Étude en inter-didactique des mathématiques et de la physique de l'acquisition de la loi d'Ohm au collège : changement de cadre de rationalité / Study in inter-didactics of mathematics and physics about acquisition of Ohm's law in high school : change of frame

Abstract

Ohm’s law is one of the first laws of physics written in mathematical form which pupils find in a french high school. This functional relation is obtained from a discrete number of measurements by a process built on a supposed homomorphism between the concept of proportionality in the mathematical frame, and Ohm’s law in the physical frame. To understand the reasons of the difficulties encountered by pupils in this phase of mathematical modelling, a didactic engineering sequence has been built. The analysis of the experimental results, based on the didactical notions of semiotic register, frame and space of reality interpret these difficulties in term of a break in rationality for three particular elements : the dimensionality of numbers, the transportability of the concept of proportionality and the difference in kind of the laws of ratification.