@ucbalumnus I asked professors at each university whether students should retake classes that they got AP credit for. Almost universally, the professors said to take the credits and start at the higher level courses. I’m not sure what UW Madison calculus looks like, but I’m guessing calculus textbooks are fairly standard across the country. I don’t know why the advice for UW would be different than the colleges I visited.
As for why professors said to take all the AP credits, the main reason was that students who scored high on AP tests would be bored with relearning the same material in college. I can see the point that learning basic integrals and derivatives for a second straight year may be discouraging for a high-achieving student. If an honors class covers different material, then that’s a different argument.
When I was in HS, 27 years ago, my school did not offer AP classes. We had an agreement with St. Louis University to offer college credit for approved classes. Looking back, I think those college credits I got were a little suspect. I don’t remember any comprehensive test at the end to confirm we covered the proper material and learned it. The AP exams my D is taking are different. They compare all students across the country and have a set curriculum that needs to be taught in order to be successful.
I won’t know enough about this until my D starts college in the Fall and maybe starts a semester or two ahead in calculus. So far, I haven’t heard the convincing argument that would make me suggest to my daughter to retake Calc I. I would love to hear from a student with some experience taking the AP credits and starting ahead of the other freshmen.