The Number Sense: How the Mind Creates Mathematics [Paperback]

Stanislas Dehaene (Author)

Book Description

Publication Date: December 9, 1999 | ISBN-10: 0195132408 | ISBN-13: 978-0195132403 | Edition: 1

The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.

Editorial Reviews

Amazon.com Review

This may surprise those who have trouble carrying the remainder in division or figuring out a 15 percent tip on a $20 lunch bill, but according to mathematician and psychologist Stanislas Dehaene, mathematics is an inborn skill. In The Number Sense, Dehaene makes a compelling case for the human mind's innate grasp of mathematics. Take, for example, the fact that place value systems (such as the Arabic numeral system we use) arose independently in four separate civilizations--evidence of a universal sense of number. Dehaene's book is filled with examples to support his thesis, from young babies' ability to "count" (i.e., to react when single objects are replaced by two or more) to examples of how brain damage affects various individuals' number sense. Even more fascinating is his discussion of the relationship between language and numbers. Though Dehaene's book is about mathematics, even those readers with the worst math anxiety will find The Number Sense an intriguing exploration of the world of numbers--and the human mind. --This text refers to an out of print or unavailable edition of this title.

From Library Journal

This interesting and informative book sets forth the latest findings by Dehaene (research affiliate, Institut de la Sante et de la Recherche Medicale, Paris) and other psychologists trying to determine how the brain understands and manipulates numbers and other forms of mathematical information. Included are many startling results of experiments involving animals and infants that shed light on the extent and nature of our inborn number sense. Dahaene also describes how brain scans and computer simulations can help us understand possible differences in the ways the brain handles similar mathematical topics such as approximation, arithmetic computations, and algebra. These findings, if they receive the consideration they merit, should have a major impact on the way mathematics is taught at the elementary and secondary level. Highly recommended.?Harold D. Shane, Baruch College, CUNY
Copyright 1997 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Paperback: 288 pages
• Publisher: Oxford University Press, USA; 1 edition (December 9, 1999)
• Language: English
• ISBN-10: 0195132408
• ISBN-13: 978-0195132403
• Product Dimensions: 6.3 x 0.8 x 9.2 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (16 customer reviews)
• Amazon Best Sellers Rank: #748,754 in Books (See Top 100 in Books)

More About the Author

Stanislas Dehaene is a French psychologist and cognitive neuroscientist. He is currently heading the Cognitive NeuroImaging Unit within the NeuroSpin building of the Commissariat A l'Energie Atomique in Saclay near Paris, France's most advanced brain imaging center. He is also a professor at College de France in Paris, where he holds the newly created chair of Experimental Cognitive Psychology. In 2005, he was elected as the youngest member of the French Academy of Sciences.

Stanislas Dehaene's interests concern the brain mechanisms of specifically human cognitive functions such as language, calculation, and conscious reasoning. His research relies on a variety of experimental methods, including mental chronometry in normal subjects, cognitive analyses of brain-lesioned patients, and brain-imaging studies with positron emission tomography, functional magnetic resonance imaging, and high-density recordings of event-related potentials. Formal models of minimal neuronal networks are also devised and simulated in an attempt to throw some links between molecular, physiological, imaging, and behavioral data.

Stanislas Dehaene's main scientific contributions include the study of the organization of the cerebral system for number processing. Using converging evidence from PET, ERPs, fMRI, and brain lesions, Stanislas Dehaene demonstrated the central role played by a region of the intraparietal sulcus in understanding quantities and arithmetic (the "number sense"). He was also the first to demonstrate that subliminal presentations of words can yield detectable cortical activations in fMRI, and has used these data to support an original theory of conscious and nonconscious processing in the human brain. With neurologist Laurent Cohen, he studied the neural networks of reading and demonstrated the crucial role of the left occipito-temporal region in word recognition (the "visual word form area").

Stanislas Dehaene is the author of over 190 scientific publications in major international journals. He has received several international prizes including the McDonnell Centennial Fellowship, the Louis D prize of the French Academy of Sciences (with D. Lebihan), and the Heineken prize in Cognitive Science from the Royal Academy of the Netherlands. He has published an acclaimed book The number sense, which has been translated in eight languages, and is publishing a new book Reading in the brain, to appear in November 2009. He has also edited three books on brain imaging, consciousness, and brain evolution, and has authored two general-audience documentaries on the human brain.

Most Helpful Customer Reviews

45 of 45 people found the following review helpful

5.0 out of 5 stars A delight! January 25, 2000

By Mark Rosa

Format:Hardcover

I immediately gave this book a glance-through upon seeing the title. The resemblance to Steven Pinker's 'The Language Instinct' and his quote at the bottom hooked me, and the inside didn't disappoint. A lot of people have written books questioning why we don't understand math; here's someone who wonders why we do.

Regarding the part about memorization - I assume that the numbers shown to the test subjects were our European numerals in all cases. I wonder what would happen if Chinese digits were used -- they all look distinct, in comparison to, say, our ambiguous 6 and 9, which can be confusing (ever see "1 2 3 4 5 SIX 7 8 NINE" on a gambling table to avoid this?). Can people recognize Chinese digits faster?

