Mathematical Brain


New Scientist, 1999
Brain Connection, 2000
Britannica & Australasian Scientist, 1999
The Science Show, 2000
The Science Show, 2001
Educational Leadership, 2001
Plus Magazine, 2002
The Science Show, 2006
All Audio Interviews  
What's New
Test and New Chapter
About Brian Butterworth
email author
Audio Welcome
Get QuickTime 
Buy Now @ Amazon, UK

Macmillan Logo


Italian Edition

Swedish Edition

Naze sugaku ga tokui na hito to nigate na hito ga irunoka?
(Why are some people good, but others bad at maths?)

Mathematical Brain
Brian Butterworth




Brian Butterworth looks at how the brain works with sounds and numbers.

He studies the cognitive processes that occur as we hear the difference in pitch of sounds. He says our brains process our thinking about the pitch of sounds in a spacial way.

One in ten people are discalculic. They have difficulty with mathematics. Brian Butterworth speculates over the difference between children who use their fingers for basic arithmetic, and those who don't. He has suggestions and offers hope for children who have difficulty with maths.


Robyn Williams: We've had Brian on before talking about how brains deal with numbers, and now he has managed t o apply the same to music, music like this:

[excerpt from largo, Violin Sonata No. 3 in
  C major, BWV 1005 by J.S. Bach]

High notes and low notes. But are they perceived by our brains as high and low, and how has mathematical brain power been linked with our fingers doing maths? Professor Butterworth is now at the University of Melbourne.

Brian Butterworth: It turns out we think about pitch in a spatial way. We have a way of demonstrating that you really do think of high notes as high and low notes as low. I'm now going to sing, I hope your listeners will excuse me ... so you might have a reference note that goes [sings high note] and another reference note which goes [sings lower note] and you ask the subject whether the second tone was lower or higher than the first.

Now, if you ask him to press the low button for "lower-than" and the high button for "higher-than", then they are quicker than if you ask them to do it the other way round. So far, so obvious. Now, the other thing we did is we also had left and right. So are high notes on the left or are they on the right? And what we found is that you're quicker if you've got the low notes on the left and the high notes on the right.

We've also tried it with singers because one of the obvious possibilities here is that musicians are very familiar with the keyboard. With the European keyboard, you've got low notes on the left and high notes on the right. But in the case of singers, for example, we find exactly the same effect. We also tested these singers for their keyboard skills, and their degree of left-right orientation seemed to be entirely unrelated to their level of keyboard skills.

Robyn Williams: Why do you think the brain is doing that, organising something in space as well as, presumably, in the wiring?

Brian Butterworth: Space is a very good model for all sorts of things. So, for example, space is a good model for personal relationships; am I close to her or am I far from her? Is she being very distant at the moment? It's also quite good for a mood; am I feeling high? Am I feeling up or am I feeling down? So there's a whole range of different, rather abstract things which for some reason or another we like to think about in spatial terms, and it may be the same for music.

Robyn Williams: Having investigated and got a clue about this spatial nature, what are you going to do with it? Where will it lead in your studies?

Brian Butterworth: We want to ask the following question. Has it got to do with pitch itself or has it got to do with music? So you can imagine non-musical tones, noises which have different pitch. Do we organise those in a spatial way? Or is it something to do with music either as a cultural artefact, something that we have to learn that we become familiar with, or is it something that, if you like, is hardwired into our brain from birth? This seems to be rather a fundamental question, and it's one that we're keen to answer in the next phase of our experimentation.

Robyn Williams: Yes, it's always fascinating to watch your work in progress, some of which ... we've talked about numerosity before. In other words, actual numbers, not vague amounts like a pile of sand or lots of people, but 14 or 17, something that's really specific. You've found that being registered in the brain as well and linked to fingers. How come?

Brian Butterworth: This is rather a long story. There is a group of people who we call dyscalculics, and these are people who find it very difficult to learn arithmetic. It's rather like dyslexia, it's something you're born with, and it's something which, as far as we know, you can compensate for but you don't recover from.

It's a serious problem and it affects over 5% of the people, so it's nearly a million Australians. One of the indicators is an inability to represent fingers mentally, so they have a vague representation of their fingers, whereas people who are good at maths usually have a rather precise representation of their fingers. This has been known for about 60 or 70 years and it is part of what's called the Gerstmann Syndrome. It's quite easy to test for.

It turns out that one of the parts of the brain that controls finger representation is in the parietal lobe, and Joseph Gerstmann a long time ago discovered that if you had a lesion in a particular part of the left parietal lobe known as the angular gyrus, you would have both impaired representations of your fingers and also impaired calculation.

People have argued about this for a long time; is the connection between fingers and numbers just like an accident of neuroanatomy, or is it functional? It's kind of peculiar that in people who don't use their fingers to count ... I don't use my fingers to count except when I'm trying to work out how many days car rental I have to pay for. But apart from that, if I have to do five plus three, I don't do it on my fingers anymore. But nevertheless, we found that if you disabled this part of the brain temporarily using a technique called trans-cranial magnetic stimulation, then this would affect both their finger representation and also their numerical representation.

