Processos do raciocínio matemático mobilizados por estudantes de cálculo diferencial e integral em tarefas exploratórias

Abstract

This dissertation analyzes reasoning processes mobilized by Differential and Integral Calculus (DIC) students in discussions from a task of an exploratory nature. The research is qualitative, of interpretative nature, and data collected for analysis are composed of (i) protocols containing written records of the discussions and (ii) audios of the discussions in small groups held in a regular class of the Engineering course of the Federal Technological University of Paraná (UTFPR), Londrina campus, in the year 2019. The discussions of four groups, consisting of 3 students in each group, were analyzed. The results obtained showed, throughout the discussion, excerpts from the groups, a cyclical movement with back and forth, to reason about mathematical relationships and develop statements. Students raise conjectures and, when conjecturing, three distinct pathways were identified, which are: (i) abandon conjecture definitively or provisionally; (ii) refute such conjectures with empirical justifications or logical reasoning, or without justifications; or (iii) accept the conjectures by trying to recognize and explain the validity (or not) of these statements by justifying them with particular cases or pattern recognition. At times, this movement culminated in extending, to more general situations, the regularities observed in particular cases (generalize).