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Individual differences in non-verbal number acuity correlate with maths achievement


Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching1,2. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults3,4,5,6, infants7 and non-human animals8,9,10,11,12,13—these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal ‘number sense’ than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children’s past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.

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Figure 1: Method and group performance.
Figure 2: Regressions.


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Longitudinal data collection was supported by a National Institutes of Health grant RO1 HD 034061 to M.M. We thank the Baltimore County Public School District and the children and parents who participated in this research, D. Naimen and R. Goodman for help with modelling, and L. Stapleton for help with statistical analyses.

Author Contributions J.H., M.M. and L.F. conceived the experiment; J.H. designed the numerical discrimination procedure; M.M. provided longitudinal data and oversaw data collection; J.H. performed the modelling and data analysis; J.H., L.F. and M.M. wrote the paper.

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Correspondence to Justin Halberda.

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This file contains Supplementary Methods and Supplementary Notes, including a description of the standardized tests used to assess maths, cognitive and other abilities of the children in our sample. (PDF 599 kb)

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Halberda, J., Mazzocco, M. & Feigenson, L. Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455, 665–668 (2008).

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