We thought that this showed that there was something rather functional about the relationship between these two capacities, even in adults who no longer use their fingers to do calculations with. And in fact one of the tests that we used of their numerical ability was their ability to automatically access multiplication facts, so something really quite far away from children's finger counting.

The work that we've been doing here in Melbourne suggests that there's something rather profound about this developmental sequence, and it came from a kind of accidental observation. We'd been looking at children who have dyscalculia, and Bob Reeve at the psychology department at the University of Melbourne noticed that some of the kids in our sample, a big sample of about 265 kids ... we started in 2002 and it's now four years later, we've been following these kids all this while, and some of the kids use their fingers, first year of proper school, when they were doing simple addition, and other kids weren't.

So the question is, what's the difference between the kids who did use their fingers and the kids who didn't? We weren't doing any experiments, we just noticed what was going on. We found that there were two types of kids who didn't use their fingers. There were kids who were very seriously inaccurate and there were kids who were better than average. So there were some kids who looked as though they didn't need to use their fingers anymore, so they were terribly good, and there were kids who weren't using their fingers, perhaps because they hadn't worked out that using their fingers could help them to add five plus three.

We followed these kids, as I said, for four years, and the differences between these two groups persisted. So even in grade 3, the kids who were not using their fingers and who were inaccurate were still much worse than the kids who weren't using their fingers and were accurate. So there seems to be a way of identifying kids who are going to end up with arithmetical difficulties. Of course they improved and they got much better, but they still weren't as good as the other group, so it seems to be something that is persistent. So we think that this is a clue to at least one aspect of how fingers might be related to numbers in development. And as far as I know, no one has noticed anything like this before.

Robyn Williams: The diagnosis would be extra one; adding the fingers.

Brian Butterworth: Right, but that's just observational. One of the things that we're trying to develop now is a proper test of finger representation. So if we've got a test we can figure out what's going on with the kids who are not very good and who aren't using their fingers in prep.

Robyn Williams: Isn't that interesting. I think you've mentioned before with animals, that animals can have a kind of feel for about four or five to see if a kitten or a chick is missing, but of course they don't have fingers. Do any animals do anything remotely like this? Apes, for example?

Brian Butterworth: Apes, as far as I know, don't use fingers, but most sophisticated arithmetic found in apes or at least that has been trained in apes has been carried out by Matsuzawa in Japan. He's got a mother ape and a son ape ...

Robyn Williams: Oh yes, Jane Goodall talked about this a couple of weeks ago on The Science Show.

Brian Butterworth: Right ... who do really very sophisticated things with numbers. They can put numbers in order, they can learn that a numeral like a written seven represents seven dots and not six dots or eight dots, and they've learned this to a very high standard. But as far as we know, they don't look at their fingers when they think "There's seven dots up there, how many fingers will I need to represent that?", whereas it may be that kids do.

One other thing that we noticed, we haven't found this in children yet, is that there seems to be a particular brain system that does what I've called numerosity. You mentioned piles of sand ... well, there are quite a lot of experiments now that show that part of the parietal lobes are active when you're making judgements of quantity. You know, is this pile of sand bigger than that pile of sand? And also, is this number bigger than that number?

But we don't know whether the brain is really responding to exactly how many objects there are or just 'seven is roughly more than three'. But we found a part of the brain that responds to non-symbolic numerosities, up to quite large ones, in a way that's different from responding simply to quantity, and it is a complicated network involving the parietal lobes and a high level visual system. So what we think is happening is there is a bit of the visual system, the occipital lobe, which says "Ah yes, I see objects out there." and then that information is passed on to the parietal lobe which says "Oh yes, well, there are seven of those" or "There are three of those, and seven is more than three'.

Robyn Williams: You have said on this program before that the ones who are the 5% unable to deal with this sort of thing needn't despair because there are ways that you can, having shown that they've got this different sort of brain, not a bad sort of brain but a different sort of brain, help them to do maths by different ways. So identifying them is important and you can do something about it.

Brian Butterworth: We're now developing some interventions to help them which focus on basic number concepts and that seems to be successful, but it's very early stages. It involves thinking about how many fingers you've got, thinking about how many objects there are in a display. But there are other ways in which you can help them. One is that by getting them to avoid doing calculation altogether and teaching them how to use calculators in a sensible way, and, of course, one of the things that I think is tremendously important is giving them confidence about maths.

So if you're in a class (and in England we're very keen on whole class teaching), if there is whole class teaching of maths and you're the one kid who can't do what everybody else can do, it is very, very depressing, very humiliating, and we have evidence about how awful kids feel about this. But there are other sorts of maths which don't involve numbers, like geometry, for example, and rates of change and stuff like that, where these kids, as far as we can tell, can be just as good as their classmates, and this will give them confidence in the whole area of mathematics. So the other thing that we're trying to do is we're trying to put more emphasis on non-numerical types of mathematics and hope that by improving their liking for and confidence in the mathematics classroom, they're actually going to get better at everything.

Robyn Williams: Good news all round. Brian Butterworth is a professorial fellow at the University of Melbourne and also at the University College, London.

Brian Butterworth, Professorial Fellow University of Melbourne





Preface Reviews What's New email author Author
Test and New Chapter

Macmillan Logo