This month, Transformation Tuesday will feature math routines that can be used to boost student achievement. Last week, I linked to a guest blog article that wrote about number talks for Rachel Lynette’s Minds in Bloom. Missed it? Check it out here! This week, Transformation Tuesday is featuring another powerful math routine called math talk.
What is Math Talk?
The National Council of Teachers of Mathematics (NCTM) defines math talk as “the ways of representing, thinking, talking, and agreeing and disagreeing that teachers and students use to engage in [mathematical] tasks” (NCTM, 1991). Effective communication about mathematics is essential to help students develop the thinking, self-questioning, and explanation skills needed to master required skills and concepts.
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.
How to Implement Math Talk through Open-Strategy Sharing
As with any lesson, it is essential to create a plan for using math talk in the classroom. During open strategy sharing, students discuss how they solved a particular problem. The students listen and share their ideas. The teacher probes the students with questions related to how they determined the solution and why they choose a particular solution path. In addition, the teacher highlights a variety of strategies and emphasizes the similarities and differences among them.
Use the following steps to help you implement math talk in the classroom.
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, choose a problem with multiple solution strategies. If you are examining why one solution is correct over another, choose a problem where students frequently make missteps in their solution strategy.
- 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, 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 obscure strategies may draw students’ attention to new methods. Similarly, beginning with the more concrete strategies will give students the opportunity to move from concrete to 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?
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).
Implementing and planning regular math talk sessions will support the development of strong communication skills and deepen the students’ ability to reason and think critically about the intended content and skills.
Freebie Alert! You can find a printable download of the two posters above here.
Reference: National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Retrieved from http://www.nctm.org/standards/content.aspx?id=26628
Sound Off! What math routines do you use?