The epistemological obstacle of the actual infinity: persistence, resistence and categories of analysis

Resumen

Epistemological obstacles often have deep roots in Mathematics itself; those roots can be explored in the history of the discipline, and are characterized both by the persistence with which they reappear in various situations and the determining role that they play for the achievement of learning. These obstacles often remain unnoticed by the instructor, either because he/ she has replaced in time his/her own (semantic) conceptions by others of a theoretical nature – overcoming thus the obstacle, but not being aware of it – or else because he/she has not yet made that substitution. In this paper, we present a particularly relevant illustration of the above, which refers to the persistence of an obstacle related to the concept of infinity in different stages of learning. Then we show an additional characteristic of the obstacle, that we call resistance. Subsequently, we use various theoretical approaches, properly didactic, to go into the question. Lastly, we put forward some reflections that can be derived from our study.

Autores: Mena, A., Mena, J., Montoya, E., Morales, A., Parraguez, M.

Journal: Revista Latinoamericana de Investigación en Matemática Educativa

Journal Volume: 18

Journal Issue: 3

Journal Page: 329-358

Tipo de publicación: ISI

Fecha de publicación: 2015

Topics: potential infinity, actual infinity, epistemology, epistemological obstacle.

DOI: 10.12802/relime.13.1832

URL de la publicación: http://www.redalyc.org/articulo.oa?id=33543068003