What Counts: How Every Brain is Hardwired for Math (Hardcover)

~ (Author) "Of all the many abilities that have raised us from cave-dwellers using stone tools to creators of great cities and modern science, one of the..." (more)
Key Phrases: Number Module, Signora Gaddi, Frau Huber (more...)

Editorial Reviews

Amazon.com Review

At first glance, neuropsychologist Brian Butterworth's What Counts: How Every Brain Is Hardwired for Math might infuriate mathphobes who insist that they just can't get a handle on numbers. Could it be true that natural selection produced brains preprogrammed with multiplication tables? Read a few pages, though, and you'll see that Professor Butterworth has more than a little sympathy for the arithmetically challenged, and indeed confesses that he too has a hard time with figures. His thesis isn't that we are born doing math, but that we are born with a faculty for learning math, much like our ability to learn language. He goes on to argue that unique individual differences in this faculty combine with our educational experiences to make us either lightning calculators or klutzes who can't figure tips.

Butterworth's style is perfect for his subject, seamlessly weaving scholarly analysis with down-to-earth humor and practical examples that will satisfy the researcher and the lay reader alike. Drawing on archaeology, anthropology, linguistics, and his own neuropsychology, he makes his case like a masterful attorney while remaining careful to leave room for scientific falsification. The history of counting is engrossing and will be new to many readers, as it has been a rather arcane field until recently--but it's just one of the many new vistas opened for the readers of What Counts. --Rob Lightner

From Publishers Weekly

Are our brains "hardwired" to count and conceptualize numbers, or are counting, and other mathematical activities something that we learn, like playing the piano? Butterworth, editor of the journal Mathematical Cognition, is convinced that evidence points to the existence of circuits in the brain devoted to identifying what he calls "numerosities," or, more simply, the number of objects in a collection of things. To this network of specialized circuits, or "Number Module," Butterworth explains, each person adds the mathematical knowledge of his or her culture. Thus, people who "aren't good in math" have trouble not because they're dumb or not applying themselves, but because their Number Module is different from the prevailing one. Not surprisingly, Butterworth has strong views on how to teach mathematics, and these form a prominent part of his book. He also shows how a person's brain can change to devote more resources to respond to mathematical stimuli. For example, a study of Braille proofreaders based on brain-scan maps has demonstrated that the part of the brain devoted to this activity grows in size after six hours work. But give the proofreaders a few days off, and their brains shrink back to normal. Butterworth's prose is marred by repetition, and his digressions to explain various well-known math puzzles and peculiarities, such as Pascal's triangle, often aren't germane to his argument (do we really need a proof of G?del's theorem here?). But these are minor caveats about a provocative book that makes an important addition to the recent flurry of titles regarding how our minds work. Teachers as well as readers curious about the brain and psychology will be challenged by the ideas expounded here. (Aug.)
Copyright 1999 Reed Business Information, Inc.

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Product Details

• Hardcover: 432 pages
• Publisher: Free Press (August 27, 1999)
• Language: English
• ISBN-10: 0684854171
• ISBN-13: 978-0684854175
• Product Dimensions: 9.3 x 6.4 x 1.4 inches
• Shipping Weight: 1.4 pounds
• Average Customer Review: 3.6 out of 5 stars  See all reviews (5 customer reviews)
• Amazon.com Sales Rank: #262,221 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

47 of 48 people found the following review helpful:

3.0 out of 5 stars Interesting but flawed, September 23, 1999

By A Customer

I'm going to assume anyone reading this has already read the other reviews in amazon.com. This leaves me free to comment on problems with the book rather than provide a synopsis.

The first two sentences in the preface to "What Counts" explain the basic fact, I am not particularly good at maths or calculation."

Butterworth proves this often enough for it to be a very good reason why he shouldn't have written of flaws, only someone who has no feel for mathematics could write a book containing many typos of the form a^2 + b^2 = (a - b)(a + b).

o He's discovered a new and amazing correspondence with any subset that is neither the whole set nor the empty set." Imagine, there's a one-to-one correspondence between the integers and the set {0,1}. Well, no there isn't.

o He's made the equally exciting discovery that the rationals between 0 and 1 are uncountable. It is revealed on page 339 that the points on the real line are uncountable "because there is points." Since the argument applies to the rationals, they too must be uncountable. Sigh.

