An inquiring-game activity to discover geometry theorems

Abstract

This article illustrates an inquiring-game activity designed within GeoGebra starting from a Euclidean geometry theorem reformulated according to the approach of the Logic of Inquiry (Hintikka, 1999). The aim of the research is to analyze the contribution that the Logic of Inquiry, implemented within dynamic geometry environments, can offer in the education of students to the discovery and logical reorganization of their mathematical knowledge. The didactic activity, experimented in the school year 2018-2019 in a secondary school scientific class, was organized in three phases: the game, the investigation and the class discussion. The analysis of students’ inquiring processes and argumentation, together with the a priori analysis of the activity, intends to highlight how this type of activity can bring students closer to what we define as the “true” work of the mathematician, which consists in exploring, conjecturing, verifying and proving theorems.