*How can I get my students to explain their thinking?*Effective discourse happens when students articulate their own ideas and seriously consider their peers’ mathematical perspectives as a way to construct mathematical understandings.

Encouraging students to construct their own mathematical understanding through discourse is an effective way to teach mathematics, especially since the role of the teacher has transformed from being a transmitter of knowledge to one who presents worthwhile and engaging mathematical tasks.

We can find ways to encourage eager mathematicians to share their ideas and to engage with others about their ideas by following three research-based recommendations:

**Clarify mathematicians’ ideas in a variety of ways.****Emphasize reasoning.****Encourage mathematician-to-mathematician dialogue.**

## The Best 3 Ways to Encourage Effective Discourse in Math

Think about all of the interactions among all the participants that occur throughout a math lesson--in the whole-class setting, in small groups, between pairs of children, and with the teacher. We will dive in deep today to learn the BEST three ways to encourage effective math discourse in your classroom.### Clarify mathematicians’ ideas in a variety of ways.

Clarification is important for English learners because it reinforces language and enhances comprehension. We often think of using this skill in reading, but it’s equally important in mathematics!

**Here’s some practical ways to use clarification in the classroom:**

- Restate ideas as questions to verify what mathematicians did. This allow also them to confirm what you’ve heard or observed.
- Apply precise language and make significant ideas more apparent.
- Look for opportunities to clarify questions to ensure that ALL students understand ideas and reasoning.
- Ask others to restate someone else’s ideas in their own words. This expresses ideas in a variety of ways and encourages listening to one another.
- Use teacher prompting. (See examples in the photo below.)

**When we pay attention to mathematicians’ ideas, we send a message that their ideas are valued. This is the key to encouraging participation of individual mathematicians.**

### Emphasize reasoning.

Getting mathematicians to explain their reasoning is hard at first! Reasoning helps mathematicians understand their own thinking and the thinking of others. As they communicate about ideas, mathematicians will make connections between relational understanding and move towards mathematical proficiency.

**Here’s some practical ways to use reasoning in the classroom:**

- Ask follow-up questions whether answers are correct or incorrect to place an emphasis on the reasoning process. This is to help mathematicians understand the others’ thinking.
- Follow-up on both correct and incorrect answers to reduce anxiety. We do not want students only having to explain wrong answers!
- Move mathematicians to more conceptually based explanations when able.
- Ask mathematicians what they think of the idea proposed by another.
- Ask mathematicians if they see connections between two of their ideas OR an idea and a concept previously discussed.
- Use teacher prompting. (See examples in the photo below.)

### Encourage mathematician-to-mathematician dialogue.

We wants eager mathematicians to think of themselves as capable of making sense of math. We do not want them to rely on teacher as the keeper of all knowledge. Encouraging student-to-student dialogue can help build this positive sense of self.

**Here’s some practical ways to use student dialogue in the classroom:**

- When mathematicians have different solutions, ask them to discuss one another’s solutions.
- Ask someone to rephrase another mathematician’s ideas or add something further to someone else’s ideas.
- Before a whole class discussion, have mathematicians practice their explanations with a peer. {This supports ALL mathematicians.}
- Use teacher prompting. (See examples in the photo below.)

**Mathematicians are more likely to question one another’s ideas than the teacher’s ideas.**

The value of student talk throughout a math lesson cannot be overemphasized. As mathematicians share their approaches, describe and evaluate tasks, and make conjectures, learning will occur in ways that are otherwise unlikely to take place.

**Remember, whoever is talking is doing the learning. Will it be you or your mathematicians?**

I hope you use the suggestions recommended in any of the three ways to encourage effective discourse in math.

*How are you currently using discourse in your classroom?*

**What recommendation would you like to add to your repertoire?**

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