Cognitive structure and phenomenology: the case of the convergent sequence

Abstract

This research describes how two «cells» of the cognitive structure (Vinner, 1991) connect to the phenomena, in Freudenthal’s (1983) sense, organized by a definition of finite limit of a sequence and the phenomena organized by a Cauchy sequence (Claros, 2010). These connections arose when we faced, as a target, to the introduction of didactic sequences or lesson plans to teach the finite limit of a sequence and Cauchy sequences. These didactic sequences appeal to the use of intuitive approach and feedback phenomena described by Claros (2010) and focuses them as essential elements in building a concept image of a convergent sequence or an image proof of it (Kidron and Dreyfuss, 2014). These two «cells» of the cognitive structure help in developing the concept definition of a sequence with limit.