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.
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
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
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