Sobre la formación de los conceptos geométricos y sobre el léxico geométrico

Abstract

Geometric lexicon is related to an equivalence criterion between figures —normally given by a transformation group (Klein)—. There can be a conflict between ordinary language, traditional geometric lexicon and the equivalence criterion that a given specific situation may suggest. In this paper we analyze the results of a set of questions aiming at discovering the equivalence criteria chosen by pupils between 9 and 11, and the influence of their lexicon. We have noted a considerable influence of the criteria based on the group of translations, and on the group of homoteties and translations. We have also observed the influence of «standard models» (i.e., figures appearing normally in their books), and some difficulties of conceptualization.