I admit, I've spent a fair amount of time thinking about what I can do to help my 11th and 12th graders excel on the IB exam. Maybe that makes me a bad math teacher to be thinking about the test so much, but I think my instruction can still be independent of the test, but I have to keep the test in mind as our collective end goal, in order not to veer too far in my attempt to bring good mathematics into the curriculum.
One of my latest conclusions is that doing well on a math test requires two skills: 1. that you can read a problem and retrieve the correct key concepts and/or procedures. 2. that you can apply the procedure without mechanical (algebraic) issues.
(Of course, being a good math student requires much more than that. I want my kids to know where procedures and formulas come from, so that when they apply a formula, it's not just blind application and they don't falter just because one small thing has been changed. I also want them to see the layering of the building blocks and be able to guess at the next logical step. I also want them to see where math is applied, to understand how to model real-world situations using math, and to ask insightful questions. But, ultimately, when they sit down in front of that big math test, I still want them to kick ass and thereby gain the confidence they need in order to do all those other things!!)
To help them with skill #2 (applying the procedure), I've decided that spiraling is very important. Every test I give in class is made up of old IB test problems, and include not just the current topic but also old topics we have already studied. The more we hold kids accountable for skills that we have already learned, the more they will retain them over time. To help them with skill #1 (recognition of cues and retrieval of relevant concept), I've recently introduced to my students the idea of making flashcards for math. It's very simple:
On the front of the card, write down some clues in the problem. (Such as, "This quadratic equation has only one distinct root.") On the back of the card, write down the concept or key math skill that the problem is looking for you to apply. (Such as the discriminant.)
As the kids work on practice problems, they should learn to recognize those major clues in the problems and make flashcards. Each time they sit down to do practice problems, they should first quickly run through their flashcards to re-inforce the cue-concept connections, and then try to approach all problems without looking back at the flashcards. They can also make a few clear example problems on flashcards. (Question on one side, work and answer on the other.) This way:
1. They can study quickly without re-doing the same problems a gazillion times.
2. It makes explicit the cue-procedure connections that "strong math students" implicitly rely on.
3. Over time, if they keep reviewing the flashcards, they will eventually not need them anymore and will hopefully internalize those connections.
4. Particularly anxious or slow test-takers will benefit from having clearly retrievable facts stored on their minds during test time.
5. It's a great way for them to accumulate invaluable study material/improve their study habits over time!
What do you think? Have you tried something like this? I am recommending it to my strugglers in lower grades as well, as a way to reinforce their test-preparation skills. I am helping my entire Grade 7 class build these flashcards this semester, as we review for the December "big exam." I'll survey them afterwards to see how many of them actually used them before doing the practice problems (like I recommended), and how many of them think it actually helped.
PS. Happy Thanksgiving!