Plan & Elevation has its "pros and cons" but he judged that GSP is more likely to attract the "young people" because many of his students had shown interest and asked him about the software during his class. He concluded that GSP was helpful in teaching the topic because it "gave clear picture, was dynamic, flexible, and enhanced the effect of teaching and gave more space for self-exploration". He found himself greatly enriched with GSP knowledge in the collaborative effort and he recommended "math teachers to form collaboration group" to encourage the teaching of geometry using GSP technology. In addition, all participant teachers unanimously agreed that they were motivated and looked forward to participate in the next teacher collaboration. Although they agreed that hectic teaching schedule and minima release time were their greatest challenge, they were encouraged and confident to continue to use GSP as a result of the support they received from their colleagues through the teacher collaboration. Students' View About the Lessons Taught with GSP Quantitative data were collected from the students upon completion of the topic Plan & Elevation. The administered questionnaire was intended to examine the students perception of the topic taught using GSP software. The four areas covered were: general perception about the topic, affection towards the topic, cognition about the topic, and classroom atmosphere during the lesson. A total of 22 completed questionnaires were returned to the research team. All the four areas received an average of more than three points indicating that students perceived well the inclusion of GSP in teaching the topic (n = 22; M general = 3.60, SD = .31; Maffect = 3.54, SD =.35; Mcontent = 3.46, SD = .40; Mclassroom = 3.51, SD = .33). On the general perception of Plan & Elevation taught with GSP, all students (100%) agreed that they liked the GSP class and they did not find the topic difficult to study. In addition, 90.5% of the students agreed that they scored high marks in this topic. All students (100%) affectionately found the lesson taught with GSP interesting. The cognitive items revealed that students were more inquisitive (92.5%), remembered better and could visualize clearly the image of the 3-D objects. The overall classroom atmospheres perceived by the students relayed a picture of active learning and peer-tutoring. Teacher was portrayed as in-control and there was a strong indication of motivation and interest to learn the subject. Table 2 lists the selected items representing the four areas of students perception.

Table 2 Students' Perception about Plan and Elevation Taught with GSP General perception about the topic I liked the GSP class. I did not find the topic difficult to learn. I scored high marks for this topic. Affection about the topic I look forward to my mathematics class. I enjoyed learning this topic. I am interested in the things I learned in this topic. I made real effort in learning this topic because I wanted to be one of the best. I am more confident in this topic than others. Cognition about the topic I made effort to ask questions if I didnt understand what he/she was saying. I could imagine/visualize the 3-D object in my head vividly. I could understand his/her teaching without much problem. I had forgotten many of the things that I had learned in the class.

% agreed 100% 100% 90.5%

100% 100% 100% 100% 100%

95.2% 95.2% 85.7% 4.8%

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I was very confused looking at the objects shown on screen in the class. Classroom atmosphere during the lesson Students helped each other spontaneously to understand the geometry problems in the learning process. The teacher was in control during the teaching. Everybody enjoyed the lesson very much. Everybody liked the animation of the object very much and always wanted the teacher to show more. Students were very active most of the time and gave the teacher their cooperation. There were more discussions in the class than in other subjects.

