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Title: Children’s understanding of the relationship between addition and subtraction
Authors: Gilmore, Camilla K.
Spelke, Elizabeth S.
Keywords: Development
Non-symbolic numerosities
Symbolic arithmetic
Issue Date: 2008
Publisher: © Elsevier
Citation: GILMORE, C.K. and SPELKE, E.S., 2008. Children’s understanding of the relationship between addition and subtraction. Cognition, 107 (3), pp. 932-945
Abstract: In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 − 9 yields 12. Here, we investigate whether preschool children’s approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding.
Description: This article was published in the journal, Cognition [© Elsevier]. The definitive version is available at: http://dx.doi.org/10.1016/j.cognition.2007.12.007
Version: Accepted for publication
DOI: 10.1016/j.cognition.2007.12.007
URI: https://dspace.lboro.ac.uk/2134/8763
Publisher Link: http://www.sciencedirect.com/science/article/pii/S0010027708000048
ISSN: 0010-0277
Appears in Collections:Published Articles (Mathematics Education Centre)

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