The Effects of Geometer ’ s Sketchpad and Graphic Calculator in the Malaysian Mathematics Classroom

This study examined the effects of using the Geometer’s Sketchpad (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. The GSP and GCs are two innovative tools introduced in Malaysia in the teaching and learning of secondary school mathematics. This study found that the students performed as well when using the GSP or the GC in the learning of quadratic functions by way of the visualisation of graphs. The FI students outperformed the FD students in both tools. The implications of this study in using the GSP and GC in the mathematics classroom are discussed. INTRODUCTION The Geometer’s Sketchpad (GSP) is a computer software system for creating, exploring, and analysing a wide range of mathematics concepts in the field of algebra, geometry, trigonometry, calculus, and other areas (Geometer’s Sketchpad, Reference Manual, 2001). Recently the Malaysian Ministry of Education (MMOE) made the unprecedented but bold and wise decision of subscribing to the license of this software in 2004. The license was not only meant for the quarter of a million teachers and educators including lecturers of public universities but also for the almost 5 million students who are under the direct authority of the MMOE nationwide (Ministry of Education Malaysia, 2001). In the case of graphic calculators (GCs), the Ministry of Education has started distributing them to several hundred secondary schools throughout the country since 2002 (Norjoharuddeen, 2004). In the teaching of algebraic functions, many teachers still rely on the chalk and talk approach or more commonly known as the traditional method. Visualisation is minimal if at all. Drawing of graphs if done are sketches which are static, not according to scale and very too often distorted. The use of visualisation tools like the GSP and GC in this research will present an alternative to overcome these instructional inadequacies. In the learning of algebraic functions, students usually find graphing tedious and time consuming (Podlesni, 1999) and they only manage to learn limited number of graphs in the limited time available in class. Little time is spared for application and problem solving, some of which problems are impossible with paper and pencil alone (Harvey et al., 1995). The availability of the GSP and GC will make these sketches instantaneous thus saving precious time for the answering of after-graphing questions, the comprehension of concepts, problem solving and application. This however does not in any way undermine the importance of skills in manual graphing which are essential in the examination. A yearly report issued by the Board of Examination, MMOE indicates that students taking SPM additional mathematics failed to possess sufficient skills and knowledge to answer MOJIT The Effects of the Geometer Sketchpad questions on completing the square method, and thus the vertex form in quadratic functions (Malaysian Ministry of Education, 2002). Current development in the field of teaching and learning of mathematics in Malaysia compels teachers to choose the instructionally better alternative tools in the teaching of mathematics, generally and in quadratic functions, specifically. The GSP and GC are such current available tools. All secondary schools technically should have been supplied with the GSP and more schools will be equipped, either through their own initiative or otherwise, with the GC. This study intends to help them make that choice. Graphs have always been a problem with certain students. In psychology these students have been found to possess, among other traits, certain cognitve styles which put these students at a disadvantage in viewing and thus in understanding graphs. Graphs are embedded figures within the axes and grids. Witkin et al., (1977) found that FD students, in contrast to FI ones, show varying difficulties in such embedded figures. The GSP and GC, while providing some excellent tools in the visualisations, also face the challenge of providing support to these students. Various visual mode options are available both in the GSP and GC. One of them is the option of showing or hiding the grid. In default, the GC hides the grid with GridOff mode but in contrast GSP shows grid as default view. Figure 1 shows the various visual modes in the GSP and GC. In this study, the researcher has maintained the default views in both tools when introducing the intervention. This decision made was based on the rationale that the developers of these tools must have very good and valid reasons to make their respective views default. This study then hopes to find the better tool in helping the normally disadvantaged students. Visuals in Figure 1 are not shown according to scale. The theoretical framework supporting this study is based upon the information processing theory (Gagné, 1984) and the dual coding theory (Paivio, 1986). All the 5 hypotheses postulated and tested were null hypotheses because of the lack of literature on studies done in comparing the use of the GSP and GC (Gay & Airasian, 2003). LITERATURE REVIEW Geometer’s Sketchpad in Learning The use of dynamic geometry software has been explicitly suggested in the curriculum specifications for secondary school mathematics (Ministry of Education Malaysia, 2001). The GSP is one such software. In GSP, Almeqdadi (2000) found a significant difference between the means of the students’ scores on the posttest of those using GSP and those using only the book in the learning of some geometrical concepts. Students using the GSP performed significantly better than those using books only. McClintock et al., (2002) did a qualitative study on students’ development of 3D visualisation in the Geometer’s Sketchpad environment. The students were taught geometric solids among other concepts for 10 to 20 weeks using GSP. They found that the GSP and the associated activities were effective in helping the students develop 3D visualisation and achieve conceptual understanding of geometry content. The immediate feedback provided by the dynamic environment allowed the students to verify or change their conjectures. They found that the students have progressed significantly in terms of their geometric thought.