The New Scientist Opinion Interview: 3rd July 1999

So you think you're bad at maths? Meet Charles, he has a normal IQ and a university degree yet has problems telling whether 5 is bigger than 3. And what about Signora Gaddi, an Italian woman who hears and sees normally but, following a stroke, is deaf and blind to all numbers above 4?

Their stories and others are told by neuropsychologist Brian Butterworth in his book The Mathematical Brain. For Butterworth, they are living evidence that the brain contains a special device for making sense of numbers. It's just a little knot of cells over your left ear, but when it's working properly, this number module doesn't just allow us to see the world in terms of numbers - it compels us to. We can't stop enumerating, says Butterworth, any more than we can avoid seeing in colour. Even as a baby, it was making you notice discrepancies in, say, how many spoonfuls of food came your way compared with how many came out of the jar.

But if most people have this innate and unstoppable number sense, why do so many numerical skills seem so hard to acquire? And why aren't most of us in the Einstein league of maths brains? Or perhaps we are? Alison Motluk talks numbers, brains and genes with Butterworth at his office in University College London.  [more]

Brain Connection: March, 2000

A cheerful English voice, crisp and elegant, asked her the question again. "How many coins do you have there, Signora?"

Signora Gaddi stared at the coins in her hand for a long time, and then looked up to smile apologetically at the doctor. It was a soft smile, warm, but tenuous and sad. The corners of her lips trembled delicately when she tried to explain the inexplicable: she knew that there were more than four, but she could not imagine how many. Were there eight? Or ten? Or some other strange number, whose name hung heavily on her tongue and could not be uttered?

"It's all right, Signora. There are six coins." The doctor's voice was kind; he understood. He knew of other people like Signora Gaddi, people who had little or no sense of numbers. These people were not simply bad at math, nor were they poorly educated. The clinical terms are acalculia, for people like Signora Gaddi who lost her sense of numbers after a stroke, and dyscalculia for people who were born without numbers. But clinical terms don't go very far towards describing the people who lead lives almost completely devoid of numbers.

S. Gaddi is a charming, middle-aged Italian woman. Before her stroke, she managed the books at her family's hotel, and led a life filled with numbers. Room assignments, charges, debits, profits, expenses - S. Gaddi was more than proficient at rapidly and accurately performing arithmetical calculations. But since the day that a small blood vessel in her left parietal lobe burst, S. Gaddi has been blind to numbers greater than four. She can readily perform addition and subtraction, she can list number names in sequence - so long as all the digits involved are less than or equal to four. Dr. Brian Butterworth, the University College London neuroscientist who worked with S. Gaddi, writes that,

"Since her stroke, [S. Gaddi's] life had been one of frustration and embarrassment. She was unable to do things that previously had been second nature to her. She could not give the right money in shops; she had no idea how much she was spending or how much change she was getting. She could not use the phone. There was no way to call her friends. She was unable to tell the time, or catch the right bus."  [more]

Interview by Ashish Ranpura

© The Brain Connection, 12000.

Britannica & Australasian Science: October 1999

A large company of chimps travels through the forest, headed by their fearless leader Brutus. To increase their chance of finding food they break up into several bands, but keep in touch by "pant-hooting" and drumming on resonant trees.

When it is Brutus doing the drumming, however, the other chimps treat the number of drum beats as instructions. One beat means "change direction." Two beats means "rest"--always for between 55 and 65 minutes. A beat on one tree and two on another combines these, instructing the chimps to change direction and then rest. Most remarkably of all, four beats instructs the other bands to rest for two hours.

These observations were made on animals in the wild, not ones that had been patiently trained by humans. They appear to provide proof that some animals are able to count and measure time. The evidence is particularly remarkable when one considers that counting is not believed to be automatic in humans, but has been passed down the generations from some "ancient Einstein." This observation, recorded by the zoologist Christophe Boesch, is one of the many extraordinary anecdotes and facts used by cognitive neuropsychologist Brian Butterworth, of University College London, to support his theory of a "mathematical brain." According to the theory almost all humans, and many animals, have an in-built ability to do mathematics.  [more]

Stephen Luntz

©, Australasian Science, 1999.

Mathematics Gene:
The Science Show: Saturday 18th November 2000

(mp3)

Our second book is by Brian Butterworth who's in Melbourne this week from Britain. I'll tell you his title in a minute. At the moment he's working on where numbers go in the brain and it really matters.

Brian Butterworth: Well, some people like, for example, Piaget, argued that really mathematics was no more than an extension of logic and the mathematician Keith Devlin in a recent book called the "Maths Gene", has argued that maths is nothing more than an extension of language. Now modern scientific approaches to how the brain deals with numbers and other aspects of mathematics show that really there are separate parts of the brain that deal with maths on the one hand, deal with reasoning on the other hand and deal with language on the third hand.

So there is evidence that there is independence in the brain. Of course it doesn't mean that there's functional independence. Clearly you learn most maths through language. But once you've learnt it, does it get stored with other things that you've learnt through language or does it get stored somewhere else? One of the things that we've been working on - and we work on these things entirely opportunistically, it depends who comes into the clinic, is about whether reading words, reading numbers and recently, reading music all use the same brain circuits or whether they use separate ones.

There's a very interesting novel by Ken Follett called the "Hammer of Eden" in which one of the central characters, I'd better not say whether he's a hero or a villain, is unable to read either letters or numbers but actually truth, as is so often the case, is stranger than fiction. We've found that there are people who can read numbers but can't read words, and my colleague Lisa Cipolotti here at the National Hospital for Neurology, has found that there are people who can read words much better than they can read numbers. I mean, they've had brain damage which has affected their number reading but left their word reading intact.  [more]

Robyn Williams.

