GilmoreBryantBJEP(2006).pdf (708.31 kB)
Individual differences in children’s understanding of inversion and arithmetical skill
journal contribution
posted on 2011-08-26, 13:16 authored by Camilla GilmoreCamilla Gilmore, Peter BryantBackground and aims. In order to develop arithmetic expertise, children must
understand arithmetic principles, such as the inverse relationship between addition and
subtraction, in addition to learning calculation skills. We report two experiments that
investigate children’s understanding of the principle of inversion and the relationship
between their conceptual understanding and arithmetical skills.
Sample. A group of 127 children from primary schools took part in the study.
The children were from 2 age groups (6–7 and 8–9 years).
Methods. Children’s accuracy on inverse and control problems in a variety of
presentation formats and in canonical and non-canonical forms was measured. Tests of
general arithmetic ability were also administered.
Results. Children consistently performed better on inverse than control problems,
which indicates that they could make use of the inverse principle. Presentation format
affected performance: picture presentation allowed children to apply their conceptual
understanding flexibly regardless of the problem type, while word problems restricted
their ability to use their conceptual knowledge. Cluster analyses revealed three
subgroups with different profiles of conceptual understanding and arithmetical skill.
Children in the ‘high ability’ and ‘low ability’ groups showed conceptual understanding
that was in-line with their arithmetical skill, whilst a 3rd group of children had more
advanced conceptual understanding than arithmetical skill.
Conclusions. The three subgroups may represent different points along a single
developmental path or distinct developmental paths. The discovery of the existence of
the three groups has important consequences for education. It demonstrates the
importance of considering the pattern of individual children’s conceptual understanding
and problem-solving skills.
History
School
- Science
Department
- Mathematics Education Centre
Citation
GILMORE, C.K. and BRYANT, P., 2006. Individual differences in children’s understanding of inversion and arithmetical skill. The British Journal of Educational Psychology, 76 (2), pp. 309-331Publisher
Wiley-Blackwell © The British Psychological SocietyVersion
- AM (Accepted Manuscript)
Publication date
2006Notes
This article was published in the serial, The British Journal of Educational Psychology [© The British Psychological Society]. The definitive version is available at: http://onlinelibrary.wiley.com/doi/10.1348/000709905X39125/abstractISSN
0007-0998Publisher version
Language
- en
Administrator link
Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC