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The role of definitions in example classification.

By L.J. Alcock and A. Simpson


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

Publisher: International Group for the Psychology of Mathematics Education
Year: 2009
OAI identifier:

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