From physical model to proof for understanding via DGS

Abstract

The widespread use of dynamic geometry software (DGS) is gathering many interesting questions and discussing the necessity and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic "Conics" which developed in a teacher education course for pre-service secondary math methods course. The idea of ​​the didactical sequence is to introduce "conics" using a concrete manipulative approach (paper folding) then to explorative DGS-based construction activity. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the physical model and the formal symbolic system of proof. The paper wants to present an analysis of participants' geometric thinking strategies, featuring proof as an embedded process in geometric construction situations.