Yesterday I gave a mock AP calculus exam for my students while the rest of the school population was taking the state-mandated exit exam (yay TAKS). Three hours and 45 minutes or so of testing. Oh my goodness. For the most part (aside from doing some chores here and there), I took the BC exam with my students. Whew! I got exhausted from the extended mental challenge, so I can empathize with them when they come back from the test looking drained.
I can also empathize with them on another aspect. This is the first year I'm teaching BC, so it's the first year in a long time (and maybe ever for some topics) that I've seen various things: calculus on polar functions, on series, parametrics, logistic growth, etc. And in my treadmill type of year, I haven't revisited those topics since I taught them weeks and weeks ago. So. As I'm taking the exam and the topics come up, I felt like the students. I remember seeing the topics. I know I understood them when we were doing them. I'm not a stupid person. I just don't remember the details on some of them. I guess I must be human.
Here's to me not thinking of review in class as a "wasted day when we could be learning something new and why don't they review on their own what kind of students are they and I'm enabling them by hand holding them through a review oh my gosh the next thing you know I'm going to have to wipe their noses for them". Here's to me thinking of a review as a necessary part of the learning process that's worth "taking a day for". I could also think of it as money in the bank for the later part of the year when we take many days to review for the actual exam. Maybe it'll be an opportunity to think of memorizing tricks.
Aside: as a class we came up with a good one for memorizing the Taylor series expansion of sin x, cos x, and e^x. The sine function contains the odd numbers of the pattern, the cosine contains the even numbers, and the e function contains all the numbers in the pattern. So. The "i" in sine looks like 1, and that's odd. The "o" in cosine looks like zero, and that's even. And. "e" for everything. Woot woot. It worked as I was taking the test.