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The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks

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Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

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 of John Biggs and Kevin Collis 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.

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Author information

Authors and Affiliations

  1. National Centre for Science, ICT, and Mathematics Education for Rural and Regional Australia, The University of New England, Armidale, Australia

    John Pegg

  2. University of Warwick, Coventry, UK

    David Tall

Authors
  1. John Pegg
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  2. David Tall
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Correspondence to John Pegg .

Editor information

Editors and Affiliations

  1. Dept. Mathematical Sciences, University of Montana-Missoula, Missoula, 59812-0864, U.S.A.

    Bharath Sriraman

  2. Centre for Learning Innovation, Queensland University of Technology, Victoria Park Road, Kelvin Grove, 4059, Australia

    Lyn English

Additional information

Dedicated to the memory of Kevin F. Collis 1930–2008.

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Pegg, J., Tall, D. (2010). The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_19

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  • DOI: https://doi.org/10.1007/978-3-642-00742-2_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00741-5

  • Online ISBN: 978-3-642-00742-2

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