First off, many of us have pointed out that "traditional" math wasn't all about computation.
I wish I had videotaped grades K through 3 with my son. It is hard to explain how much more effective our dialog became as he mastered arithmetic. I think even Lou, if he could see it with his own eyes, would be sold. The most recent example of what I am talking about is negative numbers. As I have said, I am teaching him algebra this summer and a key component of that is to give negative numbers their due. The kids are exposed to negative numbers briefly at the end of learning subtraction, but not with any of the inspection needed for algebra. Imagine trying to teach a student about negative arithmetic and its peculiarities if you can't use actual numbers that they can mentally add, subtract, multiply and divide. What would the mental result even be in that situation?