It is true that children can learn many math concepts very early, but also it is true that in ‎the last century the advance of the Math has being very poor, I think the only interesting ‎fact was The Demonstration of the Theorem of Fermat, that is.‎

The math we have comes from those who spend the first years of life learning grammar ‎and logic and then, when they were well prepare they develop the calculus and geometry ‎which our little children play today, but this children miss the enough good foundation to ‎develop something better from there.‎

So, we as civilization, are not winning teaching complex math concepts to the babies, and ‎little children, we are lose the possibility to develop great minds to solve the science’s ‎problems, the math is a tool of the science, it is the language of the science.‎

Delayed. My son, age 10, could take the derivative or integral of a polynomial if you spoke it to him. He’d visualize the polynomial, calculate the the derivative or integral in his head, and dictate it back to you.

How old were Ramanujan and Gauss when they could do figurate numbers in their heads?

Public schools in the USA have essentially given up, as badly as the prestigious schools in England a couple of centuries ago.

Fortunately, there ARE some good students, good media (the CBS-TV show NUMB3RS for example), many good books, and the Web.

There is no meaningful limit to what a child can learn, given a good teacher and a motivation for the student, and if you start early enough (neural plasticity).

Self esteem? I suggest that it be deserved, by allowing children to succeed with actual content and understanding. Not “teaching to the test.” Not “No child left behind.” Those are red herrings. I mean real education.

For the children.