The Use of Artefacts for Calculation: a Semiotic Approach

My presentation deals with the use of arithmetic artefactsi in early years for the purpose of counting, representing whole numbers and making calculations. In most countries simple arithmetic activities have been carried on for millennia by means of concrete artefacts, which, in some sense, embody mathematics knowledge. Yet it is not enough to offer them to students to be sure that students will reconstruct the expected arithmetic meanings. In this presentation I shall introduce examples of arithmetic artefacts within the theoretical framework of semiotic mediation after a Vygotskian approach. This allows, on the one hand, to analyse the semiotic potential of each of the artefacts and, on the other hand, to design effective activities to propose in the mathematics classroom under the teacher’s guidance. A discussion of the issue of cultural transposition is appended.