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Lacey Beckmann, Hilary Barth, Elizabeth Spelke; Children's amodal addition and subtraction of large sets. Journal of Vision 2006;6(6):780. https://doi.org/10.1167/6.6.780.
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Adults and preschool children integrate numerical information across visually and aurally presented sets, comparing dot arrays to sound sequences based on the number of elements in each set. Previous studies (Barth, La Mont, Lipton, & Spelke, PNAS 2005) suggest that amodal representations of approximate number mediate these operations. Adults can also perform across-modality arithmetic operations as easily as within-modality operations, adding dots to sounds and comparing the sum of the elements to a third dot array. Is this ability due to adults' experience with arithmetic? Four experiments tested kindergarten children's ability to add sounds and dots, or to subtract sounds from dots, in auditory sequences and visual arrays, respectively. The (never seen) result of the arithmetic operation was compared to the number of dots in a final array (these quantities differed by ratios of 4:7, 4:6, or 4:5, with comparison dots more numerous on half the problems). Performance was compared to a baseline comparison task with the same initial numerical value as the sum/difference, using a closely matched procedure that required no adding or subtracting. Participants were successful at all tasks; accuracy depended on the comparison ratio. Children, like adults, are equally accurate on addition and comparison tasks and less accurate on subtraction tasks. The present experiments provide evidence that abstract, non-symbolic representations of number support operations of arithmetic in the absence of symbolic number knowledge.
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