Mathematical reasoning: a study carried out in the EIEM 2013 Minutes

Abstract

This article presents the results of a theoretical research related to a Scientific Initiation project on the theme Mathematical Reasoning. The study has as theoretical support the articles contained in the Minutes of the Research Meeting Mathematics Education - EIEM, held in 2013, promoted by the Portuguese Mathematical Education Research Society. The objective was to understand the concept of mathematical reasoning and its main characteristics according to the authors of the articles presents the 2013 EIEM Minutes. For that, tables were constructed with excerpts from the texts that define and characterize mathematical reasoning. The main aspects found in the study were the definitions, types and processes associated with mathematical reasoning.  The types of reasoning presented were abductive, inductive and deductive. In addition, the processes of representation, signification, gereralization and argumentation and their contributions to the development of reasoning were highlighted. In order to organize the studied concepts, a conceptual map was constructed in an attempt to present the composition of Mathematical Reasoning. The realization of this study provided a research experience for the author, a graduate student in Mathematics, and also brought theoretical contributions regarding mathematical reasoning and its implications in the construction of mathematical knowledge.