Both the NPR news report and my experience suggests that the AP tests the material needed to pass in a second tier college or engineering school, where theory is not taught in calculus. Personally I would prefer if the AP exam was designed such that students prepared at that level got a 4 and students who learned epsilon/delta proofs etc got a 5. Then colleges like mine could give placement for 4's and top tier schools could give placement only for 5's. U Mich's solution of testing their own students is also a good idea.
I'm not sure what jvano is getting at in his posting about students in his calc I class not knowing material from their high school calc. Did they pass the AP? Every student I've had who took "calculus" in their high school but no AP exam learned pretty much nothing. Either it comes out they were failing the course and didn't take the AP with their classmates or no one in the class took the AP and the course was really an intro to concepts class.
Of bigger concern to me is that many students don't learn any proving in high school: no proofs in trigonometry, no proof by induction, no Euclidean Geometry... It is awfully difficult to teach rigorous theoretical calc when the students don't know rigorous proving yet. I had a high school with a lot of proving in trigonometry and I was a member of the math team where I learned more proving, and I still found epsilon delta proofs difficult. This is probably the ultimate reason why many colleges and the AP curriculum have abandoned the theory which used to be on the AP exam.
As this is the YMN, how about demanding a little more certification to teach AP Calc? I suspect most teacher's don't know the theory of calculus. This has definitely been my experience teaching masters students who are going for a teacher certification. Meanwhile, there are tons of underemployed math PhD's who could do the job.
