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.

Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students

“…Many studies have endorsed the importance and utility of proof in mathematics education, which continues to be deemed a topic meriting further research [2]. That notwithstanding, no consensus has been reached on the consistent theoretical framework for mathematical reasoning deemed necessary by some authors [48].…”

Measurement Model and Adaptation of Self-Efficacy toward Mathematics Reasoning among University Students

“…According to previous research, deductive reasoning skills are related to mathematical abilities. It is indeed possible to reach conclusions through deductive reasoning by following the steps in a logical chain of reasoning in which each step "follows necessarily" from the previous step (Kollosche, 2021). Students' motivation to understand mathematics reasoning and evaluate mathematical generalisability leads to In order to examine patterns and adequately understand mathematical structures, an individual's mathematical reasoning skills are required.…”

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“…Reasoning is a discursive activity which involves the justification of closely related claims (Kollosche, 2021). Students normally develop the ability to think logically and reason effectively when studying mathematics (Bronkhorst et al, 2020), and this further aid their ability to think correctly.…”