Nature 455, 665-668 (2 October 2008) | doi:10.1038/nature07246; Received 10 February 2008; Accepted 4 July 2008; Published online 7 September 2008

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

Justin Halberda1, Michèle M. M. Mazzocco1,2 & Lisa Feigenson1

  1. Johns Hopkins University, Ames Hall, 3400 North Charles Street, Baltimore, Maryland 21218, USA
  2. Kennedy Krieger Institute, 3825 Greenspring Avenue, Painter Building, Top Floor, Baltimore, Maryland 21211, USA

Correspondence to: Justin Halberda1 Correspondence and requests for materials should be addressed to J.H. (Email: halberda@jhu.edu).

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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