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.
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)