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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.


CG is funded by a Royal Society Dorothy Hodgkin Fellowship.



  • Science


  • Mathematics Education Centre

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Journal of Educational Psychology


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.


© American Psychological Association


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