The Anatomy of a Mathematical Proof: Implications for Analyses with Toulmin's Scheme

Simpson, A.

Abstract

A model solution to a proof question on an examination is explored and subjected to a detailed analysis in terms of Toulmin’s scheme of argumentation. In doing so, the ways in which the scheme has been variously used in the mathematics education and philosophical literature are contrasted. The analysis raises a number of issues concerning the scheme as described by Toulmin and as modified by other authors and suggests ways in which one aspect of the scheme might be reinterpreted. The final analysis of the proof provides insight into what examiners may be expecting from their students in terms of the level of explicit argument they consider essential and the importance played by the focus of the subject matter.

Citation

Simpson, A. (2015). The Anatomy of a Mathematical Proof: Implications for Analyses with Toulmin's Scheme. Educational Studies in Mathematics, 90(1), 1-17. https://doi.org/10.1007/s10649-015-9616-0

• Journal Article Type: Article
• Acceptance Date: Jun 8, 2015
• Online Publication Date: Jul 11, 2015
• Publication Date: Sep 1, 2015
• Deposit Date: Jun 23, 2015
• Publicly Available Date: Jul 11, 2016
• Journal: Educational Studies in Mathematics
• Print ISSN: 0013-1954
• Electronic ISSN: 1573-0816
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 90
• Issue: 1
• Pages: 1-17
• DOI: https://doi.org/10.1007/s10649-015-9616-0
• Keywords: Toulmin’s scheme, Proof, Assessment.
• Public URL: https://durham-repository.worktribe.com/output/1403169