Marco, registro y concepción. Notas sobre las relaciones entre tres conceptos claves en didáctica

Las palabras «marco», «registro» y «medio» designan conceptos de amplia utilización por los investigadores en didáctica de las matemáticas, con el fin de modelizar situaciones o de analizar las actividades de los alumnos. Sin embargo, y a pesar de una literatura importante, su uso plantea problemas recurrentes para distinguirlas y relacionarlas (o vincularlas). Proponemos una solución a tales problemas, analizando las relaciones que mantienen entre ellos estos tres conceptos clave de la didáctica de las matemáticas. Mostraremos que la distinción entre «marco» (o «encuadre») y «concepción» debe ser buscada en el anclaje problemático de cada uno de estos conceptos; para los «marcos (o «encuadres»), se sitúa en primer plano el análisis matemático, para las «concepciones», tal lugar corresponde al análisis de las situaciones generadoras de obligaciones (o limitaciones) para el sujeto que aprende. En lo que a los «registros» se refiere, mostramos que son una herramienta indispensable para el funcionamiento de los «marcos» (o encuadres), como concepciones, y de sus relaciones; entre dos marcos, o dos concepciones, los registros tienen una función de mediación semiótica

Notes for a study of the didactic transposition of mathematical proof

It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case either because following an old pedagogical tradition of rote learning proof was reduced to the formalism of a text and deprived from its meaning or, despiteits acknowledged presence anywhere in mathematics, proof did not get the status of something to learn for what it is. On the long way from its absence as such in the past to its contemporary presence as a content to be taught at all grades, proof has had to go through a process of didactical transposition to satisfy a number of different constraints either of an epistemic, didactical, logical ormathematical nature. I will follow a chronological order to outline the main features of this process with the objective to better understand the didactical problem that our current research is facing.Comment: ISSN 1465-2978 (online). Philosophy of Mathematics Education Journal, In pres

Conception, connaissance et concept

(pp.219-244). Grenoble : IMAG.Après un rappel rapide des propositions des recherches actuelles, nous proposons une définition et une formalisation du concept de conception pour résoudre le problème de modélisation posé par la coexistence chez un sujet de structures mentales contradictoires du point de vue d'un observateur de leurs mises en œuvre, et cependant cohérentes lorsqu'elles sont replacées dans le contexte d'une mise en œuvre particulière dans le référentiel du sujet (en générale une classe de situations ou de tâches)

A local optimal diastolic inequality on the two-sphere

We prove a local optimal inequality on the two-sphere between the area and the diastole - defined by a minimax process on the one-cycle space - in a neighborhood of the singular metric made of two equilateral triangles glued along their boundaries

cK¢ Modèle de connaissances pour le calcul de situations didactiques

International audienceCours à l'école d'été de didactique des mathématiques, 2003, présentant le modèle cK¢ et le cadre théorique dans lequel il a été construit, ainsi que divers exemples

cK¢ Modèle de connaissances pour le calcul de situations didactiques

International audienceCours à l'école d'été de didactique des mathématiques, 2003, présentant le modèle cK¢ et le cadre théorique dans lequel il a été construit, ainsi que divers exemples

Multidisciplinarity vs. Multivocality, the case of "Learning Analytics"

Session : Reflections on learning analyticsInternational audienceIn this paper, we consider an analysis of the TeLearn archive, of the Grand Challenges from the STELLAR Network of Excellence, of two Alpine Rendez-Vous 2011 workshops and research conducted in the Productive Multivocality initiative in order to discuss the notions of multidisciplinarity, multivocality and interidisciplinarity. We use this discussion as a springboard for addressing the term "Learning Analytics" and its relation to "Educational Data Mining". Our goal is to launch a debate pertaining to what extent the different disciplines involved in the TEL community can be integrated on methodological and theoretical levels

A curvature-free Log(2k-1) theorem

This paper presents a curvature-free version of the Log(2k-1) Theorem of Anderson, Canary, Culler, and Shalen [J. Differential Geometry 44 (1996), pp. 738-782]. It generalizes a result by Hou [J. Differential Geometry 57 (2001), no. 1, pp. 173-193] and its proof is rather straightforward once we know the work by Lim [Trans. Amer. Math. Soc. 360 (2008), no. 10, pp. 5089-5100] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the Collar Lemma in all dimensions