Notazioni e rappresentazioni come mezzo per dominare la complessità: un esempio sviluppato in ambito geometrico per e con allievi di Scuola Media

In this paper we show the results of an activity realized with the pupils of a 3rd grade of middle school (13 years old) with the aim of making the pupils understand the importance of using the right notations in the treatment of complex algorithms. In particular in the first part we resume how, in a previous experience, during an activity guided by the teacher, the pupils, using an algorithm (based on the duality bet\veen the polyedra) and some physical models had succeeded in explaining why the nets of a cube are as many as those of a regular octahedron. In the second part instead we show how the pupils, thanks to an appropriate notation, succeed in applying the above-said algorithm without the help of any physical model.