Semiotic mediation in the primary school: Dürer glass

Abstract. This paper concerns the design and early findings of a long term experiment about the Desarguesian form of geometry (usually neglected in the curricula), up to the production of early cases of geometrical proofs. The experiment is in progress in a 5th grade classroom. The theoretical framework is based on the works of Vygotsky and Bachtin, combined with recent contributions from activity theorists (such as Engestroem and Wartofsky). The classroom activity starts with the exploration of a copy of Dűrer's glass and includes the interpretation of ancient texts. The analysis of a very limited set of data from a classroom discussion will show how the dialogue between Dűrer's glass and the texts offered to pupils, on the one hand, supports the polysemy of each artifact and, on the other hand, starts a process of semiotic mediation which produces internalisation of the mathematical model of painting as intersection of the visual pyramid.