Abstract
An ongoing debate in research on numerical cognition concerns the extent to which the approximate number system and symbolic number knowledge influence each other during development. The current study aims at establishing the direction of the developmental association between these two kinds of abilities at an early age. Fifty-seven children of 3–4 years performed two assessments at 7 months interval. In each assessment, children's precision in discriminating numerosities as well as their capacity to manipulate number words and Arabic digits was measured. By comparing relationships between pairs of measures across the two time points, we were able to assess the predictive direction of the link. Our data indicate that both cardinality proficiency and symbolic number knowledge predict later accuracy in numerosity comparison whereas the reverse links are not significant. The present findings are the first to provide longitudinal evidence that the early acquisition of symbolic numbers is an important precursor in the developmental refinement of the approximate number representation system.
Highlights
Adults, young children, and infants are able to detect differences in numerosity represented by visual elements, sounds, or actions well before the acquisition of language [1,2,3]
No correlation was found between the highest number of objects correctly counted and performance in a task requiring to approximately represent the outcomes of subtraction operations on large sets [22], nor between accuracy in discriminating numerosities and performance in the ‘‘How many?’’ task [23]. Halberda and his colleagues [24] initiated a second line of research by showing that the individual differences in approximate number system (ANS) acuity at 14 years were related to math achievement scores from kindergarten to sixth grade, even after control for general cognitive factors
As indicated by the Ratio 6 Time interaction (F(2, 110) = 7.84, partial g2 = .12, p = .001), the improvement was stronger for ratio 1:2 (F(1, 55) = 35.15, partial g2 = .39, p,.001; from 75% to 91%) and 3:4 (F(1, 55) = 19.32, partial g2 = .26, p,.001; from 48% to 73%) than for ratio 2:3 (F(1, 55) = 9.75, partial g2 = .15, p = .003; from 77% to 82%)
Summary
Young children, and infants are able to detect differences in numerosity represented by visual elements, sounds, or actions well before the acquisition of language [1,2,3]. No correlation was found between the highest number of objects correctly counted and performance in a task requiring to approximately represent the outcomes of subtraction operations on large sets [22], nor between accuracy in discriminating numerosities and performance in the ‘‘How many?’’ task [23] Halberda and his colleagues [24] initiated a second line of research by showing that the individual differences in ANS acuity at 14 years were related to math achievement scores from kindergarten to sixth grade, even after control for general cognitive factors. Feigenson, and Halberda [33] have shown that the accuracy in numerosity comparison measured in children of 3-6 years could predict their school mathematics performance two years later The authors take those findings as evidence favouring the view that symbolic number abilities depend on ANS acuity. If ANS acuity and symbolic number abilities influence each other, we should obtain similar correlations between both measures across the two time points
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