Is a hot dog a sandwich?
When I first saw this question listed as an episode of the DebateMath podcast,
I asked my daughter what she thought and she was quick to say a resounding "No!"
But after pressing her to back up her answer, she talked through her reasoning and ended up changing her mind. It depends on your definition of a sandwich right?
This led nicely to my next question for my daughter: Is a square a rectangle?
The answer to this second question is more clear, but it was fun to debate back and forth with my daughter and push her to explain her reasoning.
Is Math Debatable?
If you think math is always cut and dried, think again! Many times in math, there is one clear answer, but this is not always the case. Math is much more controversial and debatable than you might think.
Take a look at the shape below and think about the definition of a trapezoid that you've always used:
This question is similar to the hotdog question: The answer depends on your definition! You would think that the definition of a trapezoid would be pretty straightforward, but there are actually TWO different definitions of a trapezoid.
The more common definition states that a trapezoid has exactly one set of parallel sides, but there is a second definition that states a trapezoid has at least one set of parallel sides.
Did you know not even all the states in the US agree on which definition to use? I didn't realize this until a teacher sent me a message about one of the questions in my Classifying Quadrilaterals Activity. (Good thing that activity is editable!)
How to Encourage Math Talks in the Classroom
We all know students can be super talkative about topics they're interested in, and then seem to clam right up when asked a math question.
One easy way to encourage students to talk about their math thinking is through debate! What is there to debate about math? LOTS!
I had the opportunity to sit down with Chris Luzniak and Rob Baier, the teachers behind the new DebateMath podcast and am excited to share with you what I've learned about using debates in a math classroom!
Think there's nothing debatable about math? Think again!
Chris and Rob like to debate things like:
What's wrong with I Do, We Do, You Do?
Should we cut quadratics?
Should students be forced to memorize?
Chris has been a math teacher since 2004, teaching in NYC, LA, and now Columbus, OH. His nearly 20 years of teaching mathematics began in New York City public schools, where he also founded and coached the Speech and Debate team. Through this combination of teaching and coaching, Chris has worked to develop debate routines that bring student voice and discussion into the math classroom. He is now a consultant and speaker who coaches teachers in both math and science to develop real-world debate activities for students. Some of his work can be seen at luzniak.com, and in his book Up for Debate! published by Stenhouse Publishers.
Rob has been a math educator for over 12 years and is now the Executive Director of STEM in a large urban school in Pennsylvania. For the last 4.5 years, he lead professional development sessions and workshops, provided math consultations for local school districts, and presented at statewide and national conferences. Most recently, Rob was the conference chair for the Pennsylvania Council of Teachers of Mathematics (PCTM) for 2021 and 2022.
Chris and Rob met in person at the PCTM conference in 2019. In 2021, they connected on Twitter over a debate about the definition of a trapezoid, where Chris brought up an idea for getting educators to discuss and debate complex topics in math and math education.
I met Chris and Rob at the PCTM conference this summer and am grateful they were willing to sit down and answer allll the questions I had.
Here's a peek into our conversation:
What is the Debate Math podcast all about?
The Debate Math podcast was designed for educators who want to hear and engage in debates about math topics and math pedagogy. Should we force students to memorize certain things? Is lecture an effective practice? And why do different states have different definitions of a trapezoid?
Too often we think of math as focused on answer-getting, but there is a lot more complexity and controversy within math and math education. We want to explore that.
Chris had an idea for this podcast, pre-pandemic, and Chris and Rob connected about the idea in 2021. The podcast is in true debate format, with opposing sides, opening statements, a questioning round, and closing arguments. We hope to make educators think more about their practice, and explore more nuance.
The underlying concern is that people are too quick to see things as neatly divided into right and wrong or 1’s and 0’s (binary), and we often forget that there is a gray area where we can agree.
We need to explore the nuances in our practice, and the DebateMath podcast aims to develop that.
Many people think of math as an area where there's always just one right answer or way to do things.
Can you give us some examples of debatable topics in math that you discuss on your podcast?
We think SO MUCH in math is actually debatable. However, in the typical American math classroom, we focus so much on getting the “right” answer or using the “right” method. For example: there isn’t only one way to solve a system of equations or factor a polynomial. Which method do you think is best? We can debate that!
Each of our episodes have made us think so much. For instance, the very first episode was about the definition of a trapezoid. We had a lot of fun with it, but we didn’t realize until we were in the debate that different states have different definitions of a trapezoid. Why is that? And why don’t we talk about that more with students. What’s great about debating (in math!) is that through the debate, learning occurs
What's been your favorite topic so far?
Chris: I think one of my favorites was Episode 3: a debate about whether or not students should be allowed to use notes on tests. Not only is it an interesting pedagogical question, but in this debate, we found four students willing to debate it. Two students talked about reasons notes should be allowed on tests, and two others debated that notes should not be allowed on tests. It was great to hear both sides of this argument from students!
Rob: I have enjoyed each episode so much, but I think one of my favorites was Episode 4: “Is a Hot Dog a Sandwich?” This was with Kyle Pearce and Jon Orr (Making Math Moments That Matter podcast) and their oldest daughters. We split them apart to show how the 3rd standard of mathematical practice (SMP) could be used with students in a classroom through debate. It was fun, silly, and insightful!
Any exciting debatable math topics coming up soon?
Yes! In September, our episode includes some excellent guests debating whether or not elementary teachers should specialize by subject, and in October we are taking on college admissions. We have teachers, a college counselor, and a university admissions director on to debate why AP Calculus seems to weigh so heavily in college admissions decisions.
And, of course, we just hosted our first-ever live debate at the PCTM conference, and the recording of that will be airing in November! It was a great debate about homework. Stay tuned for that!
Should math teachers be using debates in their classrooms with students?
What are some simple ways teachers can start incorporating debate into their teaching practices?
Chris: Absolutely! I often start class with five-minute debates. They can be whole class or small partner debates. They are great because they get students talking and thinking critically, and in math class, explanation and argumentation are so important. Throughout the year, I have students debating in many ways, short and long. The easiest way to get ideas for starting is to go to my website luzniak.com (take a look at the debate cards!) or check out my book Up for Debate! (affiliate link).
Want to learn more about using debates to encourage math talks in the classroom?
Make sure to check out the podcast at debatemath.com You can also find Chris at luzniak.com or @cluzniak and can find Rob at b3math.com or @Rob_Baier.
Thoughts? Is a hotdog a sandwich? Let me know what you think and don't forget to share this post with a friend!