What Adults Can Learn from Debate

While I speak a lot about getting students to debate in math class, I recently had the opportunity to speak about what adults can learn from debate (at the OMCA 2024 Retreat!). It’s something I’ve been spending more and more time thinking about and working on. In our highly politicized environment, where everyone seems to be competing for a viral sound byte, I think we can learn a lot by slowing down and having deep nuanced conversations (debates!). Some of the things I’ve been talking about include:

1) Everyone’s voice matters.

In an argument, people may be talking over each other. Or one person could dominate the discussion. To avoid dominance or groupthink, we need to give everyone a chance to be heard. This is where debate comes in. Debate is a structured conversation, where each person has time to share their thoughts (like an opening statement). To avoid overlooking details or brushing someone’s ideas aside, we need to give everyone, especially those who may be shy or more hesitant to speak out, a chance to talk.

2) Disconfirmation can lead to truth more than confirmation.

It’s natural for us to side with someone who we agree with or who feels “right.” However, many topics have complexities and nuances that we can easily overlook. If we only listen to people we agree with, we may miss important details. Sometimes both sides have something important to add to the conversation, and if we aren’t open to learning how we might be wrong, we may miss things. The more we try to prove ourselves wrong, the more we’ll learn what is really “true.”

3) Our brains are efficient/lazy.

In, perhaps, an effort to conserve energy, our brains often look for the easiest or most efficient solution. This is where biases can affect our reasoning. We try to fit each new situation into a pattern. This is also why groups have a big influence on our thinking. It’s easier to go along with the crowd. It takes thoughtful, conscious effort to question and analyze our reactions. Listening to debates is where I force myself to hear out both sides and think critically about the topic.

In conclusion:

To paraphrase author/debater Bo Seo in his book Good Arguments: perhaps the opposite of bad arguments isn’t calm or peacefulness. Perhaps the opposite of bad arguments is good arguments. In other words, perhaps we need to lean into arguments more. We shouldn’t avoid difficult conversations. Rather, we should have structures in place to argue in a healthy way when there are disagreements.

That’s why I’m doing my part to train adults in having good arguments (like formal debates), where we can grow and learn together.

I only hope school and political leaders can someday model this…

Making Middle School Debatable!

I’ve had the privilege this past school year to visit and work with teachers and classrooms all around the U.S., and I have loved the times I’ve been able to model #DebateMath in the classroom. I wanted to share an amazing experience I had last semester. Some quick background: Using the Learning Lab model, I work with a group a teachers to plan a lesson that I teach the very next period. In several of these Learning Labs, a focus has been on using DebateMath to increase student discourse. Teachers have seen me present about DebateMath, but many are skeptical that it will work in their classroom with their students (which is why the Learning Labs can be so powerful!).

One teacher invited me to modify her lesson plan on GCF and LCM problems with her 6th graders. So we planned a lesson that involved DebateMath, and below are some highlights of the lesson.

1) First, I had to explain to students how to debate in math class. I introduced the Claim and Warrant sentence stem, and we started with something fun.

2) Then, students solved some problems involving GCF and LCM. However, instead of asking students to just solve the problem, we asked them whether it would be a GCF or LCM problem and to defend their answer!

3) Students were given time to practice a few problems, and we concluded with a debate on who was correct, using LCM or GCF:

Takeaways:

• Students were highly engaged the entire time in solving the problems because they had to justify in the debate format.
• After the lesson, the teacher shared that the FIRST student to start speaking had NEVER spoken up in class so far this school year!
• Students did well on the exit ticket, showing solid knowledge of the difference in an LCM vs GCF problem.
• Teachers who were in the room observing wanted to you the lesson as is for their own classes!

It only took us part of an period to plan and modify the lesson to include DebateMath. Teachers were excited by easily and smoothly it can be added to enhance a lesson and by how much it increased student discourse!

50 Fun Questions to Debate!

It started during the pandemic/remote teaching school years: In order to keep students joining conversations regularly, I wanted to start class with fun, non-mathy debate questions. I asked questions that we discussed for five minutes or less, and I wanted them to be engaging questions that students could not resist. The goal was to get students talking to each other, and as side benefits, I got to know more about my students and we got to have a little fun…all while building their argumentation skills!

