On students’ concept-image of elementary notions of nonstandard analysis

Abstract

Nonstandard analysis is a reformulation of mathematical analysis introduced in the 1960s, which allows for extending the system of real numbers so as to include infinitesimal and infinite numbers, and consequently simplify, at least at a first glance, many central notions of elementary calculus. Since then, various proposals have been formulated to introduce the teaching of nonstandard analysis in universities and in upper secondary schools. Even if proponents of such an approach maintain that concepts of nonstandard analysis are closer to intuition and easier to be understood and used, there is not a body of research to support such claims. This paper is meant to contribute to this discussion through reporting on the preliminary results of a pilot-study on student’s concept-images in nonstandard analysis.