Geometrical puzzles

Geometrical discourse requires good knowledge and mastering of the terminology and the notions. On the other hand, the acquisition of geometrical concepts by the learners is facilitated when the communication is supported by the balanced use of graphical language, natural language and geometrical language. In the proposed activity the learners are asked to work in pairs, one of them providing the other with a sequence of instructions for the drawing of a geometrical figure. Both learners are then asked to describe the figure and to define it. This geometry teaching activity can represent an interesting opportunity to underline the need to promote the use of different registers of representation and their coordination through specific tasks aimed at converting one into the other. Through this didactical proposal, the trainees can also directly realize how sophisticated and challenging the transition from the description of a geometrical figure to its definition is for the learners. This proposal was prepared and piloted at the University of Pisa. It was also piloted, at the same time, at the University of Siena and, later on, at the IUFM of Paris.