A Possible Model for Developing Conjectures in Dynamic Geometry

Research has shown that the tools provided by dynamic geometry systems impact students’ approach to investigating open problems in Euclidean geometry. In particular, dragging in dynamic geometry environments (DGEs) seems to be linked to abductive reasoning used in the formulation of conjectures in open problem situations. Arzarello and Olivero, together with a team of other researchers, have observed and subsequently described a variety of “dragging schemes” (Arzarello et al., 1998; Olivero, 1999, 2002) that students used during explorations in Cabri (a particular DGE). Building on such research, I have conceived a model describing some cognitive processes that can occur during the production of conjectures and proofs in a DGE. In this paper I will focus on processes that occur during the development of conjectures. These cognitive processes seem to be related to the use of specific dragging schemes. Moreover, I hypothesized that such cognitive processes could be induced by introducing students to the use of certain dragging schemes during two teaching sessions. In order to investigate such hypothesis and test the cognitive model I carried out the study described in this paper.