On Understanding in Mathematics

Abstract

It is often difficult to teach mathematics for understanding. Many students seem to prefer to learn computational skills by rote, and seem to remember very little of the course contents the following semester. The reasons for this are surely manifold. This paper reviews the concept of understanding, looking particularly towards the meaning it has in hermeneutic philosophy. The known distinction between hermeneutical and epistemological understanding is resituated in mathematics, and we argue that it is the hermeneutic understanding which is most relevant when mathematics is taught as a support subject for engineering and other professions.