I’ve come up with many questions over time, and I wanted to share 50 with you. They are broken down into groups for easier reading. I hope these inspire you to add your own too!

(Note: these were asked to high school students. So you may need to change some of the questions.)

I usually start with very general things like:

1. What is the best movie/TV show to watch right now?
2. What is the best song of all time?
3. What is the best sports team/player?
4. What is the best book you’ve read in school?

During remote teaching, we talked a lot about things at home and with family like:

5. What is the tastiest meal you have had at home?
6. What is the strangest thing one of your family members did this week?
7. What is the best thing a parent/guardian could say to you right now?
8. If you got a new pet, what would be the best animal for a pet?
9. Which app on your phone is the most important one to have?
10. If you had unlimited funds, what would be the best vacation (one you haven’t done yet?)?
11. Who was the best middle school teacher?

I often ask questions that involve food. They always go over well:

12. What is the best pizza topping?
13. What’s the best ice cream flavor?
14. What is the best school lunch?
15. What is the best dessert: Ice Cream or Cake?
16. What is the best breakfast food: Pancakes or Waffles?
17. What is the better red snack: Twizzlers or Red Vines?
18. What is the better mac and cheese flavor: Cheddar vs. White Cheddar?
19. Where is the best place to get coffee?
20. What fast food restaurant has the best food?
21. Would you say M&Ms are more similar to Skittles or a Hershey’s bar?
22. Are hamburgers more like tacos or peanut butter sandwiches?
23. Is a hotdog a sandwich?
24. Is cereal a soup?

Animals are another fun topic for students:

25. Which animal is the cutest?
26. What animal would make the worst pet?
27. Do you think animals should be kept in zoos?
28. Are penguins more like whales or eagles?
29. Are bees more like airplanes or ants?

Some other interesting ones include:

30. Who makes better shoes: Vans or Nike?
31. What is the most relaxing: Mountains or the Ocean?
32. If you had to move, would you rather live in NY or California?
33. What is the best time of day?
34. What is the best Olympic sport?
35. Should we allow electric scooters on the sidewalks?
36. Should everyone be required to vote?

I like to hear students’ thoughts about school and math too:

37. Should high school be required for everyone?
38. Should homework be graded?
39. Should teachers allow notes on tests?
40. Should teachers allow calculators on tests?
41. Should schools offer AP tests?
42. Is it better to do work on paper or digitally?
43. Should social media be banned for students?
44. Should schools have dress codes?
45. What is more important: algebra or geometry?
46. Is a rectangle a trapezoid?

When we really want to get creative, “would you rather” questions are fun:

47. Would you rather have the ability to breathe under water or the ability to fly?
48. Would you rather have three arms or two mouths?
49. Would you rather be rich or be famous?
50. Would you rather have to constantly eat all day or have hiccups every time you take a drink?

BONUS!

My list could go on, but for now I wanted to add a few websites that you could also use for more debate/discussion ideas and prompts:

• Which One Doesn’t Belong? This site has so many wonderful prompts. There are four options for each prompt, and each one has a reason why it could “not belong.” These are great for students because there isn’t one “right” answer that we are looking for. It helps them see that there could be multiple answers at times.
• Would You Rather Math? John Stevens has put together some great prompts that have students decide on an option and use mathematics to justify their decisions.
• What’s Going On in This Graph? The New York Times has this free feature that pulls unique displays of data from past articles. The articles are not given, and students are asked to take time to make sense of the graph.
• Sandwich Chat Shelby Strong & Justin Aion have shared their presentation materials on how they use questions like Is a hotdog a sandwich?. Included in the slides are more fun questions like: How do giraffes wear ties? and How would a centaur wear pants?

Debate Math on Desmos!

I’ve slowly been turning debate cards into Desmos activities. It started during the pandemic, when I had to move things online, and I keep adding new ones from time to time. Now there is a growing #DebateMath Collection.

