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Investigating children’s understanding of inversion using the missing number paradigm
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. 301-316Publisher
© ElsevierVersion
- AM (Accepted Manuscript)
Publication date
2006Notes
This article was published in the journal, Cognitive Development [© Elsevier]. The definitive version is available at: http://dx.doi.org/10.1016/j.cogdev.2006.03.007ISSN
0885-2014Publisher version
Language
- en