The use of figures related to the complex integral and Cauchy’s integral theorem in complex analysis textbooks
DOI :
https://doi.org/10.23925/1983-3156.2024v26i3p303-326Mots-clés :
Modèle de référence épistémologique, Analyse du contenu des manuels, Figures, Transposition didactique, Analyse complexeRésumé
Pour répondre à une question relative aux similitudes et aux différences entre les travaux mathématiques originaux en analyse complexe et les manuels contemporains en ce qui concerne l’utilisation de figures (conçues comme des dessins en deux dimensions) pour aborder les concepts de cette branche des mathématiques, nous avons analysé dans cette étude la façon dont les quatre principaux manuels, qui sont référencés dans les guides de l’enseignant de toutes les universités publiques espagnoles qui proposent un diplôme en mathématiques, structurent le concept d’intégrale complexe et la preuve du théorème intégral de Cauchy. Pour mener à bien notre analyse, nous avons récupéré un modèle de référence épistémologique qui décrit la manière dont les sujets historiques ont utilisé les chiffres pour développer l’analyse complexe entre le premier quart du 19e siècle et la première moite du 20e siècle. L’étude montre que les quatre manuels universitaires structurent ces concepts de manière à les mettre en relation avec les formes les plus contemporaines auxquelles ils ont été associés dans leur développement historique. Bien que nous ne soyons pas opposés à ce que le contenu des manuels soit structure de cette manière, nous expliquerons comment le modèle de référence épistémologique peut servir d’alternative épistémologique pour l’élaboration d’un matériel didactique qui tienne compte du développement historique de l’analyse complexe.
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