I wanted it to be a similar experience to the debate cards, where a pair of students work together to solve problems in two different ways (one way for each member of the pair). Because they are both (1) solving the problem and (2) giving an argument for their method, I broke the process down to three steps. These steps are below and part of the Desmos activities.

*First, the pair has to choose (or is assigned) roles: Partner A and Partner B.

STEP 1: Solve the problem with your given directions and enter your answer. Example:

STEP 2: Explain to your partner your argument for your way of solving (verbal only). Example:

STEP 3: As a pair, decide on the best method for this problem and type your argument (written). Example:

(This part is new!)

The whole collection of activities can be found here. Let me know your thoughts if you try it out!

Everything is Nuanced (CMC-S 2022)

Started off the CMC-South conference this year with a pre-conference session by Dr. Ilana Horn, and it was fabulous (*full disclosure, I’m already in the Ilana Horn fan club)! The session shook my world a little bit, as it pushed back on the idea of “best practices,” specifically that this quick phrase inhibits teacher learning.

I’ve heard the phrase best practices used so much at schools I’ve worked at all over the country. It’s a go-to phrase for what the person saying it thinks “good teaching” is.

Part of Dr. Horn’s message (or at least how I interpreted it) was that we are quick to use this phrase “best practices,” but are there even agreed upon best practices for teaching math? Some of the books or articles we might point to are at times in contradiction with other books or articles. Teaching is very contextual and situational, and this phrase removes all that nuance. It makes it seem there are some absolute truths.

As Dr. Horn said, “Teacher knowledge is socially embedded, ambiguous, and contested.” It’s so complex, that best practices can look different for different teachers, in different years, or across different places.

It reminded me a lot of my DebateMath work and our DebateMath podcast. I want to explore/uncover how complicated and nuanced math is, in the same way Dr. Horn is talking about for this phrase.

Why Another Podcast?

For those who haven’t heard, I (with my collaborator Rob Baier) started the #DebateMath Podcast recently. The first episode two episodes are scheduled to air at the end of January 2022!

I wanted to take a moment to share some of the thinking behind the creation of this podcast, explore why we really wanted and needed to do this. There are four main reasons behind this podcast.

1. We need more than a speech (sometimes). I love attending conferences and listening to speakers, but so often we just hear one side of an idea. Sometimes, I want (and need) to hear multiple view points on an idea to really understand it, to think about the implications and consequences. I don’t want teachers to jump on a new trend just because one speaker sounded sexy. I want teachers to hear multiple perspectives as they ponder what is best for their classroom and make even more informed decisions. Additionally, when we feel strongly about an idea, in this current climate, it is important to be prepared for push-back. Hearing two sides in a debate can help us prepare for the counterarguments we may get from colleagues, parents, admin, or students. Also, through the activity of debate, listeners and speakers are engaged because there’s a “competitive” aspect to it. You want to know who will “win” or be most convincing. So you can’t help but lean in a little more.
2. We must explore nuance. I see so many ideas passed around on social media, and initially they sound good. However, we don’t always have the time or space to think through all the consequences, to think through all the nuance. I think we need to take more good ideas with a grain of salt. Also, when something is working well for someone else, there are so many things which led up to that new pedagogical move, that new technique or activity, that could be easily overlooked. We need to unpack all the layers about what made this particular idea work at this time and place, and how would it work for us in our own, unique (different) setting.
3. The voice can provide more colors of tone. In listening to podcasts and recording our own, I’ve seen how much more can be expressed in the tone of an argument through the voice than in writing. There are good ideas shared in writing both in blogs and on social media, but without the tone (serious, sarcastic, or whatever), the message can easily get confused. Listening to another human explain in the audio (plus there will be YouTube videos of the episodes as well) adds so much more detail and clarity. I’ve read about how humans have evolved to think socially, and listening to a podcast provides a version of this.
4. Podcasts are powerful. I listen to so many podcasts, when I’m driving to/from work, when I’m on the treadmill at the gym, when I’m alone at home and cleaning up, etc. It’s a great way for me to listen and think while doing simple tasks. We can listen to them in so many places and learn so much along the way. And podcasts can be as long as they need to be. We are not making TV shows that all have to be a certain length. Some of our debates may only be 20 minutes, some may be longer. Rob and I have been doing our best to give enough time to flesh out the sides of a debate, but not to let it go on too long. Additionally, podcasts can stay relevant. We are recording them once a month, and they can reflect current trends and topics that are up for debate!

