Diagramas na didática da matemática e criatividade: do raciocínio hipotético à argumentação lógica

Abstract

This work addresses the relevance of diagrammatic processes in fostering hypothetical reasoning and their exploration as a methodology for mathematics education. To develop this study, a discussion on the concept of abduction is presented, a term closely associated with the idea of hypothetical reasoning. This type of reasoning is fundamental to the work and scientific methodology proposed by Charles Sanders Peirce and other research based on this theorist, making it a key concept for the development of this work. Following the construction of the argument presented here, we highlight the importance of visualization in methods for understanding mathematical concepts and propose activities for mathematics lessons through investigation with open problems, utilizing diagrammatic processes. Finally, we will present examples from the literature in the field of mathematics education that explore visualization through diagrams as open problems, identifying how this approach can foster the development of concepts initiated by abduction.