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Title: Substitution and sameness: two components of a relational conception of the equals sign
Authors: Jones, Ian
Inglis, Matthew
Gilmore, Camilla K.
Dowens, Margaret
Issue Date: 2012
Publisher: © Elsevier
Citation: JONES, I. ... et al, 2012. Substitution and sameness: two components of a relational conception of the equals sign. Journal of Experimental Child Psychology, 113 (1), pp. 166 - 176.
Abstract: A sophisticated and flexible understanding of the equals sign is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator, and the equals sign as signalling the same value on both sides of the equation. We argue here that as well as these two conceptions, the notion of substitution is also an important part of a sophisticated understanding of mathematical equivalence. We provide evidence from a cross-cultural study in which English and Chinese children were asked to rate the “cleverness” of operational, sameness and substitutive definitions of the equals sign. A Principle Components Analysis revealed the substitutive items were distinct from the sameness items. Furthermore, Chinese children rated the substitutive items as ‘very clever’, whereas the English children rated them as ‘not so clever’, suggesting that the notion of substitution develops differently across the two countries. Implications for developmental models of children’s understanding of equivalence are discussed.
Description: This article was published in the Journal of Experimental Child Psychology [© Elsevier]. The definitive version is available at: http://dx.doi.org/10.1016/j.jecp.2012.05.003
Version: Accepted for publication
DOI: 10.1016/j.jecp.2012.05.003
URI: https://dspace.lboro.ac.uk/2134/10010
Publisher Link: http://dx.doi.org/10.1016/j.jecp.2012.05.003
ISSN: 0022-0965
Appears in Collections:Published Articles (Mathematics Education Centre)

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