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Semantic contamination and mathematical proof: can a non-proof prove?

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journal contribution
posted on 2011-07-05, 13:08 authored by Juan P. Mejia-Ramos, Matthew InglisMatthew Inglis
The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Hereweargue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

MEIJA-RAMOS, J.P. and INGLIS, M., 2011. Semantic contamination and mathematical proof: can a non-proof prove? Journal of Mathematical Behaviour, 30 (1), pp. 19-29.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publication date

2011

ISSN

0732-3123

Language

  • en

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