Semiotic Mediation in the Mathematics Classroom: Artefacts and Signs after a Vygotskian Perspective

The construction and the use of artefacts - in particular complex artefacts - seems to be characteristic of human activities, but even more characteristic of human beings seems to be the possibility of the contribution of such artefacts beyond the practical level, e.g. their contribution at the cognitive level. In the field of practice, tools have always played a crucial role; often practical problems are related to the use of an artefact, so that often the solution process of a given problem and the design of an artefact, expressly designed to support that solution, have been mutually developed. At large extent theoretical knowledge may be considered as originating from such a mutual shaping, in a long term process the traces of which can sometimes be reconstructed.The idea of artefact is very general and encompasses several kinds of objects, produced by human beings down the ages: sounds, gestures; utensils and implements; oral and written forms of natural language; texts and books; musical instruments; scientific instruments; tools of the information and communication technologies. The contribution of artefacts to education is not a novelty, since a long time books are the main artefacts used in schools, but we do not forget paper and pencil or the blackboard! More generally, the passage from the sphere of practice to that of intellect and vice versa, may be considered one of the basic motor of evolution and progress. Aim of this chapter is reconstructing a theoretical framework for the functions of artifacts and signs in the mathematics classroom, deepening the seminal idea of Vygotsky about semiotic mediation.Two examples are discussed: abacus in primary school and a dynamic geometry software (Cabri) in secondary school.