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Title: Can children construct inverse relations in arithmetic? Evidence for individual differences in the development of conceptual understanding and computational skill
Authors: Gilmore, Camilla K.
Bryant, Peter
Issue Date: 2008
Publisher: Wiley-Blackwell © The British Psychological Society
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
Abstract: 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.
Description: 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
Version: Accepted for publication
DOI: 10.1348/026151007X236007
URI: https://dspace.lboro.ac.uk/2134/8762
Publisher Link: http://onlinelibrary.wiley.com/doi/10.1348/026151007X236007/abstract
ISSN: 0261-510X
Appears in Collections:Published Articles (Mathematics Education Centre)

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