Uso di un software di Geometria Dinamica nella formazione dei futuri insegnanti

Abstract

In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an exploration of the menu of the tools menu following the first part of the first book of the elements of Euclid. The second is an activity about pentagons and pentagrams which aims at finding a more natural way of discovering their properties than that suggested by Euclid as an illustration of the method of synthesis and analysis. The third is an activity on circle inversion and its connection with polarity and the construction of the fourth harmonic point after three given point on a line. The activity continues with the reading of Poncelet's ideas about ideal secants of conics and how to use GeoGebra to make sense of them. The fourth activity shows how to use the possibility to move objects in GeoGebra to make sense of the geometric intuition behind Cremona and Hirst letters about the Bellavitis-Hirst inversion of a circle. We discuss the reasons why we believe that these kind of activities may help students to read and understand original writings in projective geometry and why we believe that they may be very effective in the training of prospective teachers of mathematics.