Here’s an interesting article by Jim Holt in the New Yorker about the work of Stanislas Dehaene on the number sense in humans. From studying accident victims, children, Amazon tribes, etc, he concludes:

… we are all born with an evolutionarily ancient mathematical instinct. To become numerate, children must capitalize on this instinct, but they must also unlearn certain tendencies that were helpful to our primate ancestors but that clash with skills needed today. And some societies are evidently better than others at getting kids to do this.

When it comes to mathematics education, what he says is both standard:

“Give a calculator to a five-year-old, and you will teach him how to make friends with numbers instead of despising them,” he has written. By removing the need to spend hundreds of hours memorizing boring procedures, he says, calculators can free children to concentrate on the meaning of these procedures, which is neglected under the educational status quo.

and nonstandard (as far as I know, these days):

“The idea that all children are different, and that they need to discover things their own way—I don’t buy it at all,” he said. “I believe there is one brain organization. We see it in babies, we see it in adults. Basically, with a few variations, we’re all travelling on the same road.” He admires the mathematics curricula of Asian countries like China and Japan, which provide children with a highly structured experience, anticipating the kind of responses they make at each stage and presenting them with challenges designed to minimize the number of errors.

A very interesting fact is that the encoding of numbers in languages does seem to affect  efficiency of arithmetic operations. Chinese has more regular number names, and they are shorter, than say English or French, and this is reflected in the arithmetic performance of native speakers of these languages.