The Common Core State Standards for mathematics call on students to "reason abstractly and quantitatively," "construct viable agruments and critique the reasoning of others," and "model with mathematics." While these are math standards, they require social and linguistic skills as well.  This tip, from RTI Strategies that Work in the K-2 Classroom by Eli Johnson and Michelle Karns, provides teachers with a four-step dialogue to engage students in mathematics, while encouraging them to reflect about their throught process, interact with others in the classroom, and use language to further their understanding of key  math concepts.

What the Math Dialogue Strategy Looks Like
Ultimately, math is the language of creating in the physical universe. The authors of math textbooks chime in with their perspectives on learning math skills and concepts. Students also need to find their “math voice” so that they can grasp the concepts that will allow them to create and build. When students engage in math conversations with their peers, they are able to contribute to serious learning. Shared dialogue helps students understand solutions to math equations. The following four-step dialogue engages students:

1. Saying “I think that . . . because . . .”
2. Understanding “I listened to what X said and now I think . . .”
3. Reflecting “My understanding was/was not correct because . . .”
4. Rethinking “I now think that . . . because . . .”

As students value the ideas of others and openly share their thinking and understanding of math concepts and processes, they will see things from additional perspectives. Instead of math being a boring time of silently solving a long list of grueling equations, math can be an interactive, vibrant conversation of meaning and understanding. This intervention will go a long ways to creating a true community of math learners.

How the Math Dialogue Intervention Works
Most any math concept can be used as a basis for engaging your students in math dialogue. It is important to clearly know what your objective is when you assign a math concept to be explored and discussed by your students, so that you can help guide them to a productive result. The following steps will help support math dialogue in your classroom.

1. Provide students with a challenging math concept and outline some of the potential difficulties they may face.
2. Place students in pairs and assign them so that stronger math students are paired with students who need more help.
3. Ask students to think, pair, and share and as students think they can draw out their understanding of the concept, identify patterns, write down an example, think of a real-life situation, and so on.
4. Give students time to negotiate meaning and question each other or poke, prod, extend, and expand ideas.
5. Place two pairs together in a group of four and then ask the students to share with the other partners.
6. Ask students to symbolize their negotiated understanding through a picture, equation, example, written statement, and so on.
7. Next, groups of four can share their understanding with the entire class through a teacher directed discussion.
8. Finally, make sure that concepts are challenged and the students’ thinking is accurate.

When students can justify their explanations verbally, then students have learned at a very high level and they will more easily retain this information for future use.