Variations et variables de la démonstration géométrique

Abstract We examine the practice of mathematical proof in geometry in the work of Euclid, Hilbert, and Legendre, each illustrated with specific examples. Our study shows the great variation in the forms of geometric proof, even in Hilbert’s books, according to variables that we enumerate. These differences come not so much from the underlying logic … Lire la suite

Ecologie des problèmes de construction dans l’espace

Abstract In this article, we propose to study the history of construction problems in solid geometry. First, we will show that construction problems have evolved during the two periods from 1920 to 1969 and from 1982 to the present and that the drawing has served different functions in the solution of these problems. To that … Lire la suite

Problèmes d’articulation de cadres théoriques : l’exemple du concept de milieu

Abstract This paper is the written version of a talk given at the summer school on the didactics of mathematics held at Houlgate, France, in August 1999. The topic for the day was to examine the domain of validity of different didactical approaches. I chose to approach the subject by starting from two questions, treating … Lire la suite

L’analyse des pratiques enseignantes en théorie anthropologique du didactique

Abstract This paper originated in a series of lectures given at the summer university for in-service mathematics teachers held in La Rochelle (France) in july 1998. It provides a straightforward presentation of some key concepts of the anthropological approach to the teaching of mathematics. It is mainly intended to help the practising didactician come into … Lire la suite

L’articulation du travail mathématique du professeur et de l’élève dans l’enseignement de l’analyse en première scientifique. Détermination d’un milieu – Connaissances et savoirs

Abstract From the difficulties of teaching analysis (or calculus) during the two years before the university, this paper points a other problem which is questionning, since a couple of years, research on didactics : the place of the teacher in didactical situations, and the tools at her/his disposal to drive the situation. Works of Brousseau, … Lire la suite

Comparaison de compétences dans les approches algébrique, qualitative et informatique des équations différentielles ordinaires en première année universitaire. (Comparaison de compétence dans les E.D.O.)

Abstract Today, teaching of ordinary differential equations can rely on three different approaches (algebraic, qualitative and use of mathematical software). By using data from a two years teaching experiment with undergraduates, we have compared the different abilities involved and studied their link to the other areas of mathematical analysis of the syllabus. The three approaches … Lire la suite

La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique

Abstract Current research in the didactics of mathematics usually underrates the role played in mathematics by what, due to their perceptual nature, we call ostensive objects, i.e. both the written and the spoken word, all kinds of symbolisms, graphical representations, and even gestures. In contradistinction to this widespread view, the anthropological approach assigns a vital … Lire la suite

Contribution à la réorganisation des savoirs pré-numériques et numériques. Étude et réalisation d’une situation d’enseignement de l’énumération dans le domaine pré-numérique

Abstract Several research works, since more than fifty years, have been dedicated to the construction by children of the concept of number, in particular whole numbers. Many aspects regarding the manipulation of collections and operations on these collections have been studied. Yet, paradoxically, enumeration has hardly ever been considered as a fundamental component of counting … Lire la suite

Evaluation of a teaching design in linear algebra: the case of linear transformations

Résumé L’article rend compte de quelques aspects d’une expérience d’ingénierie didactique dans le domaine de l’algèbre linéaire, visant la création des conditions d’apprentissage permettant aux étudiants d’éviter ce qui a été appelé, dans la littérature, l’ »obstacle du formalisme ». L’article est centré sur la notion d’application linéaire et son introduction dans l’environnement informatique de Cabri-géomètre II. … Lire la suite