Le th\'eor\`eme des accroissements finis comme question curriculaire

TL;DR

This paper examines how the mean value theorem is introduced in curricula, highlighting the pedagogical challenges and the tendency to present it as a minimal assumption theorem, reflecting deeper educational and cognitive issues.

Contribution

It analyzes the didactic transposition of the mean value theorem, revealing how curriculum design influences its presentation and understanding in educational settings.

Findings

Curriculum often presents the theorem under minimal assumptions.

Educational practices reflect unconscious notions of rigor.

The theorem's introduction is linked to pedagogical and cognitive factors.

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.