Kyle Pearce: Hey, Hey, there Math Moment makers. In this special episode of the podcast, we're going to be highlighting and showcasing one of our favorite new podcasts that are out there, it's the DebateMath Podcast. Recently, in episode 4 of the DebateMath Podcast, both Jon and his daughter, Lucy went head to head against myself and my daughter, Talia, in the debate, is a hotdog a sandwich?

Jon Orr: Yeah. In this crossposted episode, you're going to hear the two hosts of the DebateMath Podcast, Chris Luzniak and Rob Baier, skillfully posed questions that prompt some insightful thinking, as well you're going to hear some fits of laughter here in this episode. We're excited to share that with you. Let's get to it, Kyle.

Kyle Pearce: All right, here we go. Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr, and we are from Makemathmoments.com. We are two math teachers who together.

Kyle Pearce: With you, the community of Math Moment makers worldwide who want to build and deliver problem-based math lessons that spark curiosity.

Jon Orr: Fuel sense making.

Kyle Pearce: And ignite your teacher moves. My friends, we are super excited to be able to share this episode. As we said, from the DebateMath Podcast, Chris and Rob are both great colleagues, but also great facilitators of discourse, and you're going to hear that in this episode. Jon, I don't know about you when they reached out to us and said, "Hey, listen, we've got this pretty wild episode." Because usually I believe on their podcast, we've listened to the first three episodes and our episode as well, they actually bring on educators to engage in this process. And yet, we went all the way down, all the way down to Grade 2 for my daughter Talia, and Lucy's what, Grade 5, Grade 6?

Jon Orr: Six. Six.

Kyle Pearce: Grade 6 for a debate, and I'll be honest, Jon, at first, I was kind of a little nervous. Like I was like...

Jon Orr: Me too.

Kyle Pearce: ... I don't know what this is going to be like, I've never even... I was never on a debate team or anything like that.

Jon Orr: Me either.

Kyle Pearce: But we trusted the process and I'm telling you how awesome. I felt so great for the girls who got this experience. I had a little bit of fun grind in YouTube, in the conversation.

Jon Orr: Totally, totally, totally. Yeah, and Chris and Rob have done such a great job of implementing debates in their classrooms. Chris, he's got a book out on DebateMath. He's got his website that gives you so many resources on debating in math class. We actually, I think it was a couple years ago, we were in his session at NCTM, which he got people up to debate different ideas like involving debate in your classroom is such a great idea and that's the whole purpose of this new podcast that they've started in this last year. It gives you so many benefits to think about why reasoning improving can be brought out through debate.
And that you'll see that here in this episode with us. And like Kyle said, our two daughters. Before we get into our episode, if you want to listen to more DebateMath Podcast, you can search it on any podcast platform. They're on all of them. If you want a little bit more deep dive, you can head on over to Luzniak.com/podcast to learn a little more. That's L-U-Zed, hey, I said Zed, that's right, N-I-A-K.com/podcast to learn a little bit more. Kyle, let's play it on them.

Kyle Pearce: Let's do it.

Jon Orr: Let's hit record here on the DebateMath Podcast from Episode 4 of that same name. Here we go.

Kyle Pearce: All right. See you on the other side.

Chris Luzniak: Common Core Standard of Math Practice number three states that we should have students construct viable arguments and critique the reasoning of others. Let's get some practice with that.

Rob Baier: We have a very unique debate today with some possibly familiar faces and names who you normally see together, but we decided to split them up.

Chris Luzniak: We wanted to have some fun and explore a debate you may have had at some point and exercise and definitions and argumentation that can be fun or serious.

Rob Baier: Today, we have two family teams of two debating the resolution, a hotdog is a sandwich.

Chris Luzniak: And here debating for the resolution that a hotdog is a sandwich, we have a fantastic father daughter team led by a high school math teacher, Jon Orr. Hi, Jon.

