One semester of Calculus down, time to see if the rebuilding project is starting to get anywhere. Last year the theme was removing the AP Fear™ from my student's mindset. In previous iterations, students were walking into the AP Calc exam, freaking out, and leaving most of the thing blank. I confronted that problem last year in a number of ways, mock exams being part of it. Being very zen and chanting "calm down" being another part. Oh, and the whole Varsity Math thing. In 18 months taking an AP math class became the coolest thing at my school, go figure.
But can we live up to the hype?
This year I kept the mock exam idea but trotted out a crazy new curriculum. It involves multiple passes through the entire curriculum (we learned about Integrals in October) to build up the familiarity they're going to need in May. I upped the ante on the mock exams. They were going to be longer, focus on multiple choice content, and remove the multiple choices. You can either solve the problem or you can't, no relying on closing your eyes and making a guess.
I discussed this plan at length with people at TMC15. Everyone liked the intention but suggested the kids might need more time with the mock exam material. Last year we just stopped what we were doing and I gave them the exams, for realsies. This year I extended the number of days blocked out for mock AP stuff, and two of them were practice. Kids had the opportunity to discuss the problems with me and each other, and I posted solutions. Then they took a real one, once every six weeks. Before we left for break they took quite a long one.
Here's the interesting part:
Now, there are a LOT of variables involved. Big factors are the way the pacing has changed, and whatever advantages there are in having the 15-16 group a second time (90%+ took Pre-Cal with me). All that aside, I can't help but double take at the results. First of all, this particular 14-15 exam was given in March, the 15-16 equivalent (not a perfect equivalent, but close enough) the kids were ready for in December. That alone is like, whoa.
Exams as End Goals
It's in the back of your mind just like it's in the back of mine. Why all this focus on exam results? Why let a test dictate what your kids get to learn and not learn about Calculus? A fair argument and one I think about daily.
Standardized exams are helpful in that they are, duh, standardized. The AP Calc exam is administered to a kajillion students all over the world with little variation. My students hit all the metrics you read about when it comes to exam bias. All the data says that because of socioeconomic factors outside of their control, they will do worse than their counterparts in other countries, or heck, on the other side of the freeway in the same school district. Screw that. I watch these kids every day, there's no reason they shouldn't have an equal chance.
If you read through enough iterations of the AP Calc exams, you can tell there is a real emphasis on the part of the exam writers to filter out the kids who memorize steps. You've got to know what you're doing. Vocabulary is huge. Context is huge. Abstraction is huge. Forever years ago as a first time Calculus student I would've killed for better conceptual understanding.
I think the way I've hacked up the curriculum brings that to my students. I want it to make sense for them now, not 15 years in the future, if ever. There is nothing special about Calculus that makes it off limits to individuals who don't "get it" or aren't "math people" or whatever straw man you want to use (driving every kid to take it is a separate issue). My goal is that they can take an intimidating (to them) subject like Caclulus and see how it's built on really simple foundations (our slogan should be: "wait, that's it?"). That kind of critical thinking will serve them well after the exam is over.