Still reading chapter 8 of Tools for Teaching. I agree with what he is saying about homework – it should reinforce already mastered skills or involve studying. I also think it should be brief. I remember arguing with my math teacher in high school. I think it was Trig/EA. My argument was doing the same problem 20 times wasn’t going to help me learn. If I knew how to do the problems, I didn’t need 20 more times to practice. If I didn’t know how to do the problems doing them wrong 20 times was usless.
When I taught math, the homework I assigned was 10 problems and from material they should have already mastered. It took lots of my time to write the problems. One thing I did was even before I gave the pre-test – I would write problems on the 4th grade concepts that students needed to know to do the 5th grade concept we were about to start. That provided me with some excellent information about what they had mastered and were the holes were.