Raciocínio covariacional em aulas de cálculo diferencial e integral: possibilidades de desenvolvimento a partir do uso de tarefas

Abstract

This dissertation presents tasks that address ideas of the Covariational Reasoning (CR) organized through episodes of task resolution. I was implemented in the classes of Differential and Integral Calculus (CIC) in Higher Education, in regular classes of a course of Engineering of the Federal Technological University of Paraná (UTFPR) of the Londrina campus. It was listed as a general objective of the research to analyze ideas of the CR that were mobilized during the collective discussions triggered by the work with mathematical tasks. For purposes of analysis, we took cuttings of written output and excerpts from dialogue in groups. We seek to illustrated the potential of the tasks in terms of instigating discussions involving CR ideas using an interactive seven-phase analytical model used to study thought mathematical development. From the analysis made, It was possible to infer that at several moments, although the students seemed to verbalize an understanding of the situation, recognizing the covariation between the quantities involved, they failed in the representations, or were not able to establish explicit relations between CR ideas and CIC concepts. For it is a master's degree in the professional field, it presents a workbook (educational product) made available as a result of our research proposal.