Cognitive trajectory of proof by contradiction for transition-to-proof students

Darryl Chamberlain, Draga Vidakovic

Research output: Contribution to journalArticlepeer-review

Abstract

History and research on proof by contradiction suggests proof by contradiction is difficult for students in a number of ways. Students’ comprehension of already-written proofs by contradiction is one such aspect that has received relatively little attention. Applying the cognitive lens of Action-Process-Object-Schema (APOS) Theory to proof by contradiction, we constructed and tested a cognitive model that describes how a student might construct the concept ‘proof by contradiction’ in an introduction to proof course. Data for this study was collected from students in a series of five teaching interventions focused on proof by contradiction. This paper will report on two participants as case studies to illustrate that our cognitive trajectory for proof by contradiction is a useful model for describing how students may come to understand the proof method.
Original languageAmerican English
JournalJournal of Mathematical Behavior
DOIs
StatePublished - Jan 1 2021

Keywords

  • Proof by Contradiction
  • Proof Comprehension
  • APOS Theory
  • Genetic Decomposition

Disciplines

  • Science and Mathematics Education

Cite this