Proving and Proof as an Educationa Task

Abstract. Situated in the context of current research, my talk presents a point of view on proof as an educational issue. This point of view intends to combine three perspectives: epistemological, what we mean by proof; cognitive, which are the main difficulties that students meet; and didactical, what kind of didactic interventions can be proposed, among those that have been experimented and showed their effectiveness. The examples that will be presented are drawn from the current literature, but also from research studies which I have been directly involved in recently. In particular, I will discuss some results coming from long-term teaching experiments related to the use of computer-based artefacts as tools of semiotic mediation that teachers can exploit to develop the mathematical meaning of proof.