
05878681
j
2011c.00431
MejiaRamos, Juan Pablo
Inglis, Matthew
Semantic contamination and mathematical proof: can a nonproof prove?
J. Math. Behav. 30, No. 1, 1929 (2011).
2011
Elsevier, New York, NY
EN
E50
E40
C50
validity
mathematical logic
proofs
proving
linguistics
mathematical language
evaluation
experiments
mathematical concepts
natural language processing
doi:10.1016/j.jmathb.2010.11.005
Summary: 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 socalled 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 nonproof can sometimes (be judged to) prove. (Contains 2 figures and 5 tables.) (ERIC)