Skovsmose, Ole [UNESP]2020-12-122020-12-122020-11-01ZDM - Mathematics Education, v. 52, n. 6, p. 1187-1197, 2020.1863-97041863-9690http://hdl.handle.net/11449/198974Practices 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 operate within a narrow scope of reflections, seemingly located within an ethical vacuum. The consequence is a cultivation of a 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.1187-1197engBanality of mathematical expertiseCritical mathematics educationEthicsPhilosophy of mathematicsRole modelArtigo10.1007/s11858-020-01168-42-s2.0-85086365616