Subsidies for the development of an epistemological reference model for the understanding of the concept of ordinary differential equations

Abstract

The special issue of the journal Educação Matemática Pesquisa (EMP) presents the question: How to develop an Epistemological Reference Model (ERM) for the teaching of Calculus? To help answer this question, we present an excerpt from ongoing doctoral research on Ordinary Differential Equations. As factors to be considered in an ERM, we highlight the contributions of Critical Mathematics, which highlights an analysis of school failure, with a specific focus on mathematics, and how this is related to curricular practices and dominant underlying epistemological models, which emphasize the transmission of knowledge in a passive and decontextualized way. The central idea is that these models should not be passively accepted, but rather questioned and constantly revised. In this study, some historical elements on the subject were considered, as well as difficulties and advances in the teaching and learning process, taking the results of some research. The evolution of the concept of Ordinary Differential Equations over time is intrinsically linked to the contributions of mathematicians in their definition and understanding. Modeling and the theory of Registers of Semiotic Representation made it possible to compose a scenario that evidenced the necessary knowledge for the teaching of ordinary differential equations. The technological knowledge present in the research comprises the knowledge of GeoGebra that helped in the teaching and learning process of this theme. Preliminary studies of a Dominant Epistemological Model (DEM) on a mathematical object, in this case Ordinary Differential.