TY - JOUR
TI - Un obstacle épistémologique soulevé par des « découpages infinis » des surfaces et des solides
AU - Schneider, Maggy
T2 - Recherches En Didactique Des Mathématiques
AB - In keeping with the logic of euclidian geometry traditional teaching presented the homothety or similarity in a "intarfigural" way based on the properties of similar figures. Afterwards geometry with figures disappeared from the programs at the beginning of secondary school, and was replaced by geometry by transformations. Finally subsequent simplifications of the programs propose only the study of transformations, without going as far as to restore geometry with figures. The validity of such selections is not so clear. An epistemological analysis shows in fact that its development, from ancient Greece to the beginning of the 20th century, is marked by stages which should be taken into account in the teaching of homothety.
Our first hypothesis is the necessity for the acquisition of the idea of homothety of an initial experience of the different types of figures which can occur. This requires figurative analysis which without being of a strictly mathematical nature has mathematical purposes.
Our second hypothesis is that for the exploration of relations that exist between the figurative and numerical aspects, we must first separate and then articulate these two aspects in the study work of students. In this way we can organize teaching which leads to much better results, and which takes hardly more time than that commonly accepted for the teaching of this subject.
DA - 1991///
PY - 1991
VL - 11
IS - 2.3
SP - 241
EP - 294
J2 - RDM
LA - FR
SN - 0246–9367
UR - https://revue-rdm.com/1991/un-obstacle-epistemologique/
ER -