Jon Orr: Hey, Chris, thanks so much for having us, and with me today is my daughter, Lucy Orr, a Grade 6 student here in Tilbury.

Chris Luzniak: Hi, Lucy.

Lucy: Hi.

Chris Luzniak: Jon, can you tell us our listeners where you are and what your current role is?

Jon Orr: Yeah, sure thing. We live in Tilbury, Ontario, Canada, which is just a little to west of Toronto and actually a little south of Detroit so pretty close to Detroit, very close to where Kyle is from as well. I'm a high school math teacher. Right now, I am teaching three different sections. I've got a Grade 10 class. I've got a Grade 11, 12 class and I've got a Grade 9 class.

Chris Luzniak: Very good. Lucy, can you tell us what grade you're in and what math topic you're learning right now?

Lucy: Grade 6, and right now, we're learning about fractions, decimals and percentage altogether.

Chris Luzniak: Excellent. All right. Now, the question we ask all of our guests and I'll throw this to you here, Jon, when did math first become controversial to you?

Jon Orr: Yeah. You know what? I knew you guys were going to ask this because of the episodes I've listened to in the past. I feel like when I first started teaching, I felt like as a math teacher, there was one way to teach math. It was like, this is the way my dad, as a math teacher, I had seen him teach math. I had seen all my teachers teach at the exact same way he taught math. When I became a math teacher and started to realize that I needed to change the way I was teaching math, because I taught math in that very traditional way that my father did it, the way my alumni high school teachers did it. When I realized I needed to change that, it almost became controversial because I was doing something different and it was different than what my dad had done.
It was different than what my teachers had done, the teachers in my department were doing. And so, I felt like it was like I was an outsider and I know there's some other people that are like that too. I felt like I didn't realize that math could be excluding people. I felt excluded from my school and my department because I was doing those things. It was my first instance or my first glance of realizing that, that math can exclude people. Since then, I've learned so many different ways Math can exclude people and it's a big journey of mine to like, think about how can I include as many people as we can into mathematics learning. But that was my kind of first kind of switch that could possibly math itself, math teaching, math learning can be that thing, that separates individuals.

Chris Luzniak: Very good. Thank you, and welcome to you both.

Jon Orr: Thank you for having us. We're excited.

Rob Baier: In here debating against the resolution that a hotdog is not a sandwich, we have a fantastic father-daughter team led by K-12 math consultant and high school math teacher, Kyle Pearce. Hi, Kyle.

Kyle Pearce: Hey, how are we doing friends? Thanks for having us.

Rob Baier: Hey, can you tell us where you are and what your current role is?

Kyle Pearce: My current role, as you mentioned, is K to 12 math consultant. And like Jon came out of the secondary panel so I spent all of my own classroom time in the secondary panel. Now, that I'm in this role, though, I'm spending tons of time in elementary and that's where I've done, I would argue most of my pedagogical learning as well as my content knowledge learning. It's been fantastic journey and I'm in Belle River, Ontario with my daughter, Talia, I'll let her introduce herself in a moment. And that is just about 20 minutes up the road from Jon, so just south of Detroit and Windsor, Ontario and three or so hours away from Toronto. That's us.

Rob Baier: And hi Talia, can you tell us what grade you're in and what math topic you've most recently been learning?

Talia: I'm in Grade 4 and I'm learning multiplication and division.

Rob Baier: Oh wow. All right. That's exciting stuff. Now so, Kyle, the question that we ask all of our guests, when did math first become controversial to you?

