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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.

Maturity and citizenship in a democracy require that laypersons are able to critically evaluate experts’ use of mathematics. Learning to critically reflect on the use of mathematics, including the acquisition of the mathematical knowledge and skills required to that end, has been repeatedly postulated as an indispensable goal of compulsory education in mathematics. However, it remained unclear in how far such reflection is possible, even for the well-educated layperson in mathematics. We use different discussions in German mass media on the pandemic policy in the SARS-CoV-2 crisis in 2020 as examples with far-reaching individual and social consequences. The selected discussions build heavily on mathematical concepts such as mortality rates, casualty numbers, reproduction numbers, and exponential growth. We identify the concepts and discuss how far they can be understood by laypersons. On the one hand, we found that some mathematical models are inappropriate, which can also be determined by laypersons. On the other hand, we found uses of mathematics where ideal concepts are intermingled with complex statistical concepts. While only the ideal concepts can be understood by laypersons, only the statistical concepts lead to actual data. The identification of both types of concepts leads to a situation where the use of mathematics evades social control and opens spaces for misconceptions and manipulation. We conclude that the evaluation of experts’ use of mathematics by laypersons is not possible in all relevant cases, and we discuss possible implications of this result.

Although many scholars in the field of mathematics education are aware that identity discourses are highly political, research in the field usually lacks a framework theoretically and methodologically to address the political dimension of identity research. Based on Laclau and Mouffe's discourse theory and the case of a female secondary school student at a German public school, the present paper analyses identity as a socio-political process of identity work articulated around the discourse of 'refusing school mathematics' in our contemporary times. Her refusal of mathematics is constituted around issues related to a series of noted classroom practices such as collective work, being together and having fun, relevance of mathematics in society and life, respect of one's own dignity instead of becoming humiliated, and bodily activity instead of seated work. We illustrate how discourse theory allows us to see the identity work of refusing mathematics as a contingent process in a discursive field of socio-political struggle. In this process the subject moves beyond an essentialist 'refusal' of mathematics learning towards articulating her refusal of a particular mathematics education socio-materiality that needs to become subverted and reworked into more affirmative terms.