“Click, Drag, Think!”: Posing and Exploring Conjectures with Dynamic Geometry Software

Overview

DGS has become an established tool in the mathematics classroom. Though its heuristic value is often stressed, the literature on DGS usage reveals some shortcomings in its existing use. To see what is missing, we first reconsider models of problem solving and proving by Polya and Boero. With these theoretical tools, we can state our main idea: to further success in problem solving, a heuristic reconstruction of tasks is suitable, which we design analogously to Polya’s problem solving scheme. To support learners, the heuristic instrumentation of problems has also to be considered, especially for best practice in utilizing DGS. We develop a framework for this by refining Arzarello’s list of dragging modalities. Both schemes are illustrated by detailed examples from teaching material of our ongoing research on DGS based problem solving. Readers that are more interested in concrete suggestions for DGS-based teaching may skip the theoretical framework and start the subsection “Heuristic Reconstruction of a Concrete Example,” using the material before for later reference if necessary.

We also sketch an ongoing empirical study that will serve to evaluate our approach. Meanwhile, we point out its possible merits by an advanced case study that illustrates how far learners’ heuristic abilities may evolve when heuristic strategies are properly instrumented.