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Mental Arithmetic and Interactivity: the Effect of Manipulating External Number Representations on Older Children’s Mental Arithmetic Success

Ross, W; Vallée-Tourangeau, F; Van Herwegen, J; (2019) Mental Arithmetic and Interactivity: the Effect of Manipulating External Number Representations on Older Children’s Mental Arithmetic Success. International Journal of Science and Mathematics Education 10.1007/s10763-019-09978-z. Green open access

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Abstract

Manipulative artefacts are considered useful scaffolds of arithmetic during early years education, but their use is considered less important as children get older. Yet adult arithmetic performance often recruits artefacts to improve accuracy and efficiency, and so the same benefits should accrue to children beyond early years. We propose that interacting with manipulatives supports working memory by extending the mental workspace. This is a hitherto poorly explored aspect of the pedagogical benefits of manipulatives. Forty-three children aged between 7 and 9 years old were invited to assess whether interacting with artefacts supported arithmetic when under a working memory load. Interactivity and load were manipulated in a 2 × 2 repeated measures design. Children calculated the total of seven digits either with hands down—low interactivity—or moving numbered tokens—high interactivity. Additionally, in half the conditions, the children performed a second task designed to tax working memory. The children were also assessed across a battery of measures examining individual differences. As expected, performance was considerably worse under load. More sums were answered correctly in high-interactivity conditions regardless of working memory load. In the high-interactivity condition with a load, there were significant correlations between performance and both numeracy and fluid intelligence suggesting that even for more numerate children manipulatives confer benefits. The expression of arithmetic skills depends on the nature of the external resources offered by the environment. This dynamic agent–environment transaction highlights the pedagogical importance of external resources when assessing children’s arithmetic abilities.

Type: Article
Title: Mental Arithmetic and Interactivity: the Effect of Manipulating External Number Representations on Older Children’s Mental Arithmetic Success
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10763-019-09978-z
Publisher version: https://doi.org/10.1007/s10763-019-09978-z
Language: English
Additional information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Expertise, Interactivity, Manipulatives, Mental arithmetic, Working memory
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Education
UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education
UCL > Provost and Vice Provost Offices > School of Education > UCL Institute of Education > IOE - Psychology and Human Development
URI: https://discovery.ucl.ac.uk/id/eprint/10078400
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