Banality of Mathematical Expertise

Abstract

AbstractPractices within research mathematics can and do serve as models for mathematics education. However, typically such inspirations impose a devastating narrowness in relation to reflections on mathematics. This narrowness I refer to as the “banality of mathematical expertise”. Reflections on mathematics can be expressed through a philosophy of mathematics that goes beyond the traditional emphasis on ontological and epistemological dimensions, to become four-dimensional by also addressing social and ethical issues. Many working philosophies of mathematics are two-dimensional and operate within a narrow scope of reflections, seemingly located within an ethical vacuum. The consequence is a cultivation of banality, manifest in many university studies in mathematics as well as in dominant research paradigms in mathematics. This constitutes a serious limitation in providing models for mathematics education. By contrast, there exist examples of practices of mathematics education that demonstrate a richness of reflections on mathematics. Accordingly, I address the extent to which such practices of critical mathematics education could serve as models for research mathematics and mathematics education at the university level.KeywordsRole modelPhilosophy of mathematicsEthicsEthical vacuumBanality of mathematical expertise