Batchelor_MTL(2015).pdf (413.56 kB)
Download file

Magnitude representations and counting skills in preschool children

Download (413.56 kB)
journal contribution
posted on 16.03.2015, 14:54 by Sophie Batchelor, Sarah Keeble, Camilla GilmoreCamilla Gilmore
When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this mapping only occurs once children have cardinality understanding. One difficulty with the current literature is that studies have employed tasks that only indirectly assess children’s nonsymbolic-symbolic mappings. We introduce a task in which preschoolers made magnitude comparisons across representation formats (e.g., dot arrays vs. verbal number), allowing a direct assessment of mapping. We gave this task to 60 children aged 2;7 - 4;10, together with counting and Give-a-Number tasks. We found that some children could map between nonsymbolic quantities and the number words they understood the cardinal meaning of, even if they had yet to grasp the general cardinality principle of counting.


This research was supported in part by a British Academy Fellowship awarded to Camilla Gilmore.



  • Science


  • Mathematics Education Centre

Published in

Mathematical Thinking and Learning


BATCHELOR, S., KEEBLE, S. and GILMORE, C.K., 2015. Magnitude representations and counting skills in preschool children. Mathematical Thinking and Learning, 17 (2-3), pp.116-135.


© Taylor and Francis


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:

Publication date



This is an Accepted Manuscript of an article published by Taylor & Francis Group in Mathematical Thinking and Learning on 7/05/2015, available online:



Usage metrics