Publication: Límite infinito de una sucesión: fenómenos que organiza
Loading...
Official URL
Full text at PDC
Publication Date
2019-11-29
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Complutense de Madrid
Citations
Exportar
Abstract
El límite es una noción estudiada por el Análisis Matemático, y las dificultades de su proceso enseñanza-aprendizaje una de las líneas de investigación en el área de la Didáctica de las Matemáticas en las últimas décadas. Partimos de la premisa de que cada uno de los límites debe ser estudiado minuciosamente, por ese motivo, en esta tesis doctoral nos ocuparemos de uno de ellos: el límite infinito de una sucesión.Este estudio se sostiene sobre cuatro pilares fundamentales: la fenomenología dada por Freudenthal, el Pensamiento Matemático Avanzado, los Sistemas de Representación y la Teoría APOS. A partir de ellos, mediante un estudio teórico, caracterizamos tres fenómenos organizados por una definición del límite infinito de una sucesión: crecimiento intuitivo ilimitado, c-i.i. y decrecimiento intuitivo ilimitado, d-i.i., considerando un enfoque intuitivo, e ida-vuelta en sucesiones de límite infinito, a partir de un enfoque formal...
The limit is a notion studied in Mathematical Analysis and the associated difficulties in the teaching-learning process constitute an important research area in Mathematical Education. In this PhD Thesis, we start from the premise that each of the limits should be studied separately. Therefore, we will focus our attention in one of them: the infinite limit of a sequence. This study is based on four fundamental pillars: Phenomenology as understood by Freudenthal, Advanced Mathematical Thinking, Systems of Representation and APOS Theory. The first part of our study is theoretical. Here, taking into account the previous fields, we have characterized three phenomena organized by a definition of the infinite limit of a sequence. The first two correspond to an intuitive approach: “unlimited intuitive growth”, u.i-g. (c-i.i.), and “unlimited intuitive decrement”, u.i-d. (d-i.i.). The third one is “go and back in infinite limit sequences”, g.b.i.s. (i.v.s.i.), and belongs to a formal approach...
The limit is a notion studied in Mathematical Analysis and the associated difficulties in the teaching-learning process constitute an important research area in Mathematical Education. In this PhD Thesis, we start from the premise that each of the limits should be studied separately. Therefore, we will focus our attention in one of them: the infinite limit of a sequence. This study is based on four fundamental pillars: Phenomenology as understood by Freudenthal, Advanced Mathematical Thinking, Systems of Representation and APOS Theory. The first part of our study is theoretical. Here, taking into account the previous fields, we have characterized three phenomena organized by a definition of the infinite limit of a sequence. The first two correspond to an intuitive approach: “unlimited intuitive growth”, u.i-g. (c-i.i.), and “unlimited intuitive decrement”, u.i-d. (d-i.i.). The third one is “go and back in infinite limit sequences”, g.b.i.s. (i.v.s.i.), and belongs to a formal approach...
Description
Tesis inédita de la Universidad Complutense de Madrid, Facultad de Educación, leída el 18-10-2019