Uma análise de obstáculos identificados por meio da aplicação de experimentos mentais a um grupo de licenciandos em matemática

Abstract

This research proposes a complementary methodology to Mathematics teaching, called Thought Experiments, and aims to analyze its contributions to the initial training of a group of Mathematics undergraduates at the Federal University of Juiz de Fora (UFJF). These Thought Experiments are ways of representing the object of knowledge through diagrams, developing deductions and abductions that, by modifying these diagrams, lead to the formation of new concepts and/or generalizations. The choice of this methodological approach arises from the researchers' concern to recover pedagogical practices that rely on experimentation, analogies, and the use of dialectics in Mathematics teaching. Within this perspective, we will investigate the question: How does the use of Thought Experiments in the context of Mathematics Education influence the initial training of a group of Mathematics teachers? For this qualitative research, we aim to achieve the outlined objective by identifying obstacles both in the methodology and in Mathematics, especially those of epistemological and didactic origins, that emerge during the application of Thought Experiments as a methodological strategy. The theoretical foundations of this study include Peirce's semiotic concepts and Brousseau's obstacles, considered as signs in this context. The research was conducted during the classes of the course Mathematics School III, taught to Mathematics undergraduates at UFJF. The proposal to use Thought Experiments as an additional resource proved to promote a more contextualized and critical teaching approach, providing undergraduates with a dialectical understanding of mathematical concepts.