This year, the Prairie Creek staff is experimenting with a peer coaching model called "Teaching Rounds" The group I am a part of is looking at developing rich inquiry based math classrooms. Specifically, I am examining math conversations (which touches on one of our non-academic goals, conversation skills).
Amy Narveson came in to observe a lesson a few weeks ago in which Herons were designing their own calendars (we had been reading a bit about the decimal based calendar of the French revolutionaries.) I gave the students a set of sentence starters from an article in "Teaching Children Mathematics" to help them guide their discussions with each other as they shared their ideas. As always seems to happen when one is being observed, the wheels came off the lesson right away. The students were doing a great job designing a new calendar but they found the supplied sentence starters very limiting for the task I had given them. (And I realized that I hadn't created a test which forced deeper conversation.)
After watching them share their ideas but not by using the supplied sentence starters I had been asking Amy to observe and record, I gathered the Herons together to ask which sentence starters would be better. They expanded our list of five three fold. They also categorized the list by what they wanted to do.
Since then, we've been modifying and adding to the list and I've begun to use it in my foundation and exploration math lessons.
Today, during a number talk in foundation math, I asked the children to solve 3.6/.6 mentally. (See this post for an explanation of number talks.) The group had been working on dividing with decimals and had developed several approaches. I had also been using what I learned from the previous math conversation lessons to encourage talk between students, not just with me.
After getting "the right answer" one child was really questioning why the technique he had used worked (shifting the problem to 36/6.) "I know I don't shift the place value back in the answer but I don't understand why." The other students worked to try to explain what was going on with the numbers. One said, "Does this make sense? Division is the same as a fraction...so this is just an equivalent fraction." Several other children gasped and signaled an "O" with their hands which means "Oh! I just realized something." They then continued to talk to the student with initial question as well as among themselves, "I have something to add to _____________." "I think about it a lot like ___________ except that I rounded the numbers to estimate first. Then I could trust the answer."
It is hard to over estimate the importance of talk in the math classroom. If that child had simply accepted the "short cut" in decimal division and not felt empowered to insist on understanding, he would have had a wobbly block in his foundation - something that didn't make sense to him but that he could memorize. Instead, as we worked through the idea together, asking questions and sharing ideas and methods, the entire group deepened their comprehension. The strategy wasn't something they were copying from the teacher but rather something they were developing together - it was something that made sense. And the making of sense happened in the conversational space of the classroom.
I'm still working on my skill as a conversational facilitator, but it has been exciting to see the students turn more readily to each other, eager to question and share.