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

Juan Pablo Mejía-Ramos, Matthew Inglis

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)19-29
Number of pages11
JournalJournal of Mathematical Behavior
Volume30
Issue number1
DOIs
StatePublished - Mar 2011

All Science Journal Classification (ASJC) codes

  • Education
  • Applied Psychology
  • Applied Mathematics

Keywords

  • Language
  • Mathematics
  • Proof
  • Reasoning
  • Semantic contamination

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