Kyle Pearce: I knew Jon was going to say what he just said and my story is an awful lot like his, so I changed my thoughts on that a little bit. My story, I thought I knew a lot about mathematics when I went into university because my grades suggested that I did. I never really thought I knew much about it, but the grades said it, so I went with that. And going past my experience, I had a lot of struggles in university with math, but then into teaching, what I realized at some point was holy smokes, like I hadn't seen the conceptual side of the math. I know that still sounds a lot like Jon's story, but what I'm realizing more and more now, as we dig into the nuance of how the math develops, that there's such a massive story that we could tell, and we could learn as both students and educators that was never told, like I never experienced that side.
It's so interesting because now that I'm in this role and I'm trying to help other educators see that side, it's very controversial because a lot of people say like, this is just the way it is, right? Again, still mirroring a lot of what Jon said here. I just find that once you have your own epiphanies, about how, for example, Talia's doing multiplication and division that, hey, there's two types of division. We talk about it on the podcast all the time. That's my big epiphany over the past couple of years. And that it influences so many other concepts up the roadmap, including ratios and rates. That to me is like mind blowing.
There's so much controversy when we get into that proportional reasoning land when we start saying what's a ratio, what's a rate, how does it work? All of those things to me makes math really controversial when all the way through my own learning, it was pretty simplistic. Like I thought it was just like you pump in some numbers and outcome some answers and that's what it is. I look at it more like you would look at like a literacy sub, like how we look at English, how there's so many different perspectives to it. For me, I think that's such a fascinating discovery for myself and for all of us in the math world, to be able to sort of bring that to more students that are growing up.

Chris Luzniak: Excellent. Thank you both. With that, let's get into the debate. We begin with opening statements from each of our speakers, you each have two minutes to present your arguments.

Rob Baier: And based on the coin flip before this recording, we are starting with the pro side that a hotdog is a sandwich, so Jon and Lucy, you are first. Lucy, are you ready? Your time will begin right now.

Jon Orr: All right. Thanks so much, guys. Lucy is going to, we've prepared an opening statement together, but Lucy, hey, she's got the guts here. She's going to read it out loud for everybody. All right, Lucy, take it away.

Lucy: I believe that there's a bunch of things that are sandwiches like an Oreo cookie is a sandwich and ice cream sandwich is a sandwich and a peanut butter jelly sandwich is a sandwich. Also, a hamburger is a sandwich. So why can't the meat and a hotdog and with bread be a sandwich, it can because all those other things are sandwiches. They're just not called sandwiches. I believe the hotdog is between the bread or on top of the bread to be a sandwich.
Also, technically a piece of bread with any sort of filling inside is a sandwich. Just because something's not called a sandwich, doesn't necessarily mean that is not a sandwich. It's basically a special type of sandwich. Like my dad's favorite sandwich is that Reuben sandwich.

Jon Orr: That's yummy.

Lucy: It's just called something different, so that is a special type of sandwich. That's why I believe that a hotdog is a sandwich.

Kyle Pearce: Well done.

Chris Luzniak: Thank you. Now, we'll hear from the opposing side, that's Kyle and Talia. You are opposed to the fact that a hotdog is a sandwich and you have two minutes and your time begins now.

Kyle Pearce: All right, Talia is going to take us through this one as well. Go for it, T-bird.

Talia: Say you had a busy day and you're looking forward to your next meal. Your parents ask you what you want on your sandwich. You say, I'm so hungry, I will take any sandwich, but do you know what I guarantee they won't give me a hotdog? Because a hotdog is definitely not a sandwich. Here are three warrants why I think a hotdog is different than a sandwich. A sandwich has two pieces of bread while a hotdog bun is a single piece of bread. When's the last time you've heard someone ask for a single piece of bread for a sandwich.
You add toppings to a hotdog without removing a bun, while the ingredients added to a sandwich require removing the top piece of bread. You can almost add unlimited amount of toppings to a sandwich, whereas a hotdog has its limits with no bread to hold it in. For these three warrants, it should be clear to all that a hotdog is clearly not a sandwich and has its own unique category outside of the sandwich category.

Rob Baier: Wow. So you gave us a lot to think about. One side is saying that a sandwich is literally bread with filling, and the other side is saying, if I ask for a sandwich, they're not going to give me a hotdog.

