Number Sense, The: How the Mind Creates Mathematics [Hardcover]

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.)

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.