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|Title: ||Individual differences in children’s understanding of inversion and arithmetical skill|
|Authors: ||Gilmore, Camilla K.|
|Issue Date: ||2006|
|Publisher: ||Wiley-Blackwell © The British Psychological Society|
|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. 309-331|
|Abstract: ||Background 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.|
|Description: ||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/abstract|
|Version: ||Accepted for publication|
|Publisher Link: ||http://onlinelibrary.wiley.com/doi/10.1348/000709905X39125/abstract|
|Appears in Collections:||Published Articles (Mathematics Education Centre)|
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