As someone who went on to become a mathematician, I thought the New Math was great—provided, as in my case, one only started getting it in 4th grade after one had memorized one’s addition and multiplication tables and the standard algorithms for the four arithmetic operations with multiple digit numbers. (BTW, they were right to stop making kids memorize times tables up through 12.)
The real problem is that we haven’t realized that the increased importance of mathematics in our society calls for an increase in the amount of time devoted to mathematics education. Kids should get *both* constructivist, figure stuff out for yourself, exercises and the old rote learning, and that means more time devoted to the subject. It also means, if it’s to work right, we have to stop letting math-phobic ditzes get certified as teachers, since the only way the constructivist approach works is if the teacher is mathematically sophisticated enough to recognize correct, but non-standard approaches to problems, and things that (seem to) work in a particular case, but won’t work in general and how to quickly show this to the children with an example where they don’t work.
I disagree with that. It's far easier to do the math in your head than whip out a calculator and hope you get the right answer more than once in a row.
My kids have beat out public school kids in doing calculations hands down. They do it in their heads in seconds, while the public school kids are still entering it in their calculators and trying to figure out which of the different answers they got is correct.