Résumé
Les environnements numériques d’apprentissage, particulièrement ceux qui offrent des capacités de représentations multiples, sont complexes dans leur fonctionnement et dans leurs rapports aux mathématiques. C’est pour cela que les chercheurs sont maintenant sensibles à la nécessité d’un cadre didactique et ergonomique rendant compte des potentialités de ces environnements. La recherche présentée ici aborde Casyopée, un environnement logiciel géométrique et algébrique dédié à l’apprentissage des fonctions au lycée. Les situations d’apprentissage proposées visent à approcher la notion de fonction via la modélisation fonctionnelle des dépendances géométriques. Les résultats ont indiqué un développement conjoint de connaissances mathématiques sur les fonctions et de connaissances sur l’artefact pendant la genèse instrumentale, et ont montré comment l’utilisation régulière de l’artefact permet aux élèves d’articuler ces deux types de connaissances. Notre étude a éclairé les potentialités d’une Typologie d’activités pour l’enseignement et l’apprentissage des fonctions en environnements numériques d’apprentissage. Finalement, nous avons analysé comment l’usage de Casyopée peut faire émerger un co-développement des conceptions «processus» et «objet» et favoriser donc une compréhension flexible des fonctions.
Abstract
Digital learning environments, particularly ones that have the capacity for multiple representations, are complex in both their functioning and their relation to mathematics. For this reason, researchers are nowaware of the need for an ergonomic and didactic framework that takes into account the possibilities offered by these environments. The research presented here discusses Casyopée, a geometric and algebraic software environment intended for the learning of functions at the upper secondary school level. The proposed instructional scenarios aim to introduce students to the notion of the function through the functional modelling of geometrical dependencies. Results showed that during instrumental genesis, students developed a simultaneous understanding of the artefact and of mathematical concepts about functions. Results also showed how the regular use of artefacts enabled students to articulate these two types of knowledge. Our study revealed the possibilities for a typology of activities for the teaching and learning of functions within digital learning environments. Finally, we analyzed how the use of Casyopée could prompt a co-development of “process” and “object” concepts and in so doing promote a flexible understanding of functions.
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Minh, T.K. Les fonctions dans un environnement numérique d’apprentissage: étude des apprentissages des éèves sur deux ans. Can J Sci Math Techn 12, 233–258 (2012). https://doi.org/10.1080/14926156.2012.704127
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DOI: https://doi.org/10.1080/14926156.2012.704127