Growth in mathematical understanding: How can we characterise it and how can we represent it? View Full Text


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Article Info

DATE

1994-03

AUTHORS

Susan Pirie, Thomas Kieren

ABSTRACT

There has been a variety of approaches to the study of mathematical understanding, and some of these are reviewed before outlining the background to the model we are proposing for the growth of such understanding. The model is explained in detail and illustrated with reference to the concept of fractions. Key features of the model include ‘don't need’ boundaries, ‘folding back’, and the complementarities of ‘acting’ and ‘expressing’ that occur at each level of understanding. The theory is illustrated by examples of pupils' work from a variety of topics and stages. Finally one of the practical applications of the theory, mapping, is explained in some detail. More... »

PAGES

165-190

References to SciGraph publications

  • 1991. Recursion and the Mathematical Experience in EPISTEMOLOGICAL FOUNDATIONS OF MATHEMATICAL EXPERIENCE
  • 1992-10. Creating constructivist environments and constructing creative mathematics in EDUCATIONAL STUDIES IN MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01273662

    DOI

    http://dx.doi.org/10.1007/bf01273662

    DIMENSIONS

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