2134/14020
Keith Weber
Keith
Weber
Matthew Inglis
Matthew
Inglis
Juan P. Mejia-Ramos
Juan P.
Mejia-Ramos
How mathematicians obtain conviction: implications for mathematics instruction and research on epistemic cognition
Loughborough University
2014
Conviction
Epistemic cognition
Justification
Mathematics
Proof
2014-01-23 16:45:47
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/How_mathematicians_obtain_conviction_implications_for_mathematics_instruction_and_research_on_epistemic_cognition/9370634
The received view of mathematical practice is that mathematicians gain
certainty in mathematical assertions by deductive evidence rather than empirical or
authoritarian evidence. This assumption has influenced mathematics instruction where
students are expected to justify assertions with deductive arguments rather than by
checking the assertion with specific examples or appealing to authorities. In this paper,
we argue that the received view about mathematical practice is too simplistic; some
mathematicians sometimes gain high levels of conviction with empirical or authoritarian
evidence and sometimes do not gain full conviction from the proofs that they read. We
discuss what implications this might have, both for for mathematics instruction and
theories of epistemic cognition.