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The role of definitions in example classification.

Alcock, L.J. and Simpson, A. (2009) 'The role of definitions in example classification.', in 33rd Conference of the International Group for the Psychology of Mathematics Education, PME 33, 19-24 July 2009, Thessaloniki, Greece ; proceedings. Thessaloniki, Greece: International Group for the Psychology of Mathematics Education, pp. 33-40.

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.

Item Type:Book chapter
Full text:PDF - Published Version (83Kb)
Status:Peer-reviewed
Publisher Web site:http://www.pme33.eu
Record Created:08 Nov 2010 16:05
Last Modified:15 Mar 2011 12:12

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