From Pseudo-Objects in Dynamic Explorations to Proof by Contradiction

摘要: Proof by contradiction presents various difficulties for students relating especially to the formulation and interpretation of a negation, managing impossible mathematical objects, acceptability validity statement once has been reached from its negation. This article discusses how Dynamic Geometry Environment (DGE) can contribute students’ argumentation processes when trying explain contradictions. Four cases are presented analysed, involving high school, as well undergraduate graduate students. The approach analyses makes use symbolic logical chain notion pseudo-object. Such lead hypothesis, that experiencing pseudo-object during an exploration foster DGE-supported culminating in geometrical proofs contradiction, while lack experience may hinder such processes. If this hypothesis is confirmed further studies, we foresee important didactical implications since it sheds light on transition DGE-based argumentations contradiction.