Using Dynamic Geometry Software to Develop Problem Solving Skills
Bülent Barış Güven, Adnan Bakı, Erdem Çekmez · Mathematics and computer education · 2012
(ProQuest: ... denotes formula omitted.) 1. INTRODUCTION Currently, much of the research in the area of Dynamic Geometry Software (DGS) is focused on how students experiment and generate conjectures about relationships in But how students use DGS as a problem solving tool and how DGS can strengthen the user's problem solving capacity and heuristics are not generally emphasized. The purpose of this study is to examine how students interact with particular features of a software tool while solving geometric construction problems. We hope to provide insight about students' use of various software features and whether or not these uses support different methods of problem solving. Geometry education has been strongly linked with dynamically interactive software such as Cabri and Geometers Sketchpad [1, 2]. A user can drag elements of a construction while maintaining necessary constraints. This provides an environment in which students can experiment quickly and freely. They can check their intuitions and conjectures in the process of looking for patterns and checking the invariant properties of figures [3]. Luthuli [4] calls this type of instruction research-based geometry. The ease of creating a variety of results has enabled the transition from particular to general cases in a dynamic geometry environment [5]. The primary goal of this type of instruction is to discover or generalize geometric relationships via induction. Some authors use DGS differently. For example, HoIz [6] states that the general uses of DGS are often limited to verification, in the sense that students are expected only to vary or confirm empirically at the computer. He concludes that we must go beyond confirmation and suggests increasing the use of DGS to support heuristic approaches to problem solving. Guven [7] with his own experimentation shows that DGS can be used for insight to a proof. As a result of his own explorations in an interactive geometrylearning environment, Baki [8] concludes that CabrVs dragging, tabulating, and immediate-feedback capabilities greatly assisted him in determining properties, special cases, and counter-examples that could be linked to form a conjecture and a justification. 1.1 Problem Solving and DGS The design of technology tools has the potential to dramatically influence students' mathematical understanding and problem solving methods [9]. For example, Harskamp and Suhre [10] show that computer programs based on a direct instructional approach to learning or constructivist views of learning help students to improve the quality of their problem solving analysis and verification. Schoenfeld [11] contributes a framework of different factors that affect students' abilities to solve problems. In his framework, four components comprise the major directions of students' problem solving: Resources: Body of knowledge that an individual is capable of bringing to bear in a particular mathematical situation. They are the facts, definitions, procedures, rules, and intuitive understandings of mathematics. Heuristics: Rules of thumb for effective problem solving. They are strategies and techniques for approaching a problem. Control: The ways in which individuals monitor their own problem solving process, use their observations of partial results to guide future problem solving actions, and decide how and when to use available resources and heuristics. Belief systems: One's mathematical world view, the perspective with which one approaches mathematics. [Note: For the purpose of this paper, we focused on the first three aspects.] Students need to understand how DGS can affect the problem solving process. Thus, the definition of resources should be expanded to include both mathematical resources and mathematical ability with available technological tools [9]. Healy and Hoyles [12] found, in the context of a dynamic geometry environment, that the presence of particular technological features can afford or constrain the available heuristics students may use for problem solving. …