I heard about the following Atlantic article from @stevenstrogatz : October 13th, AP Classes Are a Scam which I found quite interesting.

I thought much the same in those years when I taught a lot of freshman Calculus. My main observations were that

- Most students who had taken AP Calculus in High School had to take the Calculus sequence anyway, and resented that they had to essentially repeat a course.
- Students who had not taken AP Calculus in High School felt intimidated that they were in class with students who had, and felt completely inadequate.
- As a result, the AP students barely worked at all, since they had a superficial knowledge of Calculus, while the non-AP students worked very hard.
- Since AP Calculus is not college level Calculus, the effects were clear by midterms: the AP students had fallen too far behind, and the non-AP students were learning the material, and starting to enjoy it.
- I suspected that there were other, successful AP students, who weren’t in my class, and never took another math class in their lives. Thus, some of the most enthusiastic math students at the high school level were diverted out of the math major, since they saw Calculus as the final math class.

So why did I come away with the impression that AP Calculus, presented as the highest level math class one could take in college, was essentially a terminal math class, serving to prevent bright and hard-working high school math kids from continuing in mathematics?

I’ve come to understand this more in the contrast between *acceleration* and *enrichment*. Our educational system emphasizes acceleration, and works hard to move kids rapidly through material. There are a lot of incentives for this, like granting college credit. An alternative is to enrich the curriculum, and allow students to go deeper into the material.

When I was in high school, I used math team to enrich my studies, as well as my own mathematical reading of fantastic authors like Martin Gardner. I don’t think I ever earned an academic credit for this enrichment, but it was profoundly enjoyable, and directed me into mathematics. I did benefit from acceleration as well, but my most memorable mathematical moments were from some inspirational math enrichment.

So, why do we bother with AP courses? I think our students would benefit greatly if a similar amount of resources were invested into academic enrichment. I’d love to see after-school math circles, math clubs and math teams in every school, and I can imagine similar enrichment in other subjects.

Concerning “AP is a scam”:

My son attempted an AP Calculus course in High School but was instructed by the teacher in the last week of the course not to take the final exam ; he said he had no chance of achieving a score sufficient for advanced placement. I called the teacher to ask if I might tutor him so he could take the exam (we were living in separate households at the time and I was not able to track his progress throughout the semester, day by day). The teacher replied that that would not be sufficient since he had been teaching his students a STRATEGY for getting advanced placement. The conversation ended there, though there was plenty I would like to have said that he would not have liked and I didn’t want to get my son in trouble. From my experience in college calculus (taught from Thomas) one should not be in the second semester (3-term sequence where I went) because of an exam strategy successfully applied but because he understands the first semester. This occurred 28 years ago, but I am concerned that even now AP Calculus courses emphasize strategy for passing (thus leading to a notch on the teacher’s gun, so to speak, not to mention bragging rights for the school) rather than imparting a real understanding of the material. The “lucky” student may think he knows what he needs to know for the second semester but doesn’t and the result is disaster.

For the same sort of reason, I would discourage anyone from taking calculus in summer school, since that is “lightning warfare” and leaves little time to absorb and appreciate the mathematics.