Semiotic mediation: from history to mathematics classroom

Abstract. During the seventeenth century geometrical perception became separated, so to say, into two relatively distinct forms of geometry, into two different geometrical styles. One of these is represented by the work of Descartes: the geometry of mechanical-metric activity. The straight line in Cartesian geometry corresponds to an axis of rotation or to the stiffness of a measuring rod. The other geometrical style is represented by the work of Desargues. The straight line of Desarguesian geometry is the ray of light or the line of sight’. These sentences were written by Michael Otte in 1997. Aim of this paper is to present the rationale, design and early findings of a teaching experiment, where the Desarguesian form of geometry was approached at by 5th graders, through the use of a cultural artifact and guidance of the teacher.