Approaching functions through motion experiments

The paper describes an approach to Calculus in secondary schools within technological environments. It illustrates a case study, where the concept of function is introduced in the 9th grade using a motion sensor connected to a calculator. Pupils can move and see the Cartesian representation of their movement produced by the calculator in real time, on a space-time graph. The paper analyses some protocols from working groups and class discussion. Within a general Vygotskian frame, the authors use different complementary tools to analyse the situation: the embodied cognition by Lakoff and Nuñez, the instrumental approach by Rabardel, the cultural- semiotic approach by Radford. In particular the role of the perceptuo-motor activity in the conceptualization of mathematics is stressed. In the end, some problems and lines of investigations are pointed out.