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

TY - JOUR

T1 - Semantic contamination and mathematical proof

T2 - Can a non-proof prove?

AU - Mejía-Ramos, Juan Pablo

AU - Inglis, Matthew

PY - 2011/3

Y1 - 2011/3

N2 - The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue 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.

AB - The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue 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.

KW - Language

KW - Mathematics

KW - Proof

KW - Reasoning

KW - Semantic contamination

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U2 - https://doi.org/10.1016/j.jmathb.2010.11.005

DO - https://doi.org/10.1016/j.jmathb.2010.11.005

M3 - Article

VL - 30

SP - 19

EP - 29

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

IS - 1

ER -