AGAINST EPSILON-DELTA ORTHODOXY: A MANIFESTO IN DEFENSE OF THE TEACHING OF DIFFERENTIAL AND INTEGRAL CALCULUS WITH INFINITESIMALS

Abstract

The work presented here can be read as a manifesto in defense of a teaching methodology for Differential and Integral Calculus that is based on the deliberate and ostentatious use of infinitesimal elements, privileging the students' most intuitive and spontaneous conceptions. In this sense, a manifesto in favour of the adoption of the most diverse approaches based, directly or indirectly, on the non-standard analysis developed by Abraham Robinson in the early 1960s, which rehabilitated the infinitesimal elements for analysis. Furthermore, the present work outlines a set of relevant research themes to guide future research work, whose ultimate purpose consists of the detailed definition of alternative teaching strategies, as well as the elaboration of corresponding teaching material, capable of making successful the teaching learning process of Differential and Integral Calculus’s subject in higher education courses