Prove tecniche di dimostrazione: uno studio sulla dimostrazione in ambito algebrico nella scuola superiore (Trial runs for a proof: a study on algebraic proofs in high school)

This research, conducted in several high school classes, deals with a study of proof in the realm of algebra. The students in the second and fourth years of scientific and classical high schools, already familiar with the concept of proof in geometry, were asked – periodically and throughout the year – to carry out several proofs in arithmetical algebra and in symbolic algebra on topics unrelated to what was being discussed in their classes at the time. We intend to analyze the relationship between an algebraic formalization and the ability to deduce, with the underlying hypothesis ò corroborated by our experience – that the structure of algebraic language (created specifically to facilitate manipulation, to lighten the mental tasks, and to avoid verbalization) constitutes an obstacle for the linguistic structure of a proof.