The fundamental cycle of concept construction underlying various theoretical frameworks |
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Authors: | John Pegg David Tall |
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Institution: | 1. SiMERR National Centre, University of New England, 2351, Aimidale, NSW, Australia 2. Mathematics Education Research Centre, University of Warwick, CV4 7AL, UK
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Abstract: | In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning. |
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