TY - JOUR TI - La dé-transposition de connaissances scolaires AU - Antibi, André AU - Brousseau, Guy T2 - Recherches En Didactique Des Mathématiques AB - The first part presents surprising results drawn from an experimental study about the use of some forms of reasoning; this study brings into light some clumsiness, sometimes even « errors » both among teachers and students of mathematics. In a second part, we consider those facts in the light of theoretical and experimental results of didactics, relevant to the general development of the students' conceptions. We then introduce a kind of threshhold where we find those exercises for which two conceptions provide contradictory bits of knowledge, with the first conception as a possible obstacle to the second one. Those difficulties can be interpreted as follows: some transposed concepts, presented to the student at some point in their schooling, have to be de-transposed later. It turns out that this de-transposition often is not taken into account, and is not carried out. In a third part we study similar cases where a de-transposition is not realized: proof of an equality, reasoning by analysis and synthesis, using graphs in school reasoning. Finally, some precisions about the concept of de-transposition are given. DA - 2000/// PY - 2000 VL - 20 IS - 1 SP - 7 EP - 40 J2 - RDM LA - FR SN - 0246–9367 UR - https://revue-rdm.com/2000/la-de-transposition-de/ ER -