Students’ proof styles as individualisations of the genre of proof
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Research in undergraduate mathematics education proposes that proof can be considered a genre of writing. Yet, the potential of this proposal remains underexplored. Building on the genre literature and the commognitive framework, I will introduce the concept of individualized proof styles—cumulative networks of personally adapted rules of the proof genre that one endorses and enacts to produce proofs. Hence, proof styles play a role in whether students’ productions will be accepted as instances of the genre by a wider community. The construct will be illustrated with an undergraduate student who produced textbook-like proofs with minimal substantiation gaps.
Bio
Igor’ Kontorovich is an Associate Professor of mathematics education at the University of Hong Kong. His scholarship focuses on the processes of mathematics learning and teaching, mostly at the secondary and undergraduate levels. In his research, Igor’ aims to offer theoretically-grounded and empirically-inspired insights to improve the teaching and learning of mathematics for all students.