I found this thought in Buschman's book about helping children becoming problem solvers in math. (If you'd like to improve the mathematical problem solving in your classroom, this is the perfect book to pick up.) Obviously the quote applies to any area of the curriculum, but I find myself echoing how Buschman has found it to be true in math.
I have discovered teachable moments abound when I ask mathematicians to solve problems in ways that make sense to them and then carefully listen to their explanations. On more than one occasion I've had a look at a child's strategy and thought it looked like gibberish. Instead of dismissing it, with a deep breath and a smile said, "Now, tell me about your strategy." Come to find out, it was a brilliant strategy and one worth letting the child teach to everyone else. Those moments do not necessarily occur in a situation where the teacher controls the use of problem solving strategies. There is very little chance for conversation and explanation when children don't have the freedom to invent their own ways of understanding math.
I believe Buschman is right when he says that when we let go, we give children magic moments. Admittedly, taking the risk of letting go can induce all sorts of fears. Will there be any learning? Will I be able to teach all that's in the curriculum? What if no one organically invents the strategies that I believe are most useful? And so on. I can attest to the fact that letting go does not mean that chaos ensues. Instead, magic moments occur. They learn to be problem solvers. They learn to take risks. They learn how to communicate about their thinking. They understand math. They become mathematicians. It really is magical.