The 
Mathematical Brain
 
 
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What
Counts
 

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?)
 

Chinese Edition)
The 
Mathematical Brain
 
Brian Butterworth
 
 

Reviews
 

Confidence Counts
The Mathematical Brain by Brian Butterworth
Macmillan, 446pp, £20: Rating: 4/5
 

Was Einstein's brain physically different, or did he just exercise it well? One man who has thought about it more than most is Brian Butterworth, who claims in a fascinating new book that there is indeed a physical sector of the brain, the number module, which is part of our genetic inheritance. Butterworth argues that the evidence for some sort of awareness of numbers, some sort of ability to answer the question: "how many?" goes back in human prehistory to well before the first art or the first written representations of language. The evidence also exists in the responses of newborn babies.

Thrust a white card with two black dots on it in front of a day-old baby. Replace the card with one on which the two dots are more widely spaced and the baby shows some interest, but soon gets bored. When a card appears with three dots, the baby perks up. Not because it's a different card, but because the most important factor in renewing the baby's interest is the change in the number of dots.

Nor is the phenomenon limited to humans: a pride of lionesses in the Serengeti National Park show an ability to count the number of intruders - to calculate whether their own group is larger or smaller, and plan accordingly whether to fight or run. Butterworth has also looked at people incapacitated by strokes or by degenerative brain diseases. People like Signor Strozzi, a market trader in northern Italy who, after a stroke, was unable to add two and two. Or Frau Huber, a farmer from Austria, who recovered from an operation to remove a brain tumour from her left parietal lobe - where Butterworth locates the number module - capable of talking and doing her times tables, but unable to add up. She was unable to make sense of numbers.

So is this yet another attempt to explain human difference in terms of the genetic coding which we receive? Not at all. "Everyone counts" is the central, democratic and enthusiastically-delivered message. There is good evidence that almost all of us are able, from birth, to take in at a glance if there are one, two, three or four in a collection of objects. Even for adults, it takes longer to establish the number of objects when there are more than four. This awareness of number is the foundation-stone from which subsequent mathematical ability is built. So why are some people more gifted than others? Why are some countries better at fostering numeracy than others? The answer, Butterworth argues, lies not in nature but in nurture. Just as Einstein's brain has been found to have unusually densely packed cells in the left parietal lobe, so musicians have been shown to have a bigger and more elaborately connected motor cortex - the region of the brain that controls hand and finger movements - than non-musicians. This is not a sign that these people are predisposed towards music, but simply that practice makes perfect.

The more we find out about the brain, the more we discover its flexibility. It directs more cells towards those parts that are in most use. When pianists stop practising, their motor cortices go on a diet. So does this mean we should be force-feeding maths to our children? Butterworth gives short shrift to the modern fad for rote learning, arguing that what matters is not whether children learn their tables, or whether they use calculators instead, but whether they understand, and enjoy, what they are doing. On the one hand, he says, there is a vicious circle: "Lack of understanding leads to confusion, confusion to anxiety, avoidance, and no further learning." On the other, a virtuous circle, where increased confidence leads to the inclination to practise more. Einstein starts here.

 

John Yandell

 

© Guardian Media Group plc. 1999

 

 

Numbers, their human psychology and cultural history. Restores to numerals - those Indo-Islamic signs the medieval west adopted to record transactions computed on the abacus - a depth of character and long back-stories. Four, eight and nine have dark meaningful pasts, 60 acquired in Babylon its power over the division of time and angles of space and thus over the dimensions of the known universe; the total sum of the Yupno of Papua New Guinea, who figure by naming body parts in sequence, is 33, signifying the penis (Yupno woman don't count). Mega.

 

Vera Rule

 

© Guardian Media Group plc. 2000

 

 


 
 
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What Counts:
How Every Brain Is Hardwired for Math
(Free Press, $26)
The Washington Post: Sunday August 29, 1999
  

In "What Counts: How Every Brain Is Hardwired for Math", cognitive psychologist Brian Butterworth argues that we are born with brain circuits specialized for answering the question "How many?" While all of us possess this Number Module, as he refers to it, Butterworth deftly slips in the question of whether a collection of experimentally confirmed number-crunching chimpanzees, ravens and at least one parrot possess a "predecessor" of our Number Module. Nor do we know if these savant-like animals use the same brain areas to carry out their numerical tasks. [more]

  
Richard Restak
© Washington Post,1999.
 


 
 
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What Counts: How Every Brain Is Hardwired for Math
Brian Butterworth
Free Press, New York, 1999 ($25).
Scientific American: September, 1999
 

Butterworth is a neuropsychologist (professor of cognitive neuropsychology at University College London) rather than a mathematician, but he has thought and read extensively about how people deal with math and has concluded that a basic mathematical ability is inborn. He notes that "everyone can count or tally up small collections of objects, and can carry out simple arithmetical operations, whether they are Cambridge graduates or tribesmen in the remote fastnesses of the New Guinea highlands." Why, then, do so many people have a hard time with more advanced forms of mathematics? Because "maths more than any other subject is sensitive to earlier failures to understand." And how well children understand "depends on how well they learn at each stage, and this in turn depends on how well the curriculum is designed and the teaching is carried out." Butterworth writes engagingly about the hardwiring of the brain for mathematical fundamentals and about the amazing quantity of numbers that each of us confronts every day.

