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El entendimiento de algunas categorías del conocimiento del cálculo y análisis: el caso del comportamiento tendencial de las funciones

ABSTRACT In the school-teaching context, we have encountered an argument brought by students on the subject of graphics of functions. We shall call this argument "tendential behavior of functions", because of its nature. This argument has an epistemological status quo, and can be treated as a category in the knowledge of calculus. We discuss the type of design of "situations" that follow from these reflections and the relationship that they have with didactic situations, as well as the route that we are following in order to find evidence for this category in a school reality. On a trouvé chez les élèves une conception dans les graphiques des fonctions dont sa nature nous l'avons appelé "comportamiento tendencial" des fonctions. Cet argument à un statu quo épistémologique et peut être traité comme une catégorie de connaissance du calcul. La catégorie même provoque une réflexion sur les niveaux de l'abstraction et sur les bases des connaissances du calcul. on a discuté le type de dessin des "situations" que se construisent de cette réflexions et la relation que celles ci gardent avec les situations didactiques et le chemin qu'on est entrain de suivre pour rencontrer évidences de la catégorie dans la réalité scolaire. Hemos encontrado en el ámbito escolar un argumento en las gráficas de las funciones que por su naturaleza lo hemos llamado ¿comportamiento tendencial de las funciones¿. Este argumento tiene un status quo epistemológico y puede ser tratado como una categoría del conocimiento del Cálculo. La categoría misma provoca una reflexión sobre los niveles de abstracción y sobre las bases del conocimiento del Cálculo. Discutimos el tipo de diseño de ¿situaciones¿ que se desprenden de estas reflexiones y la relación que éstas guardan con las situaciones didácticas, y el camino que estamos siguiendo para encontrar evidencias de la categoría en la realidad escolar.

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Mar 29, 2014