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The cost of multiple representations: learning number symbols with abstract and concrete representations

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posted on 17.09.2018, 08:06 by Amy Bennett, Matthew InglisMatthew Inglis, Camilla GilmoreCamilla Gilmore
Parents are frequently advised to use number books to help their children learn the meaning of number words and symbols. How should these resources be designed to best support learning? Previous research has shown that number books typically include multiple concrete representations of number. However, a large body of mathematics education research has demonstrated that there may be costs, as well as benefits, to using both multiple representations and concrete representations when learning mathematical concepts. Here we used an artificial symbol learning paradigm to explore whether the use of abstract (arrays of dots) or multiple concrete (changing arrays of pictures) numerical representations resulted in better learning of novel numerical symbols by children. Across three experiments we found that children who learned the meaning of novel symbols by pairing them with numerosities represented by arrays of dots performed better on a subsequent symbolic comparison task than those who paired them with multiple concrete representations, or a mixture of abstract and multiple concrete representations. This advantage was not due to abstract representations being inherently superior to concrete representations, but instead to the use of multiple concrete representations. We conclude that the very common practice of using multiple concrete representations in children’s number books may not be the most effective to support children’s early number learning.

Funding

CG is funded by a Royal Society Dorothy Hodgkin Fellowship.

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Journal of Educational Psychology

Citation

BENNETT, A., INGLIS, M. and GILMORE, C.K., 2018. The cost of multiple representations: learning number symbols with abstract and concrete representations. Journal of Educational Psychology, 111 (5), pp.847-860.

Publisher

© American Psychological Association

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

06/09/2018

Publication date

2018

Notes

© American Psychological Association, 2018. This paper is not the copy of record and may not exactly replicate the authoritative document published in the APA journal. Please do not copy or cite without author's permission. The final article is available at: http://dx.doi.org/10.1037/edu0000318.

ISSN

0022-0663

eISSN

1939-2176

Language

en

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