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Substitution and sameness: two components of a relational conception of the equals sign

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journal contribution
posted on 27.06.2012 by Ian Jones, Matthew Inglis, Camilla K. Gilmore, Margaret Dowens
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.
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  • Science

Department

  • Mathematics Education Centre

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.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publication date

2012

Notes

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

ISSN

0022-0965

eISSN

1096-0457

Language

en

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