The Number Sense: How the Mind Creates Mathematics

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.)


Highly recommended, especially for math educators.   November 21, 1997
15 out of 15 found this review helpful

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.


Can't say enough good things about this wonderful book!   December 6, 2001
7 out of 7 found this review helpful

If you are interested in mathematics, psychology, neuroscience / cognitive science, biology, linguistics, and/or all of the above, you will love this book. Don't get me wrong, not only is this book for those with technical interests but is well written enough and accessible enough for even laymen to get into. Read this great book!


Amazing, objective research scores an A!   January 1, 2002
11 out of 13 found this review helpful

Fascinating. That's the word I've been using to describe this book. From the information on numerical experiments with animals to the solid evidence presented for the hardwired concept of numbers from birth, the author ties together an amazing work.

The clear organization of the book, described from the onset, was my first clue that this was a bit more polished than other works. From a gradual examination of an innate "number sense" in even lower animals, through babies identifiying that 1+1 is not 1 or 3 but 2, up to the examination of innate calculatory facilities, this book covers it all. By the end, you will have been presented with practically all the evidence you need to make your own conclusion--and the case for the existance of the "number sense" is incredible. Psychology and neurology are both linked to the examination.

As a math teacher, I've even gleaned a few points to help in the presentation of the topic to my students. While I don't agree with all of the authors views on education, I do think he made some very profound points (the comment that standardized education has probably stunted natural development ofthe culture--specifically language--is a good example.)

Probably my only real disappointment with the book is the author's overemphasis on evolution throughout the text. Yes, most technical types unfortunately seem to be passionate about evolution's role in everything nowadays; it wouldn't have been that big a deal had the last few pages of the book not delved wholeheartedly into a philosophical expository of how mathematicians of the past were silly to have attributed the apparent design of the mind to match the universe numerically to a God, when evolution is an available alternative. However, this small distasteful thread didn't really detract from the research. (In fact, in practically all other maters the author is refreshingly objective and unbiased, examining counterpoints to his theories and conclusions.)

In all, the book still earns its five stars for rigor, fascinating material, objective examination, and clear presentation. Well worth the read, well worth the purchase.


Quality science, excellent entertainment   December 21, 2001
Fred Grant (London United Kingdom)
5 out of 6 found this review helpful

I received this book as a gift. I skimmed it and left it unread for months. I thought it was a cash-in on Steven Pinker's excellent The Language Instinct. But no!

When I finally read it was as impressed with Dehaene's science as with his literary flair - not to mention the excellence of his self-translation. His thesis is fascinating, his references authoratitive and his story telling masterful.

This book should fascinate everyone who can count up to two or beyond. Dry it is not. Beyond the interest he develops in the subject are the insights he gives into the ingenuity with which psychological experiments can be designed to eliminate the flaws that a layperson would think unavoidable.

There is a darker side, however. Like that other fellow with his lethal experiments with chicks to test for chemical changes relating to memory, there are allusions to intrusive experiments on living subjects . True, these were some time ago and Dehaene exhibits a proper degree of unease about them. None the less I am much more comfortable with the ingenious ape and baby tests. In my view, no matter how intriguing the question, and how beguiling arguments of research potential leading to new therapies, there is a line that should not be crossed. Dehaene, I'm glad to say, seems aware enough not to cross it.

Fascinating. Highly recommended.