This quote seems so very appropriate for where I am right now in the way I'm trying to improve my math instruction. In the past few years, I've made many changes to the way I teach math and especially to problem solving. Mathematicians share their strategies, not only with neighbors, but with the whole group. That kind of sharing obviously involves lots of talk. The change I'm trying to make this year is removing most of myself from that talk.
It used to be that a child would draw their strategy on the board, and then I would kind of take over, asking them questions and prompting them in certain ways while the class watched and hopefully listened. It was a step in the right direction, but it was missing something - less of me and more of them. Now the child who is sharing takes over from the beginning, shares whatever they want to say about their strategy, and says, "Comments or questions?" It's been cool to watch what happens next. Typically the class asks insightful questions and the child is forced to think about why they made the choices they made and then find a way to communicate those reasons to the class. Even though I'm there to turn the conversation in ways I feel would be most beneficial, it's cool to hear them doing most of the talking. I've a ways to go on this journey of learning how to improve my problem solving instruction, but hearing kids do more talking about how math makes sense to them makes me believe I'm on the right track. Comments or questions?