Mathematical Discourse

Suggested Grade Level: PK-12


The National Council of Teachers of Mathematics (NCTM) Principals to Action (2014) introduces eight research-based essential Mathematics Teaching Practices, one of which is facilitate meaningful mathematical discourse. Facilitating discourse builds studentsʻ understanding of mathematical ideas through communication.


Reasons Discourse is Critical to Teaching and Learning (Math Solutions, 2021)

  • Talk can reveal understanding and misunderstanding

  • Talk supports deeper reasoning

  • Talk supports language development

  • Talk supports development of social skills

Resources

Math Talks

Math Talks are 10 minute routines conducted 2-3 times per week. Math Talks can be around any math topic. They serve to further the understanding of math content with emphasis on mathematical practice #3: Construct viable arguments and critique the reasoning of others.

The process:

  1. Teacher presents the problem

  2. Students figure out the answer

  3. Students share their answers

  4. Students share their thinking

Sentence Stems

Giving students a sentence stem is an effective tool to increase student participation in the classroom. Sentence stems provide students language support they need to engage in discussions. When using sentence stems for the first time, it is important to model there use for students.

Questions Promote Discourse

Probing Question - help students express their thinking

  • How did you figure that out?

  • What was the first thing you did?

Connecting questions - help students respond to each other's thinking

  • Who did it another way?

  • Do you agree or disagree? Why?

5 Practices for Orchestrating Productive Mathematics Discussions

0. Setting Goals & Selecting a Task - what objective/standards do you want to address and how will the task meet these

1. Anticipating - what strategies will students use to solve the problem

2. Monitoring - listen and observe how students solve the problem

3. Selecting - what do you want to highlight from students' work? Select those that will advance mathematical ideas

4. Sequencing - what order do you want to present student work to maximize their potential to increase students' learning?

5. Connecting - how will you connect the strategies and ideas shared to help students deepen their understanding

Talk Moves: A Teacher's Guide for Using Classroom Discussion in Math

  • Revoicing - "So you're saying..."

  • Asking Students to Restate Someone Else's Reasoning - "Can you repeat what he just said in your own words?"

  • Asking Students to Apply Their Reasoning to Someone Else's Reasoning - "Do you agree or disagree and why?"

  • Prompting Students for Further Participation - "Would someone like to add on?"

  • Using Wait Time - "Take your time...we'll wait."

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