Le th��or��me des accroissements finis comme question curriculaire

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.
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}