*How did you get that?*—for math teachers to create opportunities for students to share their thinking. But knowing what to do with students' responses to that question and teaching children to meaningfully participate in discussions can be more daunting. How can teachers keep students from getting lost or disengaged when many different ideas are shared?

*open strategy sharing*or as

*targeted sharing*(Kazemi & Hintz, 2014).

*open strategy sharing*. In this type of discussion, students contribute different ways to solve the same problem. Such sharing can deepen students' understanding of a repertoire of strategies and show them that different people have different ways of thinking about the same problem.

*converge*on that idea. We call that

*targeted sharing*. This more focused sharing involves specific goals, such as defining and using key terms or concepts correctly, revising an erroneous solution, or making sense of a particular representation. The students listen to and contribute ideas to arrive at consensus. These types of discussions can deepen students' understanding of particular strategies or ideas and help students realize that thinking together can help them understand.

## Valuing Student Thinking

## Open Strategy Sharing: Mental Math

We are now going to do a strategy share. I'm going to ask different students to share their strategies. When you share, tell us how you solved the problem and why you solved it that way. As different students explain their thinking, I will write down the strategies. Your job is to listen and make sense of each solution.

#### Figure 1. Open Strategy Share

## Targeted Sharing: Compare and Connect

Yesterday, as we were listening to people think about 24 ÷ 4, we heard a variety of solutions. Today, I want our discussion to focus on making sense of two particular ways we divided by four and look for similarities in these two solutions. Raina made four groups, and Tate made groups of four. I'm going to put the two strategies in front of us, and I would like you to study them and ask yourself what is similar about them.

One has four groups, and the other has groups of four. I wonder if a problem context could help us here. Imagine these two stories, then turn and talk to your neighbor about what the four means in each of them. Story A: Our class has 24 students. When we go on our field trip to the zoo, we need to divide into four groups. How many students will be in each group? Story B: Our class has 24 students. When we go on our field trip to the zoo, we need to divide ourselves into groups with four students in each group. How many groups can we make?

*partitive*(how many in a group) and

*quotative*(how many groups):

M<EMPH TYPE="5">r. F<EMPH TYPE="5">oyle: I hear people saying that the four in the first story is about how many students are in each group. And that the four in the second story is about how many groups we can make. Let's look at the drawings of Raina's and Tate's strategies. Which drawing do you think matches which story, and how do you know that? (After a few moments of wait time) Gabriel?G<EMPH TYPE="5">abriel: I think that Raina's drawing would show a solution for Story A because she made four groups and then put all the students into those four groups. If we look at that drawing, we could see that there would be six students in each group. So, then, I guess, Tate's strategy would show Story B because he made groups of four, and he made six groups.