Y a-t-il un pilote dans la classe ? Une analyse de l’activité de l’enseignant comme gestion d’un environnement dynamique ouvert

Abstract This article shows how concepts and methods from the analysis of work can be used to study the mathematics teacher’s activity in relation to the student’s activity. The central elements of the psychology of work are first presented: the articulation of task and activity and the mutual determination of the activity by the teacher … Lire la suite

Méthodes de raisonnement et leurs modélisations logiques. Spécificité de l’analyse. Quelles implications didactiques ?

Abstract We explore the question of rigour in the field of calculus along two dimensions: How can students avoid invalid proofs in the absence of explicit logical rules for mathematical reasoning, on the one hand, and what replaces the missing logical references, on the other? To that end, we study the practise of demonstration in … Lire la suite

Régularité et variabilité des pratiques ordinaires d’enseignement. Le cas de la multiplication des nombres décimaux en sixième

Abstract This article presents four different teaching experiences concerning decimal multiplication in sixth grade (11 years), all carried out in similar circumstances. The analysis studies the preparation which went into the observed lessons and the results in the classroom. It uses a double approach : the first one applies didactics of mathematics, the second one … Lire la suite

El profesor como director de procesos de estudio: análisis de organizaciones didácticas espontáneas

Abstract We present a proposal to analyse the teacher’s practice using the framework of the Anthropological Theory of Didactics (Chevallard 1992, 1999). In this framework, the teacher is considered the director of the study process whose students carry out with respect to certain mathematical organizations. The teacher’s activity is described in terms of a system … Lire la suite

Étapes intermédiaires dans le processus de conceptualisation en mathématiques

Abstract In this article, we present the results of an investigation showing that the process of mathematical conceptualisation by primary school or early secondary school children goes through intermediate stages. The analysis of mathematical statements produced by children collectively or individually shows that there are successive degrees of decontextualisation. These intermediate stages correspond to intermediate … Lire la suite

De l’étayage à l’effet Topaze, Regard sur la négociation dans la relation didactique

Abstract In the context of the TéléCabri project, which deals with distance tutoring in geometry supported by a computer environment, we have observed and analysed didactical interactions. We have focused on the tutor’s interventions in the mathematical activity of the student: What are their consequences for the interaction between student and milieu and ultimately for … Lire la suite