Meaning the derivative in a modeling context to help understanding

摘要

Since Newton and Leibniz, the understanding of the theoretical foundations of the derivative has been a source of difficulties. This results in teaching and learning processes is chosen to achieve mastery of rules and procedures rather than conceptual aspects. The domain of the latter is desirable professions in various fields. In the case of engineering practice, this requires a high level of ability in using mathematical tools and therefore the conceptual aspects. Efforts to improve learning of the main concepts of calculus, and in particular of the derivative, including didactic proposals in various theoretical positions. However, most of these proposals rely on the definition of derivative given by Cauchy. It is suggested that this definition, received and taught as a cultural product, is the leading cause of learning difficulties. It is therefore necessary to seek new approaches to broaden their understanding. This essay describes how to obtain the derivative for polynomial functions in the context of modeling based on quantities. This context we have called the approach to modeling. It is proposed that this description of the derivative helps to understand the cultural notion of derivative and opens new lines of research in mathematics education.