The role of definitions in example classification

Alcock, L.J.; Simpson, A.

Abstract

This paper reports an empirical study of students’ classification of sequences before and after meeting explicit definitions of ‘increasing’ and ‘decreasing’. In doing so, it explores 1) students’ interpretations of the definitions and 2) the appropriateness of this apparently straightforward context for teaching students about the status of mathematical definitions. In particular, it demonstrates that students’ spontaneous conceptions in this context can be inconsistent with definitions, and it explores the extent to which exposure to formal definitions influences these conceptions. The results show an interesting pattern of modified classifications, which demonstrates increased consistency with the definitions but shows problems with some pivotal examples.

Citation

Alcock, L., & Simpson, A. (2009). The role of definitions in example classification

• Journal Article Type: Article
• Publication Date: Jan 1, 2009
• Deposit Date: Oct 28, 2010
• Publicly Available Date: Dec 6, 2010
• Journal: Psychology of mathematics education.
• Peer Reviewed: Peer Reviewed
• Volume: 2
• Pages: 33-40
• Public URL: https://durham-repository.worktribe.com/output/1537887
• Publisher URL: http://www.pme33.eu