Now that you mention it, it does seem that too much emphasis and time is spent on counting and calculations. A symptom may be how some people equate doing fast calculations with being good at math.
It's funny how that escapes detection. I only realized looking back how baroque that was. I think people do equate doing fast calculations with being good at math. While I think everyone should certainly know how to add, subtract, multiply and divide without error, there's really no reason to be able to do so obscenely quickly, given the wide availability of calculators. If you did want to be able to do very fast mental math, there are much better systems than what are typically taught in schools.
Really though, my point was that the school system spends far too little time on solving substantial problems in Math classes. I think an integrated problem solving approach that touches on many of the important branches of Math (graph theory, number theory etc...) would serve most people much better than the current system, where we spend 8 years building up to Algebra and then engage in a smattering of Geometry and Trigonometry.
In the current system, if you're smart, you do AP Calculus, which is obscenely dumbed down. If you want to proceed to study Math in college, you'll almost certainly have to re-teach yourself calc to be successful.
