Highlighting Ideas from Intentional Talk: How To Structure and Lead Productive Mathematical Discussions by Elham Kazemi and Allison Hintz
Many teachers are familiar with what Elham Kazemi and Allison Hintz, coauthors of Intentional Talk, call Open Strategy Sharing. We gather students together, ask them to think about a math problem, and facilitate a conversation using how questions, such as “How did you think about the problem?” or why questions, like “Why did you start with the seven?” Elham and Allison write that “the goal of open strategy sharing is to bring out a range of possible ways to solve the same problem and build students’ repertoire of strategies.”
But then what? Should every math discussion be an Open Strategy Share? What do we do with the strategies students bring up? Elham and Allison argue for a balance of different structures for mathematical discussions, based on the goals of the conversation. In addition to Open Strategy Sharing, they offer five types of targeted discussion that helps students dig deeper into strategies and mathematical understanding:
- Compare and Connect
- Why? Let’s Justify
- What’s Best and Why?
- Define and Clarify
- Troubleshoot and Revise
In this blog, we’ll dig into just one of these targeted discussion structures--Compare and Connect.
What’s a Compare and Connect Discussion?
After asking students, “Who solved this problem a different way?” a logical next step is to ask them what makes their strategy the same or different. The Compare and Connect discussion structure helps fine-tune this important kind of classroom conversation.
When you are planning a Compare and Connect discussion, it’s important to think about your instructional goal. What mathematical connections do you want your students to make between strategies? It may be helpful to begin by focusing students on comparing two strategies. What makes them similar and/or different mathematically? You can use this planning template from Intentional Talk to help you think through the following instructional decisions:
- Decide which strategies you want your students to compare and connect.
- Identify connections that you believe are important for students to notice between the two or more strategies.
- On your planning sheet, write out these strategies like you imagine they will be recorded on the board.
- Anticipate what students may notice as they compare and connect the strategies and how you might respond to support their ideas.
- Jot a note to yourself about the mathematical idea you want to target during the discussion and highlight at the end of the discussion. Put the note in your pocket so you can quickly remind yourself during the discussion.
As you facilitate the discussion, stay focused on the targeted strategies and key mathematical idea. It can be tempting to pursue other interesting ideas that may emerge (as we do in open strategy share); however a Compare and Connect discussion is all about delving into the connections between the strategies of focus.
Compare and Connect in a First-Grade Class
Let’s take a look at how one teacher, Mr. Delgado, planned for a Compare and Connect discussion in his classroom. After listening to his first graders share their ideas about 7+5 in an open strategy sharing session, Mr. Delgado decides to design a follow-up Compare and Connect discussion focusing on counting on by ones and counting on by bigger increments to make ten; he wants to highlight the idea that decomposing the second quantity into chunks to make ten is a good strategy for students to use as they work on advancing their strategies. Here’s the planning template Mr. Delgado sketched out as he planned for the Compare and Connect discussion.
The Compare and Connect discussion structure helped Mr. Delgado’s students notice similarities and differences between two addition strategies; from there Mr. Delgado was able to invite his students to try more efficient strategies.
When Else Might I Use a Compare and Connect Discussion?
Here are some other types of lessons that may lend themselves to a discussion about comparing and connecting strategies. You may want to have a Compare and Connect discussion in these situations:
- The problem can be solved in more than one way, and you know, based on your students, that they will have a variety of ways to approach it.
- You want to support your students in making sense of the different strategies that they have generated in order to make sure the students don’t see the mathematics in the solutions as disconnected.
- You’re prompting students along to a slightly more sophisticated strategy.
- You want to compare the use of two different mathematical tools or representations to solve the problem.
Dig Deeper into Intentional Talk
Until next time, may your Monday be mathematically marvelous!