The following quote is from the UC Berkeley math department website about Advanced Placement exams:
“While the Math Department has found that a score of 3 or 4 shows that a student is ready to take college calculus, it is not an accurate indicator of how a student will do in a college math course. High school calculus is not necessarily the same as college calculus. The professor’s expectations of what the students should know and have internalized (and not just memorized) can differ greatly from what high school students might expect.”
Berkeley is widely considered to be the top public university in the U.S., and one of the best universities in the world, so the opinion of their math department just might be worthy of consideration…
Note the very diplomatic wording above that says “ready to take college calculus” instead of acknowledging that the student has already taken college calculus.
Please also note the comment “(and not just memorized).”
Berkeley is alluding to the same problem that I frequently run into – the rush to cover too much material in AP classes and the pressure to get top grades leads to test tricks instead of long term comprehension.
The best math students are under a lot of pressure, often from peers, to stay on an accelerated math track and jump straight to calculus BC after precalculus. I have described this problem in a previous post.
For example, I have heard stories of Aragon high school students in calculus BC working through every released AP exam question on a particular calculus topic just prior to a classroom chapter test! They do this because teachers often simply lift AP problems and put them verbatim on their chapter exams. By doing every problem ahead of time, a student has already seen the solutions!
Methods like this may get a student a high grade on a test, but I find repeatedly that the knowledge gained through this type of cramming is not retained.
When students accelerate their math education by jumping from precalculus to calculus BC, they have to rush through the foundations of calculus as I have described earlier, and this leads to behaviors such as the above. I consistently find that students who take AB, and then BC, learn and retain much more mathematical knowledge than those who skip AB for the sake of keeping up with their “smart” friends and resume-building.
Berkeley’s math department does acknowledge that a student who achieves a 5, the top grade on the calculus BC exam, has learned the material, and allows them to go straight into multivariable calculus at UCB. One can read their entire set of recommendations here.
While Berkeley allows students who get a 3 or 4 on the AP exam to skip Math 1A (the first calculus class for math/physical science/econ majors), the department qualifies this permission very carefully with the quote at the top of this article.
Before concluding, I want to emphasize that I have great respect for the work ethic of many students at Aragon. Anyone who would do every AP question on a specific topic prior to a chapter exam has got to be commended for their grit and desire to succeed!
I am sorry, however, that they feel the need to take measures like this. I can’t believe that this makes them enjoy learning and encourages them to go on into STEM careers.
We adults really need to rethink the system that we impose on students. If we turn students off on STEM subjects, our country as a whole loses in the long run!