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SfN Neuroblogging: Modeling ideas of number

The views expressed are those of the author and are not necessarily those of Scientific American.


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For one of Tuesday’s Neuroblogging posts, Sci is going to go WAY out of her comfort zone and dip a toe into the world of computational modeling. Specifically, the modeling of how children learn number.

How do you learn number? Well, many of us seem to learn it this way:

But what does it mean in your brain?

Prather, R. “Connecting number cognition to the neural coding of number” Indiana Universiy, 537.09

This modeling experiment takes into account results from behavioral experiments seen in kids, and connects it with neural codings of number seen in previous work in monkeys. Basically, you take kids, say ages 4-10. You give them a number line, with 1 at one end, and 100 at the other. You ask then to place, say…the number 30, and show where it is on the line. The younger kids will make more mistakes, having less experience both with numbers and less accuracy, while the older kids become more and more accurate, eventually matching adults.

Now, when you ask monkeys to do a similar task (in this case a match to sample task where they have to choose pictures with the same number of dots, as monkeys are not good at number lines), you get a set of neurons which fire in response to each number. So a set of neurons will all spike in response to 5, with smaller responses to 4 or 6, which are nearby but not accurate. You can model this data as a inverted U shaped curve of accuracy, where the neurons all spike highest in response to 5, and some will also spike to 4 or 6, forming the tails of the curve. According to this model, the less accurate your knowledge of number is, the wider the curve would be. So you might have neurons spiking to 5, but if you weren’t so clear on 5, they might also spike some to 2, 3, or 7. In this cause, the model (called a tuning curve) would be a wider inverted U, depicting less accuracy.

The authors applied this model to the children and the number lines. They use it to show that younger children with less accuracy have wider tuning curves, showing that they aren’t so clear about the numbers, and as they get older and better at number lines, these tuning curves narrow out, until they become as narrow as adults and just as accurate.

What is this for? Well, first it’s a way to show how humans brains may encode numbers, but it also shows how our concepts of numbers may become more accurate over time (though we cannot yet measure this in humans). And it may be a good way to help model numerical learning disabilities in humans, looking at how their tuning curves develop. This is still theoretical, but it may help us to understand ideas of number.

Ok I have to share this one. I LOVE this one. :)

Scicurious About the Author: Scicurious is a PhD in Physiology, and is currently a postdoc in biomedical research. She loves the brain. And so should you. Follow on Twitter @Scicurious.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. rramnath 11:36 am 11/16/2011

    Hi Sci,

    I am wondering, and maybe you didn’t get a chance to ask this, but how are large numbers encoded ? Surely we don’t have a separate neuron for each number, since there are always more numbers than neurons, but where does the one-to-one mapping break down ?

    Cheers,
    Rohit.

    Link to this
  2. 2. RW Prather 9:53 pm 11/21/2011

    Hi, Rohit. Sorry for the late response. I would imagine that any sort of one-to-one correspondence might break down relatively quickly. It may depend on experience.

    Link to this

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