Our goal is to release one episode a month. Rob and I are doing this in our spare time as educators, and we want to take time and care with each episode to give everyone something great to listen to. It is a lot of work to coordinate people/teams on two sides of a debate, give them time and help to prepare for the debate, and then actually do a live recording. But we enjoy it! It just will take us time to do one episode at at time.

I have to note that it has been a pleasure having chats with educators who are potential guests and asking them what they are passionate about. It has been wonderful to hear topics come up that I never thought some people were deeply pondering. And I’m excited that these passions can be shared with listeners on the podcast.

We are always looking for new guests and topics, too. We are slow moving, but anyone can suggest a name or topic idea on the website: debatemath.com.

I am so looking forward to putting this out in the world soon. I hope my fellow math educators will enjoy. Hope you subscribe ASAP on Apple Podcasts, Spotify, or wherever you listen to podcasts so you don’t miss one episode! And follow the Twitter handle @DebateMathPod and #DebateMathPod so you can get all the updates, join in the follow up conversations, and vote for your “winner” of each debate!

ps. A special “Episode 0” will be the first one, airing January 20, 2022. Enjoy!

pps. When I listen to podcasts, I usually play them at 1.25 or 1.5 speed to get through them a little faster. I’m not sure how ours will sound sped up, but it’s an option for those who are short on time!

CMC 2021

Waking up at the start of Day 2 of CMC – South 2021 and my mind is abuzz with so many great ideas I learned yesterday. I need to write some things down. I was first so excited/overwhelmed just to finally be in person with wonderful math teacher people again. It was emotional for me. I loved it! Some sessions that stick out right now:

1) Mike Flynn’s session on being a teacher and advocate really stands out the most. I think a lot about the current political climate we are in and all the school board meetings in the news right now with lots of aggressive and angry speakers. How can we, as teachers, be effective advocates for our students, our curriculum, etc?

Mike talked about the roles in advocacy (Agitator, Innovator, Orchestrator) and how each one is important. He stressed how we need to have a team (an advocacy team) that works together. The superhero mentality (one person making all the difference) does not lead to change. He also talked about the mix of advocacy and inquiry. There need to be times that advocates listen, observe, ask questions. We need to hear what people are thinking and build relationship (just like in our classrooms!).

2) Dr. Cathery Yeh gave a talk titled “Mathematics as a Human Right,” which immediately drew me in. Early on, she had a slide that said “All students should have access to rigorous mathematical learning that respects and honors their identities and ways of knowing.” Boom.

On top of that, one big take away was that Dr. Yeh asks students:

• What are your access needs?
• What supports your learning?

Then she asked us to take time and write or discuss with a neighbor about our access needs (us adults!). I really struggled with this, as my table talked about, because I don’t think anyone had ever asked me this. In the American culture of “power through” and “figure it out” for yourself, I’ve never been asked or took the time to think about what my access needs are for various things. It lead to a great discussion with the teachers I was chatting with!

Debate Questions on Assessments

Since debate and argumentation are a regular part of my math classes, I also find it important to incorporate them into assessments. That is, I want students to create arguments on tests and quizzes. I’ve played with a few varieties over the years, but what I use most often (and what my students have come to expect) is a question like the following on every test.

This question is from a test early in the year in PreCalc. I don’t intend these questions to be too involved in the beginning of the year. I mostly want to see if they can give a decent argument, and I spend a lot effort giving written feedback on their arguments. My goal is to make clear what I expect on future tests (when I will be a little pickier in my grading).

Question B is one of my favorites to give feedback on and talk about with the whole class afterward. It is pretty clear to all students that the angle drawn is way more than 200 degrees. However, this is where I really get to talk about a quality and convincing argument.

