4 Simple Ways to Engage Students in Meaningful Mathematical Discourse

math upper elementary common core


If your students are like mine, they love to talk! They love to talk about anything and everything...what happened on the bus, their favorite podcasts or TV shows, what their younger brother or sisters are up to, and even what book they are reading. But when it comes to engaging in meaningful math discourse, it can sometimes be crickets! I learned quickly that even though my students loved to talk, they did not always love to talk about their mathematical thinking.  The fear of being wrong often set in and kept my students as quiet as mice during math.  This was a mindset that I wanted to change and change quickly.

The National Council of Teachers of Mathematics (NCTM) defines mathematical discourse, as "ways of representing, thinking, talking, agreeing, and disagreeing ."  When students are engaged in meaningful math discourse every day, it provides you with many opportunities to listen into their conversations with peers and get a better understanding of what concepts students fully grasp and which ones remain a struggle for them. It also provides you the opportunity to give on the spot support, take anecdotal notes, and informally assess students. By providing students with the time and appropriate tasks that are specifically designed to spark these types of math discussions, students grow as mathematicians at a quick rate. They strengthen their own mathematical skills, help their peers' level of understanding, and learn from others' knowledge, too. Mathematical discourse in the classroom is a win for everyone involved!

With all of those benefits taking place in one math lessons, engaging students in mathematical discourse is a MUST DO in every upper elementary classroom. Follow these easy to implement tips to get your students discussing math in meaningful ways this school year.

Plan Explicit Instruction

As with any expectation you have, having students engage in mathematical discourse is something that needs to explicitly be taught.  Taking time at the beginning of the year to explicitly teach the expectations you have for math discourse will allow students time to practice how to talk about math problems and strategies with partners in meaningful ways. I always create class anchor charts of how to engage in math discussions with my students during the first few days of school. I use prepared math discussion stems and discussions questions that I expect students to use when they work with their partner,  as a guide to get our discussion going. I always am sure to include students' ideas on the charts, too. Just like turn and talk expectations during reading workshop, students are expected to make eye contact with their math partner, refer to the problem at hand, stay on task, and use the discussion prompts and questions given to them to guide their discussion. As the year progresses, students will not need the prompts and questions as they have fully embraced these prompts as their own, but they should keep a copy in their math journals as a reference. Another expectation that I explicitly teach is for students to use specific math vocabulary in their discussions. This means that they can refer to unit specific math terms on our word wall, from our journals, or from our math alphabet. By being specific, students conversations will truly serve as a tool to increase their understanding. As with any new skill and classroom procedure, be sure to model, model, model your expectations.  Grab FREE math stems and questions to engage students in mathematical discourse at the bottom of this post.

math discourse grade 3

Create Safe Partner Zones

When it comes to expecting students to engage in meaningful discourse it is important to create a classroom climate that welcomes mistakes! Students must absolutely feel safe to share their mathematical thinking, especially if they know they do not understand a concept. One way that I create a safe zone for students is by giving them two different math partners. (These math partnerships change every marking period.) Students have a red and green partner during math.  Red partners are partners that are at the same math level and green partners are partnerships of one higher math student and one lower math student.  Students develop strong and trusting relationships with both types of partners and are able to learn from both, too. Having both types of partnerships gives all students the chance to shine, help others, get support, and work as a team to complete any task. Most times, red partners are used during instructional work times and green partners are used during math mini-lesson instruction and discussion.  By having designated go to math partners, students will feel safe in your classroom environment and begin to take risks knowing that someone will always have their back. Their interest in solving math problems increases, too! Read more ways to strengthen your classroom community HERE.

Use Manipulatives

When students are given simple manipulatives to encourage participation and discourse, excitement and involvement increases tremendously. Two simple manipulatives to use to increase participation in your classroom discussions are paddle dry erase white boards* and agree and disagree cards. Students love to use the paddle dry erase boards to show their work and compare their thinking.  Kids love holding these by the handle and These are so easy to stack in the classroom and take up very little space. Agree and disagree cards are simple cards that you can make to provide students the opportunity to agree or disagree with their partner or classmate's thinking. Students love using these cards and the best part is that when students agree or disagree, they have to provide a rationale to support their opinion. Try these FREE 3rd grade math error analysis tasks to get students agreeing, or disagreeing with mathematical work. 5th grade version HERE and 4th grade version HERE.

Teacher Tip: When copying your agree and disagree cards, color code your cards so you can see quickly who agree or disagrees with a given answer.


math discourse grade 4


Provide Specific Math Tasks and Prompts

While it is possible to ask students to discuss any question in math, including how to solve an equation, the most meaningful discourse takes place when students are knee deep in problem solving and error analysis tasks. Problem solving activities require critical thinking and understanding, planning steps to solve, and then completing multiple steps to figure out the solution. Error analysis math tasks are also a great way for students to work with math partners to engage in meaningful math discourse. These are especially perfect for math discussions as students are expected to agree or disagree with how a problem was solved and explain their rationale. 

Talking about math truly helps students understand math concepts and self-reflect on themselves as mathematical learners. Math discourse aligns with the Mathematical Practices set forth from the Common Core State Standards. Remember,  just like any other lesson or activity, engaging students in meaningful math discourse must be planned.  You can use any problem solving activity that you already have to try this out, but instead of having students head off to work independently, pair them up, send them off with math discussion stems and discussion questions, throw in some manipulatives, and get ready to listen in and support your learners as they begin to love solving and discussing math tasks! Their interest in solving math problems increase, too! Read more ways to get your math students to LOVE math problem solving HERE.



math discourse grade 5





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How to Get to Know Students as Workers and Partners

back to school get to know you activity

As teachers we know that nothing motivates students more than working with a partner or within a small group. This is true for all subject areas. When a partnership or small group works well together there are so many benefits. Some include students engaging in meaningful discourse, taking ownership of their own learning, taking risks and sharing ideas, learning from others, and of course strengthening their collaboration and teamwork skills. And these are just a few! We also know that when a partnership or small group does not work well together no learning takes place, arguments develop, and student relationships become strained.

getting to know you back to school activity
That is why I love to spend some time at the beginning of the year getting to know how each of my students like to work, their learning style, and what type of partner they want to work with during project time and cooperative group learning. By discussing this with students and getting them to discuss it with each other, students quickly learn these important lessons:

  • Friends do not always make the best working partner
  • Everyone has their own learning and working style
  • The stronger a group is, the better they can work and learn

The classroom discussions that take place during the first week of school about individual learning and working styles are my favorite. They not only help me get to know students and better plan partnerships and groups, but it also helps the students to better know each other and their learning styles', and build classroom community too!

Grab this easy to use and engaging partner activity that I use during the first week of school to help you get to know your students AND to help your students get to know each other at the bottom of this post. (See more back to school getting to know you activities HERE.)



back to school getting to know you activity


Click through to find more Back-to-School activities and freebies to help build relationships from the first day of school!







Get to Know Your Students with the 4 C's of Engineering // Kerry Tracy




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