Recurrent geometry: a learning path on the recursive process in geometry

Abstract

The learning path described here was carried out with eleventh grade students attending an Italian scientific upper secondary school, with the aim of stimulating the activation of conjectures and argumentation towards demonstrative thinking, using the dynamic geometry software GeoGebra. To this end, we chose to work on recurrent geometry, developed by the French mathematician Gaston de Longchamps, which is closely related to the recursive process and the mathematical induction. In this paper we show how such a course can promote the learning of Euclidean geometry topics and educationally develop students’ argumentation skills. A qualitative analysis of the students’ productions was carried out to evaluate the achievement of our goals.