Typically, when I pose a question or a problem to the class, there are a few things that impede learning. First, the focus is still on me, so most of the students are just waiting for me to give the answer. Second, whenever a student does contribute an idea or question, it is directed at me. Not what I'm going for.
So, this week I wanted the class to work though a proof together. I drew the diagram on the board, asked the question, and then sat in the back row. This helped in two significant ways. For one, the focus was no longer on me; it was on the problem on the board. There was also a clear implication that with me sitting in the back - that this was their problem, and I'm giving them the time to do it (instead of the usual wait-long-enough-and-Mr.-Krenz-will-do-it-for-us game).
Additionally, the discussion of how to do the proof changed significantly. Questions and ideas were now being addressed to peers and the rest of the class rather than me. It wasn't me piecing together different students' correct responses to put a proof on the board with the false impression that the students did it. The students were offering ideas, critiquing, and collaboratively deciding on the next step.
When they completed a solidly challenging proof with almost no assistance, which they have been struggling with, I was still sitting in the back row. And I could not have been more proud of them.
It isn't perfect. I still give some guiding hints from the back, which I'm going to try to cut back on. The discussion can be confusing and solutions offered may not be correct. The path that is taken is not necessarily the most direct. But these are good things. Students start to understand that the perfectly linear proofs and thinking in the book isn't the way you need to think. I'm not sure it's the way that anyone thinks.
I'm sure other teachers have tried this. If so, I'd love to hear your experiences. If not, try it. Sit in the back and let me know what you think.