(And Ronald, I too immediately formed a Japanese mnemonic upon seeing the string of digits in that chapter. Unconsciously, in fact. The five/nine ambiguity disappeared!)

One quibble is that Dehaene seems to fall into the trap that many people - mathematicians included - blindly accept as fact; the idea that the European numerals that we use every day are superior to anything else. 'It's hard to see how they could be improved upon', he says, (or something to that effect - I'm doing this from memory). Arabic numerals (by which I mean those used by Arabic-speaking people, not the European variations that 'we' use) have the advantage of all being written without lifting your pen, and Chinese digits, for which trying to distinguish between, say, "160" and "180" in very small print is no problem. When you think about it, any place-value system with a zero is equally effective regardless of the forms of the numerals.

All in all a fascinating and informative look at a subject that's been largely neglected; at least in the popular press. Well worth reading. Does Dehaene have another book in the works?

(Recommendations from me? 'The Great Mental Calculators' by Steven Smith, which is tough to find, 'Innumeracy' by John Allen Paulos, and most of all 'From One to Zero/The Universal History of Numbers' by Georges Ifrah. All fantastic.)

26 of 26 people found the following review helpful

5.0 out of 5 stars An excellent book April 13, 1998

By Ron

Format:Hardcover

I have not yet finished Stanislas Dahaene's excellent book "The Number Sense". But I would like to add an observation on chapter 4. The author discusses many studies which show that persons whose native language uses number names stemming from Chinese, such as Chinese, Japanese, or Korean, can remember much longer strings of numbers, on average, than speakers of such western languages as English or French. He attributes this to the shorter length of the spoken names of the numbers in the eastern languages. However, another important factor in Japanese, at least, must be the ease with which meaningful mnemonics can be made. Japanese effectively has three different ways to name each digit. One stems from Chinese (ichi, ni, san, shi, go, roku, shichi, hachi, kyuu, juu), another is the native Japanese counting system predating Chinese influence (hitotsu, futatsu, mitsu,yotsu,itsutsu,mutsu,nanatsu,yatsu,kokonotus,too) and the third is from English (wan, tsuu, suree, foah, etc.). The digit zero can be named as "oh" from the English letter "O", or "ma" from "maru" meaning circle, etc. It is almost always possible to make an easily remembered mnemonic. This way commercial telephone numbers are made easier to remember in advertisements. (Japanese telephones have only digits on the buttons, no added letters.) Telephone numbers for pet shops and veterinarians often have pairs of ones, "11". Because "wan wan" is the Japanese equivelant of "arf arf". The dentist downstairs in my building uses the number "1818" because "ii ha, ii ha" means "good tooth good tooth". Mr. Dehaene does not make it clear whether studies have been done attempting to measure number memory span, isolated from the effect of mnemonics. If this could be done I would be very interested in learning of the results. As of the end of seven of nine chapters, I say this is a very well written, and extremely interesting book. I highly recommend it.

19 of 20 people found the following review helpful

5.0 out of 5 stars Highly recommended, especially for math educators. November 20, 1997

By A Customer

Format:Hardcover

I am very grateful to the friend who directed me to an article in last July's issue of "Discover" that describes Stanislas Dehaene's new book "The Number Sense: How the Mind Creates Mathematics." The article highlights the examples Dehaene gives of people who have brain injuries that destroy their ability to do parts of arithmetic, while leaving other skills intact. Dehaene combines these examples with evidence from reaction time experiments and from new brain imaging techniques to make a compelling case that we share with other animals an analog method for dealing with quantitative information. He uses the metaphors of a mental number line and an analog accumulator, and notes that these may be more than just metaphors. Anyone interested in the teaching and learning of arithmetic must read this book. And it is so well written -- in English by a Frenchman! -- and contains so much new informnation that it can be recommended to everyone.

Dehaene goes beyond the biological heritage we share with other animals to consider how the language processing parts of our brain contribute to our ability to do arithmetic. He also gives a clear and complete description of why hindu-arabic numerals are now universal, noting that place value systems arose independently in four different civilizations. In all, he makes a compelling case that those of us interested in the teaching of arithmetic have to pay attention both to evolution and to the intelligent design of numeral systems.

Dehaene gives examples of how our non-linguisitic, linguistic, and cultural heritages interact in our doing arithmetic, and of what can go wrong when they are out of sync. He notes that speakers of English fall considerably behind speakers of languages that use the Chinese way of saying numbers, first in learning to count beyond twelve and later in skills such as "borrowing" and carrying." In Japanese, "thirteen" is "ten three" and "twenty-one" is "two ten(s) one," etc.

My current interest is in introducing young children to the numbers between the whole numbers that are needed for measuring things. Dehaene's book encourages me to continue searching for ways to delay fraction talk and fraction ways of saying decimals. But that is another story. I am sure that others interested in education will find ideas in this book that will help them in their work. And that everyone can enjoy the exciting story that Dehaene tells.