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Investigating children’s understanding of inversion using the missing number paradigm

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journal contribution
posted on 26.08.2011, 13:18 authored by Camilla GilmoreCamilla Gilmore
The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same (e.g. 15 + 8–8 = □ ). However, we do not know whether children can perform the complementary inference that if the initial and final quantities are the same there must be an inverse relationship (i.e. 15 + □ −8=15 or 15+8−□ = 15). This paper reports two experiments that presented inverse problems in a missing number paradigm to test whether children (aged 8–9) could perform both these types of inferences. Children were more accurate on standard inverse problems (a + b−b = a) than on control problems (a + b−c = d), and their performance was best of all on rearranged inverse problems (b−b + a = a). The children’s performance on inverse problems was affected by the position of the missing number and also by the order of elements within the problem. This may be due to the different types of inferences that children must make to solve these kinds of inverse problems.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

GILMORE, C.K., 2006. Investigating children’s understanding of inversion using the missing number paradigm. Cognitive Development, 21 (3), pp. 301-316

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publication date

2006

Notes

This article was published in the journal, Cognitive Development [© Elsevier]. The definitive version is available at: http://dx.doi.org/10.1016/j.cogdev.2006.03.007

ISSN

0885-2014

Language

en

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