Enhancing reflection on the critical attributes of the figures: the height challenge game

Abstract

Geometrical concepts are characterized by the intertwining of theoretical and perceptual aspects, where examples play a crucial role from an educational perspective. We focus on the concept of height of triangles and propose an inquiry-game activity within GeoGebra, with the goal of prompting students to consider non-prototypical cases of triangles and enhancing their reflection on the critical attributes of this concept. After outlining a theoretical framework on the role of examples in geometrical reasoning, we present the Height Challenge Game and report some excerpt from a grade 7 classroom discussion. An emerging model for the role of different kind of figures at play in the game is proposed.