Here are some specifics to illustrate other problems in "What Counts".

o The discussion of cognitive archaeology is highly speculative and frequently unconvincing. For example, he speculates that counting lunar phases is important to women so they'll know when their baby is due. This isn't of value without a citation of "primitive" peoples who do this.

o Butterworth seems to believe that math is the same as arithmetic, though of course he does know better. The book is almost exclusively about our "natural ability" to add, subtract, multiply, and divide. Geometry, the other "basic" mathematics, is almost completely ignored. The omission is a major deficiency.

o He also has a very strong opinion that there is no such thing as a mathematical gift. Rather, it's a manifestation of interest, good teaching, and hard work. The argument is made quite intensely, but not convincingly, and probably would almost universally be disputed by mathematicians (which doesn't prove it wrong, of course). What is convincing and should have been the point of the discussion is that we could be doing a much, much better job of teaching mathematics. (The previous reviewer has correctly pointed out the value of Butterworth's critique.)

o The appendix contains a less-than-satisfying discussion of Godel's Incompleteness Theorem, which has no apparent purpose other than to dazzle and confuse the naive reader.

There's quite a bit more that's objectionable, but the point should have been made adequately with this list.

On the other hand, the quote from Oliver Sacks on the dust jacket about how the book "solicits the reader's own thoughts" is correct. I came away from the book with ideas for dozens of experiments and possible research areas. Of course, since my background is mathematics and not a cognitive neuropsychology, I can't comment the non-mathematical assertions but can only hope them to be accurate.

The book is valuable as it has nuggets of great interest and the subject matter is fascinating. There aren't many popular books covering this material, so I'm giving it 3 stars. Good editing and minor collaboration with someone who is "good at maths" could turn it into a 5 star book

11 of 11 people found the following review helpful:

5.0 out of 5 stars Simply outstanding... Could revolutionize math learning, August 6, 1999

By	Rob Hutter ([e-mail]) (Palo Alto, California) - See all my reviews

In this highly readable book, Prof. Brian Butterworth (a cognitive neuroscientist at the University of London) argues persuasively for a new comprehension of the development and exercise of mathematical ability. Proponent of a separate center for mathematical intelligence, Butterworth nevertheless argues that the existence of a biological 'numerical center' means that nearly everyone has the capacity to become highly proficient at mathematics and mathematical thinking. Especially interesting to me was his demonstration of the futility of rote learning--and his trenchant dissection of the educational causes of most people's mathematical anxieties and related math difficulties... I've read widely on this topic, and have heretofore remained unenlightened. In addition to advancing a new basis for the way we must view math skills and teach them, Butterworth writes cogently and compellingly, adducing powerful evidence for his findings from provocative new research. This is an optimistic book. It makes clear that, Hollywood be damned, Will Hunting lives in all of us.

9 of 11 people found the following review helpful:

4.0 out of 5 stars A Challenge to a Popular Myth, June 9, 2000

By	J. Malloy - See all my reviews (REAL NAME)

"What Counts" is a necessary rebuttal to the idea of mathematical giftedness or genius in general which pervades our culture and manifests itself in Hollywood movies like "Good Will Hunting" and, more tragically, in our system of education. The author confronts both of these issues in detail.

For example, on Hollywood's prodigy Will Hunting he challenges anyone to come up with a real life example of this character which would be a counter example to his premise which states that higher mathematical learning/ability is a result of zeal, hard work (10 years for truly great achievements), and exposure to the necessary culture, i.e. teachers and books.

As Butterworth explains, Will Hunting seemingly has no zeal for anything but girls and spends most of his time in bars yet he knows all about and comprehends arcane mathematical concepts and myriad other subjects.

Mathematicians may like to hang on to the idea of their own giftedness for the sake of their egos and most people who see "Good Will Hunting" think the character is believable so this book is a definite challenge to a popular myth.

Except for the chapters dealing strictly with mathematics which are not necessary (and hence the lack of 5 stars) this book may inspire people to work hard instead of making excuses.

Look for more on this subject from author/mathematician Keith Devlin with his book (coming out in August) "The Math Gene: Why Everybody Has It, but Most People Don't Use It."