The Editors Recommend
© Scientific American, 1999.
 


 
 
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Counting on our brains: Stanislas Dehaene
The Mathematical Brain by Brian Butterworth
Macmillan: 1999. 480 pp. £20
Nature 401, 114 : 9 September, 1999
  

"One, two three, four. My mathematics finishes here." Those are the words of Signora Gaddi, an alert, 59-year-old Italian woman whose puzzling impairment has helped neuroscientists understand how the brain does arithmetic. Signora Gaddi suffered a stroke that damaged the left parietal lobe of her brain. Since then, she has become largely hopeless with arithmetic. She cannot read, write, compare or calculate with any numbers other than one, two, three and four. Even with numbers below four, she is definitely not performing normally. For instance, when shown two wooden blocks, she has to laboriously count on her fingers in order to establish their numerosity. Because Signora Gaddi performs normally on many other tests that do not involve numbers, her affliction can be described as a selective loss of arithmetic. [more]

Stanislas Dehaene is at Unicog, INSERM 562,
Service Hospitalier Frédéric Joliot,
4 Place du Général Leclerc,
F91401 Orsay, France.
   
© Nature Macmillan Publishers Ltd 1999
 



 
 
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Try holding up your fingers to represent the number three. The result is more informative than you might expect, as Brian Butterworth demonstrates in "The Mathematical Brain" (Papermac, 446 pages, published in US as "What Counts", Free Press). If you flourished your index, middle and ring fingers, he states, you are from Northern Europe or one of its former colonial outposts; if instead you raised your thumb, index and middle fingers, then you hail from the Mediterranean. [more]

 

Ludovic Hunter-Tilney

 

© The Financial Times, 2000

 

 
 
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Commendations
 

Brian Butterworth is one of the most distinguished exponents of cognitive neuroscience in Great Britain. He has had the courage. and foresight to tackle a difficult and somewhat neglected field of human capability. In what is clearly a ground-breaking work on the psychology of mathematics, he has written a lucid and entertaining book with an enormous range of reference. It is a significant contribution to the history of ideas and a fascinating account of experimental work in this perplexing subject.

 
Dr Jonathan Miller.
 

Brian Butterworth shows that mathematics is as natural as breathing. In his fascinating book he tells its where it comes from, how it can go wrong and where it is going. "The Mathematical Brain" is a book that counts.

 
Professor Steve Jones.
 

This is a rich, fascinating and important book,which explores every sort of evidence bearing on the innateness and development of our mathematical powers. Brian Butterworth presents his theme vividly, challengingly, but always courteously and fairly, and seems to solicit the readers own thoughts at every point. I found "The Mathematical Brain" a delightful read.

 
Dr. Oliver Sacks.
 



 
 
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Reviews
Everything counts: Margaret Wertheim
The Mathematical Brain by Brian Butterworth
446pp. Macmillan. £20.
0333735377
Times Literary Supplement
December 24th 1999: Page 24
  

How is it that Homo sapiens - evolved to meet the raw contingencies of life on the African savannas - came to have brains capable of handling calculus and trigonometry, or the arcane abstractions of topology and group theory? The mystery of humankind's mathematical ability has become the focus of intense research and speculation in recent years, as few of our abilities seem so extravagantly unnecessary from a Darwinian point of view. Brian Butterworth, Professor of Cognitive Neuropsychology at University College London, is the latest to weigh in on this fascinating subject with his new book, "The Mathematical Brain". [more]

 
© Times Literary Supplement, 1999.
 



 
 
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Counting Body Parts: John Allen Paulos
The Mathematical Brain by Brian Butterworth
Macmillan: 1999. 446 pp. £20
0333 735277
The London Review of Books:
20th January 2000: Pages 27-28
  

Most people nowadays who claim to lack a "mathematical brain" can easily sit down to multiply 231 by 34 or divide 2119 by 138 and come up with the answers. Yet in the 15th century Northern European merchants had to send their mathematically gifted sons to Italy to learn how to accomplish these feats. Arabic numerals were not yet in wide use, and German universities weren't the place to find out about the arcane arts of multiplication and division. Before smiling indulgently, however, try multiplying the Roman numerals DCL and MLXXXI or dividing MDCCCVII by CCLXIV without first translating them into our own system of numerals. So who has more number smarts, the present-day self-styled innumerate or the mathematically gifted German student from five hundred years ago? [more]

 
John Allen Paulos is the author of Once upon a Number,
among other books.
 
© London Review of Books, 2000.
 



