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Substitution and sameness: two components of a relational conception of the equals sign
journal contribution
posted on 2012-06-27, 11:10 authored by Ian JonesIan Jones, Matthew InglisMatthew Inglis, Camilla K. Gilmore, Margaret DowensA 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.
History
School
- 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
© ElsevierVersion
- AM (Accepted Manuscript)
Publication date
2012Notes
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.2012.05.003ISSN
0022-0965eISSN
1096-0457Publisher version
Language
- en
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