Styles of reasoning for mathematics education

Abstract

Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in the philosophy of mathematics and in mathematics education research in general, it is argued that it is necessary to give a relativist account of mathematical reasoning. Hacking’s framework of styles of reasoning is introduced as a possible solution. This framework distinguished between at least six different styles of reasoning, many of which are closely connected to mathematics, and argues that these frameworks define what we accept as decidable assertions, as justifications for such assertions, and as possible objects of such assertions. The article ends with a discussion of the implications of the framework for chosen fields of mathematics education research, which may motivate more focussed studies in the future.