Why is it that so many college teachers judge the AP calculus program on the students who come to their classes having either failed the AP exam or done poorly on it? Most of the time it is quite obvious those same teachers have never looked at the AP syllabus nor looked at AP exams, which are readily accessible. The multiple choice tests are released to the public every four or five years, the show-your-work portion every year. If you still feel the exam does not meet your standards of teaching for understanding, not just skills, the AP testing committee would welcome your observations.
I taught AP Calculus for over 30 years. I have also taught calculus at a community college and a small private college. I know I did a better job in high school. How could I not do so when we met 5 days each week, not 3 or 4, and had two or more weeks each semester? Further, most of my high school students had more natural ability and had a more consistent background.
Did I teach the derivative for understanding? Certainly. Did I have students in AP who, despite underlines, bold print and being explicitly warned, found the derivative the short way when I was testing for understanding of the derivative concept from the definition? Yes indeed. Our physics teacher, who did not have time to teach the derivative concept, often taught short cut rules before I got to them. This did not justify my getting upset with the physics teacher. I patiently had to explain to the students why I wanted them to demonstrate to me their understanding of the definition. Most students complied with my demands; a few stubbornly did not want to bother.
It is not the AP program that is at fault but frail human nature that wants to take the easy way out. Perhaps I understand this because of my own college experience. Fifty-one years ago, when I was a freshman at Purdue I came with a background heavy in algebra , but no trig. The frosh engineering math course in those days alternated 3 weeks of college algebra and trig. I was doing poorly in algebra but very well in trig. The old prof I had was wise enough to surmise I was not doing much studying while we worked on algebra. I thought I new it all. He asked me to drop in and we had a talk that brought me back around.
At every level of high school and college teaching I met students who only wanted to know what to do, not why. (Examples: "Don't make me understand what a radian is, just tell me how to change radians to degrees; just tell me the distance formula or equation of a circle and not bother me with seeing these are just variations of the Pythagorean theorem, etc., etc.") Most such students remain C students and worse. On the AP, they get 3 or less. Over the last few years I met more and more students who wanted to know only what, not why. My challenge was always to make them realize that knowing why was ultimately to their advantage.
So, Dan H's claim that the AP exam is the closest thing we have to a national standard is still on target. I often wished that colleges were held to this same standard for their calculus courses.
A college teacher on the Calc Reform group recently admitted having given an AP exam as a final some years ago. The results were not outstanding. Even in the multiple choice questions the AP exam does a good job of testing for understanding as well as algorithmic skill.