Conrad Wolfram hits the nail on the head with this talk. His ideas about the misplaced emphasis on hand computation resonate with my personal experience. I can remember thinking over 20 years ago in college calculus how insanely powerful calculus was but how worthless it was to learn how to do it by hand when, even then in those dark ages called the 80's, it was clear that I could get a computer to do the computation for me. We need to teach our children (and ourselves - learning is after all a lifelong endeavor) how to figure out what the problem is, translate it into Math and let the computer compute. Last, he points out we need to teach how to bring the answer back out of the Math and verify that it solved the problem. We cannot fall into the trap of assuming the computer answered the right problem! It is long but worth the time.