Three typical pitfalls include:

• Assuming – every year I get students who say that the pictured angle is 300 degrees because that is roughly what matches a point on their unit circle diagram. These students are only considering the key angles that our class has memorized coordinates for (every 30 or 45 degrees). My comments include the question: what if this is 302 degrees? They are correct that the angle is not 200, but their argument is not necessarily a true statement.
• Vagueness – other students correctly say the angle is not 200 degrees, but then say vague ideas, presumably to have something written but possibly unsure how to be convincing. This includes statements like: This angle is not 200 and my warrant is that it is big and probably bigger than 200. A student who says this might have been able to give a convincing argument but was never pushed or had it made clear what was expected. This is where I like to talk with the whole class about precision.
• Missing Connections – This last group is the one I really want to talk about with the whole class. This includes students who might say something like: This angle is not 200 and my warrant is that it is in the 4th quadrant. This student is SO CLOSE to having a solid argument (and at the beginning of the year I may give them credit, but with lots of comments). They are just missing a connection. I ask what about the 4th quadrant makes that angle not 200?

There are definitely some students who give a good argument from the start, and I show those to the whole class as well. I really like to show when someone says something like

My claim is that angle is not 200 degrees and my warrant is that it is in the 4th quadrant and angles in that quadrant are between 270 and 360 degrees.

This gives me a great contrast to show the students who have a missing connection to see what exactly they were missing.

*One more note about these argument questions is that they really help emphasize that there is not just one correct way to answer a problem. You don’t have to talk about the 4th quadrant to be correct. Other students might say:

• That angle is not 200 degrees and my warrant is that 200 degrees is in the third quadrant and this angle is not.
• That angle is not 200 degrees and my warrant is that it is greater than 270 degrees.

And this is just the start. I love building from here!

Igniting a Softer Side of Math

I’ve been privileged to be invited to give some Ignite talks (5 min talks with 20 powerpoint slides automatically advancing every 15 seconds) at conferences in the past two years. I have recordings of both, and I wanted to put them here to refer back to. Both are part of my journey into seeing math as more than a place where we focus on right answers, where we embrace ambiguity and the human side of learning math.

The first one “Math for Healing” was from late 2019.

It was given at the NorthWest Math Conference and then at CMC South (where the recording was made).

The second is “Non-Binary Math” from early 2021. It was given at two virtual NCTM conferences.

In Praise of Warm Ups

I haven’t blogged much at all in this year of remote teaching, but I’m getting back at it now!

I’ve done a lot of work with teachers in the past few years, and one thing that keeps coming up is how much the warm up activity can be a game changer for classes.

As teachers, we can easily feel so overwhelmed with all the content we *must* teach, all that we have to somehow squeeze into one school year, that it can be really difficult to think about the other things you want to focus on. This includes the standards of math practice (persevering, problem solving!), number sense and estimation activities (Clothesline math, Estimation180), and stats and data exploration (What’s Going On in This Graph?), not to mention just having time to Play With Your Math. And of course, there’s always a need to find time to DebateMath!

So how do we fit it all in? How do we help develop mathematical and problem solving skills? How do we make time to help students see that math is more than this year’s curriculum?

My solution is to use the warm up time for this. I take 5-7mins (sometimes a little more or a little less) at the start of each class to do something that is outside the curriculum. Once a week, we notice and wonder at a NYTimes graph. Once a week we have a short debate or solve a math riddle. Each day, we start by seeing math as interesting, playful, and/or relevant. We might start an interesting puzzle or discussion that we can’t finish, but the rest is left for students to explore as they want to. Math might spill over into their lunch or family time later that day or another.

Not only does it get students wanting to get to class on time and get started, but it provides a joyful moment to start the class. It also shows students that math is not just about learning to use the quadratic formula. Students always write on their end of year surveys that those 5mins of “outside the box” math really changed the way they see math class. They see math as interesting and important.

And as a bonus, I see the students being more resilient and playful in the rest of the class. When they hit challenges in the curriculum, they approach them as puzzles. “Let’s see what we can figure out,” is a phrase I often hear.