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.

尽管推理是数学教育研究的中心概念，但该学科仍需要一个统一的数学推理理论框架。关于该学科中证明，数学建模和后真理政治的主流论述中的认识论问题，并根据数学哲学和一般数学教育研究的趋势，有人认为有必要给出相对论的数学推理。作为一种可能的解决方案，介绍了Hacking的推理风格框架。该框架区分了至少六种不同的推理方式，其中许多与数学紧密相关，并认为这些框架定义了我们接受的可断定的断言，以作为此类断言的理由，以及此类断言的可能对象。本文最后讨论了该框架对所选数学教育研究领域的影响，这可能会在将来激发更多重点研究。