The Frontal Cortex

Mathematical Intuitions

Let’s say I flash you a picture containing a mixture of blue and yellow dots for one-fifth of a second. You clearly don’t have time to count the dots – you barely have time to register the image – but I ask you to guesstimate the ratio of blue to yellow dots anyways. Sounds like a pretty meaningless quiz, right? If anything, it would seem that I’m testing your visual cortex, or the ability of the brain to quickly make sense of its senses.

Well, a new paper in Nature argues that I’m actually testing your mathematical intuition. Furthermore, this intuition strongly correlates with your past scores on standardized math achievement tests, extending all the way back to kindergarten. It’s a pretty jarring example of how even abstract elements of cognition – like pre-algebra – are built out of a basic set of primitive instincts. Even our fanciest computational software is assembled from used evolutionary parts. Does this mean we should test kids with blue and yellow dots at a young age and then sort them accordingly in math class? Gosh, I hope not.

Here is the paper:

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 teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-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.

via Mind Hacks


  1. #1 cg
    September 10, 2008

    I’ve seen this mentioned in a few places now, and I’m not sure that this convinces me that what they tested was an innate ability.

    It seems intuitive to me that the ability to estimate the number of items in a grouping would be improved by math education. If that’s true, then I would expect the kids with the highest scores throughout their schooling to do better with the task they tested. This would make the results of the experiment somewhat mundane.

    Maybe I’m missing something. Is this “intuitive number sense” an ability that is unchanged through specific instruction or general math education? If education can’t improve it, that seems really interesting to me.

  2. #2 Lee Pirozzi
    September 10, 2008

    Glanced it – guessed 14, hated algebra – go figure.

  3. #3 Wheels
    September 10, 2008

    So, does this mean the more advanced you are in the mathmatical field, the more likely you are to getting closer to the correct ratio? Is there a link to test this demonstration?

  4. #4 Alex Dodge
    September 17, 2008


    You hope that’s not what we should do, or you hope we don’t even if we should?

    Alex Dodge

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