Abstract : This works deals with the teaching and learning of multiple integrals used in order to calculate areas and volumes, in Brazilian universities and French technological preparatory classes to “Grandes Ecoles”. Our Goal is to better understand difficulties encountered by students, with these computations and to study in which measure the use of a software like Maple may help them overcome these difficulties, by favoring interactions between graphical and analytical representations of objects at stake.
On the basis of the instrumental approach of computers in teaching, we start from the hypothesis that succeeding to this type of mathematical tasks requires, beyond knowing adequate commands and their syntax, learning specific instrumented techniques, in a context taken in charge by the institution. In our thesis, a technique to represent graphically solids, names “geometrical riddle” occupies a central part, as a means to force interaction between graphical and analytical representations.
The works includes an institutional analysis (ecological analysis of curricula and textbooks) about the teaching of multiple integrals and the use of Maple, as well as two experiments, without and with Maple.