Debate Math
by Dee Crescitelli (University of Louisville)
I love a good math argument. The teachers and students I work with often hear me say, "Oh - we have a disagreement about mathematics - GREAT!" I am excited to have students share an opinion about mathematics worth being passionate about.
For this reason, I was so excited when Chris Luzniak's Up for Debate: Exploring Math Through Argument book came out. In the book, he shares stories of students debating math in real classrooms, structures for getting students to talk, listen, and debate, and ideas for transforming math problems from existing curriculum resources into debatable ones.
Students are introduced to the structure of debate:
- An argument is a statement made with sound reasoning.
- Every argument has two key parts:
- Claim - the statement being made
- Warrant - the justification for the claim
- An argument is a claim plus a warrant: "My CLAIM is_________, and my WARRANT is__________."
He suggests establishing the routine with short debates about non-curricular subjects.
A student would state their argument about the best pet by making a claim and supporting it with their justification: "My claim is that dogs are the best pets, and my warrant is that they cheer us up when we are sad." Another student would then respond with a claim and a warrant. These responses may be making the same claim, but with different justifications, or making a different claim and warrant. For example, a supporting claim might be "I claim that dogs are the best pets, and my warrant is that they are extremely loyal." An opposing claim could be, "I disagree, and I claim that cats are the best pets, and my warrant is that they require less time to care for."
Students may be presented with a debate card with two sides for discussion. (See resources to learn more about and access debate cards.)
The best way to solve this problem is...
Students would then make a claim and a warrant for their selection of the "best" way to solve the problem.
A student may claim that Make 10 is the best way, with the justification that because 9 is so close to 10, it makes sense to see this problem as 10 + 7. What warrant would you use for a claim that Double + 1 is the "best" way to solve this problem?
In this case, the justifications are the heart of the mathematics as students share their understanding of addition in ways that make sense to them. This is the beauty of debating mathematics - students are naturally constructing arguments and using reasoning skills to justify their claims. Debates become more interesting when we push students to support their own opinions and preferences, such as asking, "What is the coolest way to represent 3×4?" or "What is the best way to solve 49 + 52?"
What I love most about the idea of math debates is how versatile this structure can be. The book was written for grades 6-12, but the basic structure of making a claim and justifying it can be adapted to elementary-grade topics as well. All you need is a problem with more than one possible solution path… and I have found that most math problems fit that category! I encourage you to experiment with ways to bring debate into your classrooms.
Resources
- Luzniak. C. (2020). Up for Debate! Exploring Math Through Argument. Portsmouth, NH: Stenhouse.
- Debate Math author site
- Bringing the Power of Debate to Math Class: Blog post with links to additional resources, including pre-made debate cards
