Mathematical Discussion and Perspective Drawing in Primary School

The aim of this paper is to analyse the functions of semiotic mediation in a long term teaching experiment on the plane representation of three-dimensional space by meansof perspective drawing, that has been tried out from grade 2 to grade 5 in three different classrooms within the research project Mathematical Discussion. On the one side, drawing has a functional role in the overall development of the child; on the other side, perspective drawing has a phenomenological role in the genesis of modem geometry. The experiment aims at connecting (1) pupils' spatial experiences to the development of the geometry of three-dimensional space and (2) pupils' drawing experiences to the geometry of twodimensional space, up to the mastery of early geometrical strategies of plane representation of space. Classroom activity alternates individual problems and classroom discussions orchestrated by the teacher. The paper is divided into several parts: after a brief introduction containing some contextual information, the problem of the social construction of knowledge is addressed and some theoretical constructs mainly borrowed from the Vygotskian school are elaborated; then two analyses of the experiment are made, according to the motives of activity and to the sequence of actions; finally the role of semiotic mediation in the whole experiment is analysed; in the final section some results are recapitulated and compared with the literature on the teaching andlearning of geometry and the function of semiotic mediation is discussed with reference to the other distinctive features of the teaching experiment.