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  3. Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada "Unidad Legaria"
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  5. Doctorado
Por favor, use este identificador para citar o enlazar este ítem: http://repositoriodigital.ipn.mx/handle/123456789/11424
Título : Un estudio socioepistemológico sobre el método de Euler como generador de procedimientos y nociones del cálculo en el contexto del estudio del cambio
Fecha de publicación : 16-ene-2013
Descripción : This research is part of a collegial working on the conceptualization of a proposal for what to teach and how to teach Calculus. The proposal seeks to promote in the classroom, the emergence and development of procedures and basic concepts of calculus in such a way as to fairly assess the formation of Calculus as a conceptual system structured logically. This proposal responds to a broad vision of mathematics according to which its role as human activity to solve problems makes this science of crucial importance for the study of other areas of knowledge. The proposal is developed for higher level of education, particularly for an institution in northern Mexico, and responds to the instrumental nature of the courses in the curriculum of Mathematics for the different university programs offered. In its design intends to integrate, educationally speaking, a Newtonian approach with a Leibnizian approach to the genesis of Calculus, in the belief that a discourse of this kind offers greater opportunities for the student to take ownership of the ideas behind the construction of notions and procedures of Calculus in their role as tools to solve real problems related to the study of change. The purpose of this paper is to consolidate the implementation of the proposal at its first part, one in which the practice of predicting the value of a quantity that is changing with respect to other works as a prelude to introducing the Newtonian approach in school discourse. In this introduction plays a key role incorporating a numerical procedure to approximate the value of magnitude. Euler's method, the name which finally identifies this procedure in the classroom, has been introduced in the calculation of the school discourse allowing simultaneous incorporation of the notions of rate of change and cumulative change, thereby fostering the notions of derivative and integral being involved from the beginning of a first course in Calculus. The effect of early and simultaneous incorporation of these notions raises new questions to be addressed in an effort to strengthen the proposal. The inquiring about the conditions affecting the student ownership of the numerical procedure to approximate the value of the quantity that is changing becomes a research problem. The interest on further analysis of this problem lies in the very stage where the interaction takes place between teachers, students and mathematical content, in the classroom. The aim of this work consists of: 1) design activities for the introduction of the Newtonian paradigm through numerical procedure known as Euler's method, 2) carry out a sequence of performances that include such activities in the first course of Mathematics for Engineering careers, 3) capture data to assess the effectiveness of the acquisition of this procedure in each staging and to suggest items for improvement and 4) strengthen the establishment of a teaching sequence that functions as the epistemology of the notions of rate of change and cumulative change. Both, the aforementioned proposal and this work are framed within the Socioepistemological approach to research in Mathematics Education in responding to an epistemology of practice rather than concepts. Consistent with this approach is considered a systemic action of the four dimensions of knowledge: cognitive, didactical, epistemological and social, assuming that the latter, social, restates each of the above dimensions and incorporates social practices and with them, the human activity so intentionally. Based on appropriate frameworks are made Epistemological, Didactic and Cognitive Analysis, outlining a method for addressing the research problem. Within the Cognitive Epistemological Analysis is included the review of studies that report historical items related to the numerical procedure under consideration, and the related cognitive difficulties, as well as reports dealing with the Euler's method in connection with the study of change. In the Didactic Analysis lies the role of this procedure in the current curriculum, in particular, Differential Equations, the interest is to distinguish the role of this method in the structure of the proposal to introduce the Newtonian approach. Finally, the core of this work is on the Cognitive and Didactic Analysis, where qualitative research is conducted that includes the monitoring in three semesters in the fall (August-December) of the appropriation process of the Euler's method located in the classroom and guided by activities that are refined during this process so that eventually becomes the teaching sequence, as the product of this research. As a result we have the teaching sequence for introducing the Newtonian approach in the teaching of Calculus. The establishment of the applicability conditions that allow its implementation and analysis of the cognitive difficulties in this process likely accompany this result. With the above is provided a didactic material that supports innovation in teaching and learning Calculus, acting under the belief that educational research must be assumed as a leading activity of teaching practice, which commits the decision-making and supports innovation.
URI : http://www.repositoriodigital.ipn.mx/handle/123456789/11424
Otros identificadores : http://hdl.handle.net/123456789/939
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