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Elementary algebra as a modelling tool: A plea for a new curriculum

  • Autores: Heidi Strømskag, Yves Chevallard Árbol académico
  • Localización: Recherches en didactique des mathématiques, ISSN 0246-9367, Vol. 42, Nº 3, 2022, págs. 371-409
  • Idioma: inglés
  • Títulos paralelos:
    • El álgebra elemental como herramienta de modelización: Argumento para un nuevo currículo
    • L’algèbre élémentaire comme outil de modélisation: Plaidoyer pour un nouveau curriculum
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • español

      El álgebra elemental es la base sobre la que se levanta todo el edificio matemático moderno. Pero el currículo algebraico, generado por el proceso de transposición didáctica desde hace más de un siglo, ya no puede asegurar esta función esencial. El presente estudio se centra en la noción de fórmula y en cómo su evolución curricular parece ser testigo y causa de la degradación del álgebra enseñada como herramienta de modelización. Este examen implica un análisis minucioso de hechos curriculares que parecen no haber atraído atención de los investigadores, como la desparametrización del álgebra o los efectos no previstos de su encuentro con el análisis matemático. Apoyándonos en la teoría antropológica de lo didáctico (TAD), esto permite esbozar la perspectiva de una imperiosa revigorización del currículo algebraico.

    • English

      Elementary algebra is the foundation on which the entire modern mathematical edifice rises. But the algebraic curriculum fashioned by the process of didactic transposition for more than a century is no longer able to ensure this essential function. The present study focuses on the notion of formula and how its curricular evolution appears to be a witness and a cause of the degradation of taught algebra as a modelling tool. This examination involves careful analyses of curricular facts that seem not to have attracted the full attention of researchers, such as the deparametrization of algebra or the unplanned effects of its encounter with mathematical analysis. Drawing on the anthropological theory of the didactic (ATD), this allows to outline the perspective of an imperative reinvigoration of the algebraic curriculum.

    • français

      L’algèbre élémentaire est la base sur laquelle s’élève l’édifice mathématique moderne. Mais le curriculum algébrique façonné par le processus de transposition didactique depuis plus d’un siècle n’est plus en mesure d’assurer cette fonction essentielle. Notre étude examine la notion de formule et la manière dont son évolution curriculaire apparaît comme un témoin et une cause de la dégradation de l’algèbre enseignée en tant qu’outil de modélisation du monde. Cet examen suppose des analyses minutieuses de faits curriculaires qui ne semblent pas avoir attiré l’attention des chercheurs, telle la déparamétrisation de l’algèbre ou les effets non prévus de sa rencontre avec l’analyse mathématique. En prenant appui sur la théorie anthropologique du didactique (TAD), cela conduit à esquisser la perspective d’une revigoration indispensable du curriculum algébrique.

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