I'm new to this group and noticed the calculus discussion. I just wanted to get my two cents worth in.
All of the previous discussions treated "calculus" as this monolithic entity. There are many aspects of calculus and many different perspectives of it. For most students, calculus is their first meaningful introduction to the concepts of limits and continuity. The ideas behind rates-of-change should be meaningful to many people who don't go onto engineering. The idea of deriving/approximating areas for regions bounded by curved lines is another aspect which some laypeople might appreciate. How about maxima and minima. Many people are intriqued by the fact that the square encompasses the most area of all rectangles of the same perimeter.
I question whether we must teach all of "calculus" in order to convey the true beauty of the structure behind it. My 11 year old was recently given a problem with trying to figure the distance an object falls over various periods of time. He was guided to do this in one second intervals and was very much intriqued by the novelty of the problem. He even grasped the fact that he was making an approximation. I'm sure that other kids in the class felt the same way.
Thus, IMHO, I believe that some of the concepts behind calculus should be taught and that these concepts should be brought to the attention of children at the earliest possible age. However, the method of presentation should be changed to meet the needs of students who are not planning to go on in engineering, math, economics etc.
-- Ron Reiner
"A sieve will not hold water but it will hold another sieve."