Analyses of activity design in geometry in the light of student actions

Abstract

The goal of this study is to show that inquiry activities in a dynamic geometry environment, intentionally designed to confront students with contradictions and uncertainties, push them towards explanations that include deductive elements. Three different but dependent aspects of the activities are characterized and analysed: The epistemological, which includes all possible inquiry paths; the didactic, which involves only those paths that reflect the intention of the designer; and the cognitive, which accounts for actual student actions (conjectures and explanations) and their analyses. The research conclusions are based on the interplay among these three aspects. The analysis of students’ investigations and the analysis of their explanations fulfil, to a broad extent, the design goals.