An AP English teacher passed on this idea from a conference she attended, and I thought it sounded effective and cool and will try it soon. Give the kids a sheet of good multiple choice problems (the non answers are based on common mistakes). Say there are 4 choices. White out the correct answer choice for each question and leave the 3 non answers (the kids know what you've done ahead of time). This way, the students work through the problem, and if they see their answer there, they know they made a mistake, and work harder at figuring out what's what.
I tried something a bit different last week - something I thought would work well. Well, it worked in that it gave me insight into what the kids DON'T know.
I had a sheet with 3 AP calculus questions. Stuff we've just covered. Stuff I thought they would be great at - integral of e^(-4x), derivative of (x^2)(sin(2x)), setting up a u-substitution integral. There were 5 answer choices. I gave all answer choices. I picked 3 of the letters (one being correct). I told them for each of the 3, either indicate it's the correct answer, or describe what mistake the student made if they picked that answer.
Well, talk about a stressful time in class. First of all, things they nod at you at when you're teaching, things they do homework on, and you think they know, things you've seen them do successfully. Out the window. Don't trust it until it comes down to proving it without any aids or support or notes or hints or prestudying for a test. So, it basically worked well in that it taught me to be careful and be more thorough in checking and rechecking their understanding individually NOT in a test situation. Second of all, it was fascinating how needy some of them were: am I right? can you just tell me if I'm on the right track? can I work with so-and-so? ... I kept telling them no to all questions, that that wouldn't help me know what they know. It was very hard not to help them, but I think that's what got us into this in the first place.
Whew. I have some work to do. But better to know that now than when it's too late.