Manifestações do raciocínio criativo de estudantes de cálculo de mais de uma variável ao lidar com tarefas matemáticas

Abstract

The purpose of this paper is to identify manifestations of students' creative reasoning (CR) when dealing with mathematical tasks in the context of Calculus of more than one real variable (CDI 2), and to infer relationships between these manifestations and the characteristics of these tasks. The theoretical basis includes an exploration of the concepts of creativity and Creative Reasoning (CR), as well as their interconnections, in addition to a discussion of the different types of mathematical tasks and their characteristics. The research approach is qualitative, exploratory and the participants were students of the CDI 2 subject, from two classes of Engineering courses at the Federal Technological University of Paraná (UTFPR), Londrina campus, in the 2nd semester of 2022. mathematical tasks. The data analyzed consisted of records of the students' resolutions and audio recordings of discussions when dealing with three mathematical tasks. The results discussed the characteristics of these tasks, such as their challenging profile, open nature and semi-reality context, which boosted CR, encouraging creativity. The manifestations of CR were identified when analyzing the resolutions and discussions, revealing novelty, flexibility, plausibility and mathematical foundations in their approaches. Another result, of a theoretical nature, was the identification of the close relationship between creativity and creative reasoning, based on a comprehensive analysis that highlighted the similarities in the characteristics of these two concepts. Finally, an educational product was organized, the e-book "Exploring Creative Reasoning in Higher Education: analysis of tasks in Differential and Integral Calculus of more than one variable", with the aim of discussing and exemplifying the aspects of creative reasoning mobilized by students when solving mathematical tasks.