I think that I just noticed another piece of the problem-solving puzzle. I've just finished a really good unit on factoring with my ninth graders, and a lot of the frustrations that I've had with this group have been absent for the unit. I think I know why.
Before, I would have anywhere from a half to two-thirds of the class working hard on problems, and the remainder goofing off. They would either be stuck, not interested in doing any work on the day or just punching each other in the head. (I teach high school boys. They do this sort of thing.)
Anyway, that didn't happen with this unit. They self-organized into helpful little groups. They started saying mature things like "I need more practice on multiplying binomials" or "What's the next step after this?" They taught each other. They shared tips and techniques.
Why? Here's my quick analysis:
1) The unit was set up well. I taught them the concept of factoring when we were doing the distributive property in October. I taught them about multiplying exponents in November. They were all comfortable with the prerequisites to this unit.
That means that they could self-assess. They knew that if they got no x^2 term, that something was up. There was very little of that x * x = 2x sort of thing.
2) More importantly, I think, is that I was clearer than I had ever been about what they needed to learn. After the first day or so, I told them that there were four levels of sophistication that they needed to hit: Multiplying polynomials, Factoring the Diff of Two Squares, Factoring Trinomials, Factoring Stuff Completely. I told them that their job each day was to move themselves up a level. I started class with a "Reality Check" that helped them (and me) assess what they needed to work on. I had problems and activities available for every level. Students got to choose what to work on, so if a kid was feeling frustrated he knew exactly where to head back to.
The lesson for me is this: always share the map with the students. If they know where they're going, they'll feel more empowered to make sure that they get themselves there.