 
 
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Author Argues that Everyone Is Born with a Head for Numbers:
Malcolm J. Sherman
The Mathematical Brain by Brian Butterworth
Free Press: 1999. 320 pp. $26
American Scientist: Scientists' Bookshelf:
September - October 1999

0333 735277
  

Brian Butterworth, a British cognitive neuropsychologist and founding editor of the journal "Mathematical Cognition", has summarized several lines of evidence pointing to the conclusion that the normal human brain contains a "number module" - a highly specialized set of neural circuits that enable us to categorize small collections of objects in terms of their so-called numerosities. When we see three brown cows our brains immediately tell us both that there are three of them and that they are brown. Just as we see colors automatically and involuntarily and without being taught the concept of color, so we immediately recognize and distinguish small numerosities without being taught the meaning of number. In order to communicate, we need to learn the words "brown" and "three," but our perception of small numerosities is as innate and as automatic as is our perception of color. [more]

  
Malcolm J. Sherman is a professor in the Department of Mathematics and Statistics at the University at Albany, State University of New York, where his primary interests include statistics and mathematics education.
  
© The American Scientist, 1999.
 



 
 
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The Mathematical Brain
Two Authors Say We Have Innate Ability With Numbers
Commentary by John Allen Paulos.
 

Sept. 4 - The new school year looms ominously for many who claim to lack a "mathematical brain," and so it may be a good time to review the findings of Brian Butterworth and Stanislaus Dehaene, two cognitive psychologists who have done much work on the neural basis of mathematical thinking. [more]

 

Professor of Mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including "Innumeracy" and "A Mathematician Reads the Newspaper". His "Who's Counting?" column on ABCNEWS.com appears at the beginning of every month.

 
 



 
 
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Journal for Research in Mathematics Education

Neuropsychologist Brian Butterworth (University College, London) weaves scholarly analysis with down-to-earth humor and practical examples as he argues that the ability to do mathematics is inborn, not learned. Butterworth proposes the existence of a "number module" in the brain, an area devoted to the ability to count and to understand numbers. The evidence for this proposal is drawn from history, animal studies, infant learning, and a range of other disciplines. The abilities to distinguish between quantities and to perform primitive calculation seem inherent in infants and even in those animals and birds that have been tested. Studies of stroke patients who have lost their mathematics ability indicate that key mathematical functions reside in the left parietal lobe of the brain. A chapter on the history of various methods of counting on fingers (or other body parts) shows a similar relationship between another specific brain region and mathematics ability. In other chapters, Butterworth explores the question of why some people are particularly good or bad at mathematics and the ways that children learn mathematics at home, on the streets, and in school.

Telegraphic Reviews: November 1999: Page 590
 
© JRME, 1999.
 

 
 
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British Journal of Healthcare
Computing & Information Management.
Vol 16, No 10: Dec 1999: pages 33 - 34.
 
Brian Butterworth (1999). The Mathematical Brain. Macmillan.
 

Walking from house number 3555 in ascending order to 3832 is a 15 minute stroll through several streets in Venice that takes you back to the square from which you started. This short journey is one of many illustrations incorporated within a wonderful historical and cultural voyage of discovery mapped out by Brian Butterworth. The central thesis is that humans have a hard-wired number module within the brain which provides the foundations for our mathematical knowledge. Evidence is collated from all sources, starting with marks on prehistoric bones, progressing through records from ancient civilisations, and comparing counting mechanisms within present-day tribal cultures. The conclusion is compelling: the ability to count and calculate is not the result of an invention but due to the evolution of specialist neural organisations for perceiving "numerosity"---the amount of objects within a set. It is supported by developmental psychology, animal studies, and neuropsychological research into people who have suffered brain-damage.

This is an uplifting book which demystifies mathematics. Apart from a few special cases, we are all capable of being numerate and the main attribute that distinguishes geniuses is copious practice. An important chapter convincingly argues that our innate number abilities require development through understanding relationships between numbers and operations, not by rote learning of tables and abstract procedures. Among the many asides is a splendid slap-down of Kenneth Baker and the previous Conservative Government's attitude to maths and science. However, there is no room for complacency and Brian Butterworth has some salutary words about the current "numeracy hour". Teachers and politicians should read this book and plan strategies based on psychological reality rather than retrogressive ritual.

 
C.D.Buckingham,
Computer Science, University of Aston.
 



 
 
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Two books about mathematical thinking
Helen Joyce: "Plus" Magazine: April, 2002.
 
The Mathematical Brain: Brian Butterworth
The Number Sense: Stanislas Dehaene
 

Over the last decade, the discipline of neuropsychology has shed light on many aspects of human thought. Brain scans, carefully structured behavioural experiments, and the study of individuals who have suffered brain damage, have taught us much about which abilities are native to humans and which learned; which abilities can be lost and what happens when they are. [more]

 

The Mathematical Brain: Brian Butterworth
Paperback - 448 pages (2000): Papermac
ISBN: 0-333-76610-5
 
The number sense: Stanislas Dehaene
Paperback - 288 pages (1999): Penguin
ISBN: 0-14-026134-6
 

Plus Magazine: Issue 19: April, 2002
 
 

 
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