Abstract
The aim of this paper is to demonstrate that in spite of some superficial similarities the current mathematics reform in the US based on constructivist principles differs substantially from mathematical education based on Vygotskian cultural-historical theory (V.V. Davydov’s mathematics program), and to illustrate the manner in which Davydov’s program virtually obliterates the conceptual-procedural division that has fueled the current “math wars”. Both constructivism and Davydov’s approach emphasize the active character of students’ acquisition of mathematical concepts. Constructivists, however, begin the instructional process from the children’s preexistent concepts while Vygotskians reorient it toward acquisition of what Vygotsky defined as “scientific” rather than “spontaneous, everyday” concepts. A three-year study of the implementation of Davydov’s elementary mathematics program in a school setting in the US found that the American children overcame the initial challenges of the program, consistently resolved computational errors conceptually, and finally demonstrated the ability to solve high school level mathematics problems. The curriculum appeared to foster the development of theoretical thinking, an explicit goal of Davydov’s program, which constitutes its major value and educational significance.
Résumé
Malgré quelques similarités superficielles, la réforme courante des mathématiques aux Etats-Unis qui est basée sur les principes constructivistes differe considérablement de l’éducation basée sur la théorie culturelle-historique de Vygotsky. Le programme d’études pour les mathématiques élémentaires de V.V. Davydov, basé sur la théorie de Vygotsky, résout la division conceptuelle-procédurale qui a intensifié les récentes “guerres de maths”. Et le constructivisme et la théorie de Davydov soulignent le caractère actif de l’acquisition des concepts mathématiques par les élèves. Cependant les constructivistes commencent le processus de l’instruction d’après les concepts préexistents des enfants tandis que les Vygotskiens le dirigent vers l’acquisition de ce que Vygotsky a défini comme concepts “scientifiques” plutôt que “spontanés, quotidiens”. Les deux théories different dans le développement de l’algorithme comme un produit culturel et historique qui est entièrement conceptuel (Davydov) plutôt qu’un règle de calcul qui peut être remis à une calculatrice (constructivisme); et l’inclusion des modèles schématiques (absente dans les théories constructivistes) qui fonctionnent comme outils psychologiques dans le programme d’études de Davydov. Une étude de trois ans sur le programme de l’enseignement des mathématiques élémentaires de Davydov mis en pratique dans une école aux Etats-Unis a trouvé que les enfants ont résolu des erreurs de calcul d’une façon conceptuelle et ont démontré la compétence pour résoudre des problèmes de mathématiques typiquement trouvés aux niveaux du collège et du lycée. Le programme d’études a encouragé le developpement d’une réflexion théorique, un but explicite du programme d’études de Davydov, qui constitue sa valeur principale et son importance éducative.
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Schmittau, J. Vygotskian theory and mathematics education: Resolving the conceptual-procedural dichotomy. Eur J Psychol Educ 19, 19–43 (2004). https://doi.org/10.1007/BF03173235
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DOI: https://doi.org/10.1007/BF03173235