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Commentary on 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

This paper first summarises and discusses Pegg and Tall’s (this volume) fundamental cycle model of conceptual construction from action to object and its relationship to particularly the SOLO UMR framework. Then the paper compares this with another model of different psychological theories of learning mathematics and discusses how these models can either be merged or learn from each other. This includes a discussion of another use of the SOLO framework. This leads to a general discussion about the problem of having many different theories and fashions, how knowledge grows and accumulates, and if there is a unifying theory to be found. The paper concludes that the development of meta-theories, such as in the work of Pegg and Tall, is necessary rather than uncritical complementarism.

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Author information

Authors and Affiliations

  1. Centre for Science Education, Faculty of Science, 1110, Aarhus University, 8000, Aarhus C, Denmark

    Bettina Dahl

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  1. Bettina Dahl
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Correspondence to Bettina Dahl .

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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

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Dahl, B. (2010). Commentary on 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_20

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  • DOI: https://doi.org/10.1007/978-3-642-00742-2_20

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