Did I Hear Anybody Say "Sample Selection"? -- Why Colleges Think They're Better Than AP (washingtonpost.com)

Tuesday Washington Post's Jay Mathews had an interesting article: Why Colleges Think They're Better Than AP (washingtonpost.com). He discussed whether advance placement classes (for non-US residents that is college-level courses that you can take in high school and get credit for when you enroll in college) were good enough and whether the requirements for getting credit for the course should be thighter. The basic question is whether it is better, in terms of how much you learn, to take an introductory course in, say, calculus in high school instead of when you enroll in college. I do not have a strong opinion either way, but what was interesting was how he defended the AP courses:

I found another selective college has done another small study that reaches a different conclusion. At Claremont McKenna College in Claremont, Calif., students who skipped introductory calculus by getting a grade of 4 or 5 in AP calculus AB or BC had an average grade of 11 out of 12 points in its follow-up calculus course. This was better than the average grade of 9.51 for all students in that follow-up course. The same thing happened in Spanish. Students who skipped the equivalent course at Claremont McKenna by scoring 4 or 5 in AP Spanish had an average grade of 11.29 in the college's follow-up course, which was higher than the average grade of 10.68 for all students in that course.

The problem with this arguments is, of course, that it completely ignores any potential selection bias. There are two parts to this. First, the high school students who are more likely to take AP courses are also likely to be "higher ability students" than those who do not. This means that the college students who have take AP courses before entering are also likely to be better or at least more interested in the topic than those who did not. Second, since the average grade is only given for those who scored a 4 or a 5 in their AP, those who got a lower grade are presumably counted with the other students. Hence, it is impossible to tell whether the AP courses were in some sense better or whether they simply attracted better students. What I would argue that Mathews should really be interested in is whether the improvement in students' knowledge is greater from taking a AP course instead of an equivalent college course.

Another study that he mentioned found that:

[those] who got credit for scores of less than 5 did not do as well in follow-up courses as students who had taken the college's introductory courses.

This seems more relevant for the direct question of whether to allow a student to opt out of a introductory course by taking AP courses. Other than for that reason, taking an AP course is simply a signal to the college admission that you are a serious (and bright) student. If that is the case, the question then becomes why do you need an outside company to teach those courses?

On a more general note. Anything that increase what high school students are taught before going to college has my sympathy. I continue to be dismayed about how little students know when they enter college (especially math). Instead of arguing who is best at teaching introductory calculus it makes sense to increase the required level of math in high school and then do the same for the introductory courses at college level (but then again, I am probably biased by the Danish high school system).