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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    ABSTRACT: The research reported here is the social construction of the mathematical knowledge in engineering field in higher education. It takes that knowledge is built according to the rules and practices are established explicitly and implicitly by the social community in which knowledge is situated, be it in this case engineering in schools. It proposes an approach to the Trigonometric Series Fourier (STF), promoting a functional mathematics. Thus the research shows how mathematical knowledge of known knowledge, is disrupted, changed and amended to take into the classroom, when they take the impact of institutional, socio-cultural environment of the engineering community in training and learning functionality of knowledge within the activities of the engineering community teachers. It's considered that mathematical knowledge will provide a sense and meaning to the student if it is built within a community and gradually incorporate it relates to their activities and social practices of their cultural environment thus encouraging the learning of mathematics articulated integrated and functional.
    Procedia - Social and Behavioral Sciences 01/2010; 8:57-63.
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    ABSTRACT: We start from the assumption that school mathematics knowledge could be better explained if social practices were considered to be generators of knowledge. This perspective changes the way we look at what school mathematics knowledge is and what it takes to teach and learn it. In this article, we will present a teaching situation about periodic functions, which was designed with this perspective in mind. The design was based on the assumption that the scientific notion of periodic function is related with the social practice of prediction. In the situation, prediction as a social practice is transformed into a situational line of argument which redefines that which is periodical. The situation brings into play meanings for the repetition of a movement, which takes place in time in the context of graphs of functions. Our analysis of the situation will focus on the prediction tools that participants generated in order to define that which is periodical. We will conclude with some implications of our observations for the teaching of mathematics.
    Educational Studies in Mathematics 02/2005; 58(3):299-333. · 0.55 Impact Factor

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