Banality of mathematical expertise
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ORIGINAL ARTICLE
Banality of mathematical expertise Ole Skovsmose1,2 Accepted: 22 May 2020 © FIZ Karlsruhe 2020
Abstract Practices 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. Keywords Role model · Philosophy of mathematics · Ethics · Banality of mathematical expertise · Critical mathematics education There does not exist any single well-defined practice of mathematics; rather we are dealing with a multitude of practices in both research and applications.1 Neither does it make sense to talk about the practice of mathematics education; also in this case we are dealing with a multitude of practices. Despite all these ambiguities, in this paper I address the relationships between, on the one hand, the practices of mathematics as found at universities and research institutions, and on the other, the practices of mathematics education as found in school contexts. The relationships between the two set of practices are opaque, which can be illustrated by an observation made by Burton (2004). She completed an extensive study of how mathematicians were doing their research. She interviewed more than 70 research mathematicians working in different areas of mathematics, both pure and applied, and she identified a variety of approaches being used. Some mathematicians were thinking in images and movements, while others engaged in extensive manipulations of symbols and * Ole Skovsmose [email protected] 1
Aalborg University, Ålborg, Denmark
Universidade Estadual Paulista (UNESP), São Paulo, Brazil
2
formulas. Some created new ideas by writing out formulas, not on paper but with a hand moving in the air. For some, the work could be undertaken after going to bed—and I wonder if such writing would work equally well in the dark. Some were grasping new connections while taking a shower. Through her study, Burton revealed the existence of a huge variety of creative practices in mathematics
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