Submitting Campus
Worldwide
Department
STEM Education
Document Type
Article
Publication/Presentation Date
2021
Abstract/Description
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.
Publication Title
Journal of Mathematical Behavior
DOI
https://doi.org/10.1016/j.jmathb.2021.100849
Grant or Award Name
DUE-1624906
Scholarly Commons Citation
Chamberlain, D., & Vidakovic, D. (2021). Cognitive Trajectory of Proof by Contradiction for Transition-To-Proof Students. Journal of Mathematical Behavior, (). https://doi.org/10.1016/j.jmathb.2021.100849