(mp3).

Reading in the Brain:
The Science Show: Saturday 18th August 2001

The strange case of the former bank manager who is now able to read only number words as the result of a neurodegenerative condition.

Brian Butterworth: What's fascinating about him is that he can only read one sort of word. He can only read number words and it's never been reported before and that's why we're so interested in it. But it's theoretically very important because the standard theory of reading goes something like this: that when you see a string of letters you do two things simultaneously; you try and find the sound of that string of letters. You might do that by taking each letter and finding the sound of each letter and putting them together. You might try and recognise it as a whole word and try and find the sound of the whole word but, at the same time, you're trying to interpret the meaning of that string of letters, you're trying to find the meaning of that word and these two processes converge to give you the pronunciation of the word.

Now the problem with the theory up to now is that it's never really been tested properly. We don't know whether you can pronounce the word accurately just going via the meaning. So for example, if you see a letter string like t-r-e-e- you get the meaning of a tree and then you have to say what that meaning is. Now what we want to know is: is that route via meaning sufficient to give you just "tree", and we haven't been able to do that up to now.

This case is very interesting because this man can't use the route via sound alone. We know this because if you give him a very simple string of letters he hasn't seen before, like y-i-t- he can't say it. He used to be able to say it but he can't say it anymore. Even if the letter string sounds like a real word, like y-o-t- he still can't say it. Now the other really interesting thing is that he can't say words that he doesn't understand. So he can't say y-a-c-h-t says yacht either, he can only say words that he does understand and if he does understand them then he says them accurately. And we know that he has a very precise understanding of numerical concepts because he can calculate accurately. So he knows the difference between 1 and 2, and 3 and 4, and 13 and 15 and he can read all these words with perfect accuracy, but words he doesn't understand, and these are very common words like "take" and "give", and yet he can't read because he doesn't understand them.  [more]

Reading in the Brain:
The Science Show: Saturday 18th August 2001

Educational Leadership

Interview: Marcia D'Arcangelo

Neuropsychologist Brian Butterworth describes the brain's innate ability to process numbers and explains why some students, nevertheless, have trouble understanding mathematics.

Marcia D'Arcangelo: One of the most fascinating ideas in your book "What Counts: How Every Brain Is Hardwired for Math" (Free Press, 1999) is that we are born with a sense of numbers. What exactly is this number sense?

Brian Butterworth: The number sense is having a sense of the manyness, or numerosity, of a collection of things. We believe that babies are born with a kind of start-up kit for learning about numbers that is coded in the genome. Even in the first week of life, babies are sensitive to changes in the number of things that they're looking at, and at six months they can do very simple addition and subtraction. Then, with this start-up kit, they build all the cultural tools - the number words, the counting practices, and the arithmetical procedures and facts that they learn from parents and from school.

Marcia D'Arcangelo: How do we know that babies can add and subtract?

Brian Butterworth: If you show a baby a doll, cover it with a screen, and show a second doll being placed behind the screen, the baby will expect there to be two dolls when the screen is removed. If there is a different number of dolls - more or fewer - then the baby will look longer than if there are two. This "violation of expectation" experiment was carried out by Karen Wynn in 1992 at the University of Arizona.

Marcia D'Arcangelo: Your book suggests that even prehistoric man had a mathematical brain, as you call it.

Brian Butterworth: Yes, and other species may have different versions of mathematical brains as well. Chimps, for example, can learn to do sophisticated numerical tasks. Ten years ago, David Washburn showed that chimpanzees trained to understand numerals - 1, 2, 3 - can also be trained to select the larger of two numerals presented to them. More recently, researchers trained monkeys to select the larger of two arrays of objects. Perhaps the best example of wild animals using numbers is the Serengeti lions. Lions defend their territories against intruders, but they will attack only if they outnumber the intruders. They have to figure out how many lions versus intruders there are.  [more]

Marcia D'Arcangelo (mdarcang@ascd.org) interviewed Dr. Butterworth about his work when she developed ASCD's The Brain and Mathematics video series.

Copyright © 2001 by Association for Supervision and Curriculum Development

Understanding Learning Differences:

Wired for Mathematics

Educational Leadership: Volume 59 Number 3:

3rd November 2001

Plus Magazine
April 2002

Natural born mathematicians
by Helen Joyce

One day old, and already a mathematician When was your very first mathematical thought? At age four? Three? Two? It may surprise you, but it was certainly earlier still - in fact, you were born a mathematician...

In the last few years, researchers have become accomplished at finding out what goes on in the minds of tiny children, even new-born babies. This is done either by watching their gaze (looking away indicates familiarity or boredom, staring intently indicates surprise or interest) or by giving them a dummy (the more they suck, the more interested they are). This means that we can tell what expectations babies have in different situations, and when those expectations are violated. What we have learnt is that, amazingly, we all come into this world ready-supplied with basic mathematical understanding.

"We are born with a core sense of cardinal number", says neuropsychologist Brian Butterworth, author of The Mathematical Brain, reviewed in this issue of "Plus". "We understand that sets have a cardinality, that is, that collections have a number associated with them and it doesn't really matter what the members of that set are. Infants, even in the first week of life, notice when the number of things that they're looking at changes.  [more]

New Scientist, 1999
Brain Connection, 2000
Britannica & Australasian Scientist, 1999
The Science Show, 2000
The Science Show, 2001
Educational Leadership, 2001
Plus Magazine, 2002
 
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