Processos de superação dos obstáculos epistemológicos na história do conceito de limite de função : potencialidades conceituais e didáticas para a formação de professores de matemática

Abstract

Difficulties in Mathematics in Higher Education have been much discussed in several studies in Mathematics Education, mainly in the context of Calculus. Concerning Calculus, researches point to the fact that the teaching and learning of the involved notions present many questions that deserve to be deepened, particularly in relation to the concept of limit. In this work, we take as a research question: how epistemological prejudices were overcome along the historical development of the function limit concept? Based on this question, we delimited as an objective: to discuss the processes of overcoming the epistemological objectives that emerged in the historical development of the concept of limit of function, with a view to the potential for an approach to the subject in a degree in mathematics. To achieve this goal, note a literature review on the historical development of the limit-of-function concept in textbooks on the history of mathematics published in Portuguese, Spanish and English, as well as in works produced by philosophers, mathematicians, and epistemologists dedicated to studies on the subject, mainly regarding the mathematical contributions produced by D'Alembert, Cauchy and Weiertrass in the development of the subject. Based on the principles of content analysis, we interpret the processes of overcoming the epistemological processes concerning the subject, both in its conceptual and didactic perspectives.