Learning with touchscreen devices: game strategies to improve geometric thinking

In this paper, we describe the design engineering and the didactical transposition of game-activities based on geometric theorems in which two players play against each other in a multi-touch Dynamic Geometry Environment (DGE). The aim of the gameapproach is twofold: on the one side, enhancing students understanding on what a proof is and how to construct it; on the other side developing logical thinking skills starting from students' reflection over the game. The design of the game-activity is based on a new type of logic, the Logic of Inquiry, which helps students to develop a strategic thinking. The didactical transposition includes a part of work-in-pairs activities followed by a discussion into the classroom orchestrated by the teacher. Thanks to the mediation of the teacher, it is possible to exploit students' reflections on the game, and to make the Logic of Inquiry enter more deeply into the classroom.