Mathematical discourse is what students write and speak about math to show their thinking. The Common Core State Standards for Mathematical Practice call for constructing arguments and critiquing the reasoning of others. In order to connect content and practices, students in a *Math Trailblazers* classroom need opportunities to talk about their strategies as well as time to listen to the solution strategies of others. The discussions need to be strategic and purposeful.

To increase participation during classroom discussions, *Math Trailblazers* lessons create a balance between:

- Whole-Class Discussions
- Small-Group Discussions
- Partner Talk

When using whole-class discussion, the teacher is in charge of the class, but is not just delivering the information or quizzing the students. Rather, the teacher is **working to get students to share their thinking, explain their reasoning, and build on one another’s thoughts and strategies**. Whole-class discussions give students the opportunity to participate in sustained reasoning. The teacher’s focus is not on providing answers, but on *facilitating, guiding, and engaging students’ thinking*. Whole-class discussions provide students with the practice in mathematical reasoning that will further their mathematical learning.

In small-group discussions within the *Math Trailblazers* classroom, the teacher typically poses a question or a problem that students discuss in a small group. In this format, the teacher circulates among the groups. The teacher** does not guide or control the discussion, but listens to the discussion and at times asks clarifying questions or questions to extend the discussion**.

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Partner talk is similar to small-group discussion except that after a question is posed, students spend a short time sharing their thoughts with their neighbor or with a specific partner. These discussions are typically very short and very targeted. The goal is to **provide opportunities for students who may be more hesitant** to share their thinking. In a *Math Trailblazers* classroom, partner talk is often used as a vehicle for getting students ready for a whole-group discussion.

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To **build productive math communication** in the *Math Trailblazers* classroom:

- Establish and maintain a respectful, supportive environment
- Focus talk on the mathematics
- Provide equitable participation
- Set clear expectations for classroom talk
- Try only one challenging thing at a time

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Teachers need to **establish classroom norms** and model and reinforce specific behaviors. Explain to students that in order to meet the learning expectations, a set of group norms needs to be developed to guide the class as they act and learn as a group. As you work to create the norms together, discuss:

- rules for listening
- ways to agree and disagree respectfully
- how to critique the reasoning of others rather than the person
- personal responsibilities
- how to take turns
- ways to support facts or opinions

A *Math Trailblazers* teacher can use the following **strategies to promote effective math discussion** in the classroom:

**Revoicing**: (“So, you are saying that it’s an odd number?”)**Repeating:**(“Can you repeat what he just said using your own words?”)**Reasoning:**(“Do you agree or disagree? Explain why you think so.”)**Adding on:**(“Would someone like to add something more to this?”)**Waiting:**(“Take your time and gather your thoughts…”)

Try incorporating these phrases to orchestrate productive math discourse:

- “What did you know about this problem before you started to solve it?”
- “Would you explain your thinking?”
- “Could you please repeat that? I heard you say this, but did you mean something else?”
- “Do you agree with Max’s reasoning?”
- “Did anyone solve this problem a different way? Explain.”
- “Who would like to explain Tasha’s solution?”
- “Does anyone have a question to ask Marcus about his solution?”

Teachers must create an environment where it is acceptable to make mistakes. **When misconceptions and errors are explored (as opposed to simply discussing correct answers), students begin to see mistakes as a natural part of the learning process. **Teachers can facilitate this by c*arefully selecting problems to discuss*, including problems where there are often misconceptions. Further, teachers must *respectfully react to incorrect answers and communicate that these errors provide important learning opportunities*. In addition, it is crucial that teachers **provide time for student exploration and inquiry, and allow students to grapple with problems**.

To help **facilitate purposeful and strategic discussion** in the *Math Trailblazers* classroom:

- try to anticipate the strategies students will use in solving a problem
- monitor students’ work as they solve problems
- select students’ strategies to be shared rather than choosing random students
- organize students’ sharing so that it will be helpful to the class discussion
- encourage students to make connections between a variety of strategies so that they see the math behind them is the same

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