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Can children construct inverse relations in arithmetic? Evidence for individual differences in the development of conceptual understanding and computational skill

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journal contribution
posted on 26.08.2011, 13:20 by Camilla Gilmore, Peter Bryant
Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the inverse relationship between addition and subtraction, in problems where it was transparently applicable (e.g. 17+11−11=□) and where it was not (e.g. 15+11−8−3=□). Most children were able to construct inverse transformations and apply the shortcut in at least some situations, although they used the shortcut more for problems where it was transparently applicable. There were individual differences in the relationship between children's understanding of the inverse relationship and computational skill that have implications for theories of mathematical development.
Loughborough Publications

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  • Science

Department

  • Mathematics Education Centre

Citation

GILMORE, C.K. and BRYANT, P., 2008. Can children construct inverse relations in arithmetic? Evidence for individual differences in the development of conceptual understanding and computational skill. British Journal of Developmental Psychology, 26 (3), pp. 301-316

Publisher

Wiley-Blackwell © The British Psychological Society

Version

AM (Accepted Manuscript)

Publication date

2008

Notes

This article was published in the serial, British Journal of Developmental Psychology [© The British Psychological Society]. The definitive version is available at: http://onlinelibrary.wiley.com/doi/10.1348/026151007X236007/abstract

ISSN

0261-510X

Language

en

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Loughborough Publications

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