Contribution to the analyse and to the modelling of the process of conceptualisation in inter-didactics of mathematics and physics : example of Ohm’s law.
Didier  MALAFOSSE, 1999

A theoretical model of analysis of the process of conceptualisation in inter-didactics of mathematics and physics is expounded. It is based on two notions of the didactic of mathematics (frame of rationality from Lerouge and semiotic register from Duval) and on a new element : the space of reality. A didactic engineering sequence built about experimenta! study of Ohm’s law in high school allows us to test the model. An investigation realised with students of the fourth and fifth levels in the French high school allows to generalize these results. This experimental research lead us to make a critical analysis of the didactic notions used in the model. To complete this study and to illustrate the continuity-break of rationality between the frame of mathematics and the physics one, we present a reflection about the articulation of the following notions : concept, mental representation and conceptualisation. Moreover, we try to make an historical and methodological synthesis ofdimensional analysis.