Le th\'eor\`eme des accroissements finis comme question curriculaire
Abstract
Beyond the difficulty to give true practical motives to introduce a theorem, the didactic transposition of scholarly knowledge in a school setting often leads to freezing a technical tool into a theorem given under minimal assumptions. Probably whole categories of exercises have no other justification than establishing the necessity of introducing a theorem under minimal assumptions in a curriculum. The mean value theorem represents a paradigmatic situation, showing not only the expectations of the curriculum writers, but also part of the school unconscious that manifests itself in the very notion of rigor.
Cite
@article{arxiv.1606.08967,
title = {Le th\'eor\`eme des accroissements finis comme question curriculaire},
author = {Jean-Pierre Bourgade},
journal= {arXiv preprint arXiv:1606.08967},
year = {2016}
}
Comments
in French in IVe congr{\`e}s international sur la TAD, Apr 2013, Toulouse, France. {\'E}volutions contemporaines du rapport aux math{\'e}matiques et aux autres savoirs {\`a} l'{\'e}cole et dans la soci{\'e}t{\'e}