Des croquis comme support de raisonnement et de changement de registres

Abstract

We are convinced of the usefulness of sketches and diagrams during mathematical work but the observation is made in our practices that they are not spontaneously used by students. In order to study the understanding and use of sketches by mathematics students, we designed and then proposed a test at different university levels. The test consists of five exercises.The first concerns different representation registers of a set of numbers, the second on a graphic proof of an implicative algebraic proposition and the last three on the graphic approch to the notions of injectivity, surjectivity, bijectivity in the context of the analysis. The sketches, proposed or requested in each exercise, are intended to be aids to changes of register and reasoning. We present what motivated the choices and developments of the exercises then we analyze the results of these tests. In each case, we see difficulties in understanding and the sketches proposed, which leads to think that the sketch must be the subject of specific work at the university level.