Phil Daro was a lead author of the Common Core State Standards for Mathematics (CCSS-M) and works with teachers, districts, and developers to improve math teaching and learning. He has worked with SAP most recently on Math Milestones. He was invited by the Lesson Study Learning Alliance and Project IMPULS in Japan to spend 2 weeks visiting schools and engaging in workshops with Japanese and American mathematics educators focused on improving math teaching through Lesson Study. He shares his observations and work through this series.
Today I saw three great teaching moves to manage lesson flow and differences among students’ pacing.
- Teacher presented problem by giving height of 10 cards and asking how many cards in a tall stack of cards on his desk. Not enough info to answer. He assigned to students working solo: “Write a plan for solving problem. I am going to ask you what additional information you need.” This is a writing assignment based on Polya’s problem solving strategy. No race to answers. Then, he had them share and compare written plans with partners or triads. He said, “If you haven’t finished your plan, you can get some ideas from your partner.”
The move: Assign writing a plan to solve a problem rather than just “solve.” Withhold a piece of info so solving isn’t possible. Use think (write) pair (revise) share.
- After giving missing info, teacher assigned solving problem. After a few minutes, he said, “Get up and look at what other students are doing. Ask them to explain.” About half the class got up and visited others. This accelerated those seeking help: 15 students getting feedback and help simultaneously. It also slowed down speedsters in a productive way; they had to understand the math they used deeply enough to explain to others.
The move: Tell students to get up, look at the ideas of other students, use ideas in their own work. Parallel personal attention just in time.
- Teacher said, “Ok, let’s stop work and talk about your way of thinking. I know you may be in the middle, but it’s time to talk about your thinking.”
The move: Don’t wait until most students get the answer. That takes too long, and students work at such different speeds. The learning target is the mathematical ideas we want them to think about and be able to use.
All three moves free the lesson flow from the tyranny of waiting until students get the answer. They are writing their math in their notebooks. A lot of attention to what they write from teacher and collaborating students.
Something else I learned: students assigned to write a reflection on “how your thinking changed today.” Students are learning to pay attention to their own thinking. Nice.
