What Is Math Talk?
Why Is It Important?
A successful mathematics program emphasizes communicating mathematically frequently in the classroom. In addition to NCTM’s standards, most state standards include competencies related to communicating effectively through mathematical language, justifying solutions, and evaluating the mathematical thinking of others.
What Does It Look and Sound Like?
The picture below illustrates the interaction between the teacher and the students during effective math talk and demonstrates how knowledge is constructed through these interactions and exchanged with others. For a free download of my Looks Like/Sounds Like Poster, click here.
Creating a Math Talk Community of Learners
In order for math talk to be successful, students must understand how to collaborate fairly and hold a respectful exchange of ideas. Before implementing math talk in the classroom, brainstorm a list of classroom norms for how community members will participate and behave during the discussion. (See the picture below for an example of some of the norms you may want to include.)
How to Implement Math Talk through Open-Strategy Sharing
Before the Discussion
- Define your goal: What do you hope to accomplish? Goals for math talk include wanting students to: listen and compare methods used to solve a problem, look for the most efficient way to solve a problem, generate explanations for why a particular solution works, or examine why one solution is correct and why another is not.
- Choose a Problem: This depends on your goal. If you want to highlight a variety of strategies that can be used to solve a problem, then choose a problem with multiple solution strategies. If you are examining why one solution is correct over another, then choose a problem where students frequently make missteps in their solution strategy. Use my Back to School Math Problem Solving Pack to get you started! You can find it in my TpT store.
- Anticipate Student Responses: In order to create the best discussion opportunities, think about how students may respond to a particular problem, and create a plan to address any misconceptions that may develop. In addition, if there is an obscure solution that you think may be missed, then plant the seed with a student group or be prepared to introduce the strategy yourself. For example, you can say, “When I looked at this problem, I thought that I could solve the problem like this (show the strategy). How does this strategy compare to the others we used today?”
During the Discussion
- Monitor Student Responses: During this time observe the interactions of the groups and make notes about their solution strategies. Also, note any observed areas of concern to address at a later time.
- Select Students to Present: Based on your observations, determine which solution strategies to highlight that will best help you accomplish your goal. For example, if you want to emphasize a variety of strategies to solve a particular problem, select solutions that vary from one another.
- Sequence Student Responses: Order the presentation of the solution strategies in a manner that will allow you to maximize the students’ learning experience. For example, beginning with the most widely used strategy and then moving to the more abstract strategies may draw students’ attention to new methods. Similarly, beginning with the more concrete strategies will give students the opportunity to move from a more concrete to an abstract understanding.
- Connect Student Responses: The most important aspect of using math talk in the classroom is the connections between solutions that you and the students make. In the beginning students will need your support to make these connections. For example, if you sequence the presentations from less sophisticated to more sophisticated, you can have students discuss the similarities and differences between the solutions. You can also discuss efficiency. Which process is more efficient?
- The “Open-Ended Questions” chart above has a great list of questions both you and the students can use during math talk to make connections and analyze solution strategies. Find the download for my Open-Ended Questions for Accountable Math Talk in my TpT store.
- Use the “Math Talk Moves” poster above to teach students how to make connections and respond to others during math talk. The poster describes moves made by the student. The teacher should teach these moves and encourage their use during discussion. You may even want to have a “Move of the Day/Week” to highlight ways to connect student ideas. Additionally, you may want to include these in the students’ math notebooks or tape a copy to their desks to refer to during the discussion. Please note: Several resources describe “Turn and Talk” as a math talk move. Because I chose to focus my poster on student moves, I did not include it; however, it is a useful move to use during math talk so that students have another participant to share ideas with during large class discussions. From that point, they can choose a student move to keep the conversation going or choose one move for a class-wide share-out. To get your own copy of my Math Talk Moves poster, please visit my TpT store.
- Participation is key! Sometimes it’s hard to get all students to participate because they’re afraid to take risks. One of the ways you can get your more reluctant students to take part in the conversation is through the use of hand signals, such as teaching students to use the American Sign Language symbol for Y (see picture below) to indicate that they agree with someone else’s thinking. Once reluctant students see that they’re not alone, they may be willing to participate more.
After the Discussion
After reviewing the students’ solutions and listening to their presentations, use the information that you gathered to determine the next steps. The following activities will help extend and deepen the students’ understanding of the intended content and skills.
- Look for Areas of Concern: Reviewing the solutions for common errors or misconceptions may provide material for a mini-lesson or content for an additional problem solving task at a later date.
- Check for Reasonableness: It is essential that students develop the ability to verify their solutions and check them for reasonableness. After the discussion you can ask each group to develop a method to check their strategy for reasonableness or choose a specific solution and ask students to determine a method to check for reasonableness. Be sure to have students share and compare their strategies.
- Justify the Solution: In addition to being able to make sense of a solution, students should be able to explain why a specific solution strategy leads to the correct answer. For this activity have students use pictures, numbers, and words to make sense of the solution and explain why it works.
- Look for What Went Wrong: One of the most powerful activities for students is to examine their mistakes. Use one of the solution strategies that did not lead to the correct answer (if available) and explore where the solution went wrong. After determining the misstep, allow students an opportunity to complete the remainder of the solution strategy. If you don’t have an incorrect solution strategy to use, create one yourself and say, “What if someone had done (show the strategy)?” Then, allow the students to discuss the error(s).
- Classroom Discussions by Suzanne H. Chapin, Catherine O’Connor, and Nancy Canavan Anderson
- Five Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein
- Intentional Talk by Elham Kazemi and Allison Hintz
Shametria is a newlywed and has been a Texas educator for 13 years. She’s currently a Teacher Mentor for first- and second-year teachers and is working toward a Doctoral degree in Mathematics Education. She is also a blogger (emerging, anyway) and teacher-author for all things math! Check out her Routty Math Teacher blog and Teachers Pay Teachers store for some additional teaching tidbits and freebies!
Books and Web Resources