David Johnson has these 3 great (small) books about teaching math that I reread (or at least skim) every summer to remind myself of good teaching practices. One of his suggestions is to make sure that every day by the end of the period you know where each of your students stands in terms of understanding the current material. This is a great idea. This is a great idea that gets lost in the tons of other things that I'm keeping in my mind to get done each day. This is a great idea that I have to keep reminding myself of.
I gave a short 10,000 point quiz the other day before we got started on the new material (okay, no points, but they always ask if it will be graded and such, so I told them that it was worth 10,000 points) . I handed out 1/2 sheets of scratch paper, and on the overhead put 3 basic questions all about the same technique/concept we had been studying with the 1st being simple, the 2nd a slight upgrade, and the 3rd an even bigger upgrade. It only took 5 minutes, and I collected them and graded them after class in various free "pockets of time".
This was enlightening, and I was able to make comments on papers of students who had varying degrees of misunderstanding. This is especially helpful because I only grade homework on completion (collected every day), and kids slip through the cracks. Note to self. Keep this up.
I also just gave the finals retest in calculus. In December, they bombed their final, which I had retooled from old released AP exams. I still want them to master the material. I didn't think that test corrections would be helpful this time because I wouldn't know if the kids understood the topics or if they got help from others and understood the explanation of OTHERS doing the problems. SO. I handed the tests back (multiple choice). I told them all the correct answers. I gave them 3 weeks to study and said that they would be having a test with the exact same questions (a shortened version) and that they would have to show work. I'm crossing my fingers on them doing well.
I did have various students within that 3 weeks come and ask for help on various questions, so that's a positive note. I also had 3-4 students cut my class the day of the exam. Negative note. Boogers. I'm deciding what to do for/to them.