Teorias cognitivas do Pensamento Matemático Avançado e o processo de construção do conhecimento: um estudo envolvendo os conceitos de limite e continuidade

Abstract

The aim of this thesis was to conjecture about which mental structures and mechanisms need to be built by an individual in order to lead one to comprehend the concepts of limit and continuity of a function. For that, the research was organized in two stages. In the first stage, based on the theory of concept image and concept definition (VINNER, 1991), a preliminary study was developed, by which it was possible to analyze the elements that composed the concept image of mathematics students about such concepts. In the second stage, it was presented a genetic decomposition to limit and continuity, having as reference these mathematical objects, their historical-conceptual development, teaching experiences in the field of Calculus, multiple representations of such concepts and, specially, some assumptions of the APOS theory (DUBINSKY et al., 1984; ARNOON et al., 2014). As principle results, it was observed that various comprehensions about limit and continuity were evoked in the first stage, which led to reflections about the parts of the genetic decomposition that was elaborated from different mathematical objects, such as function, limit‟s definition, relation, relation between lateral and bilateral limits, limit properties, limits involving infinity, continuity at a point and along an interval, among others.