Regard institutionnel sur la transposition didactique du Théorème de Lagrange en mathématique et en économie

Abstract

Because of its many uses, the constrained optimization problem is presented in most calculus courses for undergraduate mathematics and economics students. Since the Theorem of Lagrange and the consequential method of Lagrange multipliers (named after Joseph-Louis Lagrange (1736-1813)) provide an appealing strategy for finding the maxima and minima of a function subject to equality constraints, we are interested in studying the teaching of this theorem in both branches of study, mathematics and economics. In particular, this thesis aims to answer the following questions: - What are the main characteristics of the mathematical organizations around Lagrange’s Theorem? - What important part does the proof of Lagrange’s Theorem play in the teaching and understanding of Lagrange’s Theorem? - What kind of difficulties do mathematics and economics students encounter when being taught Lagrange’s Theorem? Didactic transposition and the Anthropological Theory of Didactics are our main theoretical frames and guide most of our analysis.

Date of Award	2 Nov 2011
Original language	French
Awarding Institution	University of Namur
Supervisor	Valerie HENRY (Supervisor), Jean-Jacques STRODIOT (Co-Supervisor), Suzanne THIRY (President), France CARON (Jury), Maria- Alessandra MARIOTTI (Jury) & Jacques Bair (Jury)