9.5%

100% 100% 100% 100% 100% 85.7%

Conclusion It is not an easy task to change the ethos of a school especially teachers teaching practices without the help of knowledgeable others. Teachers would not change unless effective strategies were proven and made known to them. The above study has shown that teachers can be trained to harness the power of GSP technology through teacher collaboration amidst their hectic teaching schedule and despite being novice to the technology. The result revealed that teacher collaboration motivates teachers to learn to use GSP through group discussion. Teachers were able to plan the lesson and produced practicable content templates to teach Plan & Elevation within a period of four months. Evidence of teacher creativity was seen in the creation of animated and colourful objects for content deliverance as well as utilizing the special designed templates for "practiceand-drill" purposes. Remarks from the teachers reflection indicated that confidence and willingness to learn new technological skills can be cultivated consciously or unconsciously through collegial support. Contrary to McDougalls (1996) study on teachers experience with the GSP, it was apparent that the participant teachers in this study were neither succumbed to lose control in the "control-as-management" which associates teachers ability to maintain discipline of the learning environment nor did they lose "control-as-personal" which links teachers feeling of vulnerability with the introduction of new technology. Result also shows that students agreed and perceived positively towards a GSP learning environment. Students feedback confirmed that GSP had facilitated their visualization and exploration of geometrical concepts. Similar to Khairirees (2004) observation, students worked and learned cooperatively to explore the geometric properties in the presence of GSP. Based on the above results, several challenges and constraints were identified. The biggest obstacle that hindered the smooth implementation of new technology in the classroom is the time factor. This obstacle corresponds to the difficulties faced by Beauchamp and Zoller (2002) and Shafer (2008) in allocating teachers time for collaborative work and lesson improvement as well as getting sufficient release time for teachers to experiment with the GSP. This study also espouses the observation that teachers yearn for more collegial support especially when learning new task related to technology. Besides, it contends that support from the administrators is equally important to bring about pedagogical changes in the mathematics classroom. It too learned an invaluable advice from McDougall (1996) that in order to sustain classroom teachers involvement in the initial implementation of GSP we need to get a technology specialist or colleague who can serve as a mentor with technological experience. Although the result of this study may not be generalised, the ability to develop mathematics in service teachers confidence and competence in teaching with GSP technology through teacher collaboration is definitely encouraging and rewarding. Acknowledgement This study is part of a research project made possible with funding from the Research University Grant of Universiti Sains Malaysia, Penang. References Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33, 131-152. Dixon, J. K. (1997). Computer use and visualization in students' construction of reflection and rotation concepts. School Science and Mathematics, 97(7), 352-358. Dwyer, D.C., Ringstaff, C., & Sandholtz, J.H. (1991). Changes in teachers beliefs and practices in technologyrich classrooms. Educational Leadership, 48(8), 45-52. Galbraith, P. (2002). "Life wasn't meant to be easy": Separating wheat from chaff in Technology Aided Learning. Proceedings of the Second International Conference on the Teaching of Mathematics. Greece. Retrieved from http://www.math.uoc.gr/~ictm2/Proceedings/ICTM2_Proceedings_Table_of_Contents.html Hannafin, R. D., Burruss, J. D., & Little, C. (2001). Learning with dynamic geometry programs: Perspectives of teachers and learners. The Journal of Educational Research, 94 (3), 132-44.

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Jackiw, N. (2001). The geometer's sketchpad, Version 4.03. Berkeley, CA: Key Curriculum Press. Juersivich, N., Garofalo, J., & Fraser, V. (2008). Student Teachers' Use of Technology-Generated Representations: Exemplars and Rationales. Retrieved from http://center.uoregon.edu/ISTE/uploads/NECC2008/KEY_42078046/ Kasmawati, C. O. (2006). Meninjau penggunaan Geometer Sketch Pad (GSP) di kalangan guru matematik sekolah menengah Pulau Pinang. Unpublished M.Ed thesis, Universiti Sains Malaysia, Penang. Khairiree, K. (2004). Exploring geometry with the Geometers Sketchpad. In Yahaya Abu Hassan et al. (Eds.), Integrating Technology in the Mathematical Sciences (pp. 145 -153). USM. Mcdougall, D. E. (1996). Mathematics teachers' needs in computer-based geometric environments. Paper presented at the 8th International Congress on Mathematics Education. Seville: ICME 8. Retrieved 30 September, 2008, from http://mathforum.org/mathed/seville/mcdougall.html Means, B., & Olson. K. (1994). Tomorrows schools: Technology and reform in partnership. In B. Means (Ed.), Technology and the Education Reform (pp. 191-222). San Francisco: Jossey-Bass. Ministry of Education Malaysia (2001). Education in Malaysia: A Journey to Excellence. Kuala Lumpur: Ministry of Education Malaysia. Ng, K. E. D., & Teong, S. K. (2003). The Geometers Sketchpad for Primary Geometry: A framework. Micromath, 19(3), 5-9. Nurul Hidayah Lucy b. A. (2005). The Effectiveness of using dynamic geometry software on students' achievement in geometry. Unpublished M.Ed thesis, University Malaya, Kuala Lumpur. PISA (2003). PISA 2003 Student Questionnaire. Section E: Learning mathematics. Retrieved from http://pisa2003.acer.edu.au/ Rana, I. K. (2007). Technology and Teaching Mathematics: An Indian Perspective. Retrieved from http://atcm.mathandtech.org/EP2007/Invited/Rana.pdf Shafer, K. (2008). Learning to teach with technology through an apprenticeship model. Contemporary Issues in Technology and Teacher Education, 8(1), 27-44. Retrieved from http://www.citejournal.org/articles/v8i1mathematics1.pdf Shimahara, N. K. (1998). The Japanese model of professional development: Teaching as craft. Teaching & Teacher Education, 14(5), 451-462. Teoh, B. T., & Fong, S. F. (2005). The Effects of Geometers Sketchpad and Graphic Calculator in the Malaysian Mathematics Classroom. Malaysian Online Journal of Instructional Technology, 2(2), 82-96.

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