One of the standards for mathematical practice in the Common Core is to "construct viable arguments and critique the reasoning of others.” That’s a tall order for students used to sitting quietly in a math classroom passively receiving instruction. Knowing that improving the quality of math discussion in their classrooms won’t be easy, educators are applying the "lesson study" technique to improve their craft.

During a "research lesson," only one teacher will deliver instruction, but other teachers in the lesson study group will be present to observe how students react, what sorts of solutions they come up with, and how they interact with one another. This is very different from many classroom observations that focus primarily on how the teacher delivers the lesson.

In a research lesson, the observers helped develop the instruction ahead of time, and are gathering data that can give them insights into how well the lesson worked so they can discuss it later. “The key to having a good discussion is to have good data about how the lesson impacts the student,” said Tom McDougal, one of the main advocates behind the Lesson Study Alliance, a non-profit working to promote lesson study practice. “To get that data you have to be watching the students, not the teacher.”

During the planning phase, the lesson study group is thinking about all the small steps that might enable them to teach a little differently. For example, when it comes to discussing math arguments and critiquing one another, teachers know kids are often afraid to put their ideas forward. So one way to structure the lesson could be to ask students to put their solutions on a whiteboard. That makes their thinking visible, but they may feel less vulnerable. And there are bound to be differences in problem solving when all those ideas are out there, a good jumping-off point to critique one another’s thinking.

As the group of lesson study teachers are thinking through the research lesson, they’re asking themselves: Will the lesson they’ve designed together elicit the kinds of errors they hope to see? Will it make students curious? In what order should the ideas be presented? How are they going to make sure the student ideas are visible to everyone in the class? It sounds like minutia, but these details could be the difference between the lesson going well or poorly. These teachers are trying to look into the future and predict how the lesson will go.

To help them take accurate, helpful notes that can be discussed later, teachers are using an app called Lesson Note, developed by the Lesson Study Alliance in Chicago. Proponents of lesson study have found that many teachers new to the method don’t know what to look for when observing a classroom and they tend to sit in the back and focus on the teacher.