Chris Luzniak: Let's dive into a little more here, then our question around, does temperature matter? This is for both teams. Does it matter if it's hot or cold to call it a sandwich? And maybe start over here with Talia, I see you nodding.

Kyle Pearce: Yeah, I don't know if this came up in our pre-planning meeting here, what do you think?

Talia: For a hotdog usually it has like the hotdog is usually warm.

Kyle Pearce: Okay.

Talia: Then a sandwich, you could have something warm in it, but it's usually not a hotdog.

Chris Luzniak: Lucy, do you want to add anything to that?

Lucy: A hamburger's warm.

Jon Orr: Yeah, that's the warm sandwich.

Kyle Pearce: Ooh, there you go. Okay.

Rob Baier: Are you able to have a cold sandwich?

Jon Orr: I was just saying, I especially like on Thanksgiving the next day, hot turkey sandwiches. And you know what an interesting thing about a hot turkey sandwich, even though the sandwich is hot because obviously we've all had sandwiches that are cold, but a hot turkey sandwich, a lot of times it also called it open-face sandwich and which is one piece of bread, right? One piece of bread opened and then you put the meat on and then there's gravy on top of that. Yeah, open-face sandwich with one piece of bread is a hot sandwich. Still called the sandwich.

Kyle Pearce: When he said open-face sandwich, it made it sound as if you have to specifically articulate that part of the actual sandwich was missing. Like it was like it's open-face because it's not like a regular sandwich.

Jon Orr: If you went to a restaurant and asked for a hot turkey sandwich, you don't have to articulate that it is an open-face sandwich. It's just a special name we give to that type of sandwich.

Kyle Pearce: I feel like the story changed. What do you think? I don't know, but that's good. That's good.

Jon Orr: I don't know if the story changed.

Chris Luzniak: Kind of following up then, I'm curious about both sides your definition, does it have to have like a top and a bottom bread or whatever on top and bottom? Or can it be just open-faced?

Kyle Pearce: Yeah, see, I think our definition and this is what makes this and many other debates very interesting as sort of what is your definition, I think we've used the definition that a sandwich has two pieces of bread, right? Because that was something in your warrants as well.

Talia: Because a one piece of bread is not really a sandwich.

Kyle Pearce: Yeah, that just feels so intuitive.

Talia: A sandwich has two pieces of bread to hold it all together. But I don't know, like if you have one piece of bread, it's not a sandwich.

Jon Orr: Right.

Rob Baier: Talia, can I ask you a question? When we think of a sandwich, does it have to be bread? Could we have two leaves of lettuce and have some toppings in between the lettuce? Would that still be considered a sandwich?

Talia: Yeah.

Rob Baier: Or does it have to be bread?

Talia: It doesn't have to be bread, but it just has to be two things that holds all the stuff inside.

Kyle Pearce: Oh, so it's almost like you're... Yeah, that's a really good question, because I think you and I were saying bread, but now we're sort of saying that didn't matter as much as the twoness of it, right? Would you agree? We were thinking like you have to have these two things to hold it together.

Jon Orr: I think we're curious over here about a question for you guys.

Lucy: Is a wrap a sandwich?

Jon Orr: Yeah, if you use a wrap, it's a sandwich, is that a sandwich?

Kyle Pearce: No, not for us.

Talia: Because it's called a wrap, because if it was a sandwich, it would be called a sandwich, but it's called a wrap.

Jon Orr: Gotcha.

Kyle Pearce: Special own category. Just like a hotdog.

Jon Orr: It's definitely special. Almost curious also too, it's like the fact that you're saying two separate pieces, but we could have this bending nature that creates a top. Wouldn't you say like if I took a big piece of bread instead of cutting, because really two pieces of bread is from the same loaf, wouldn't you say so? Right? It's like, we cut the same piece of bread, which is a loaf of bread is the same piece of bread. You cut it and then you put it on top. Now, isn't that the same as just say, let's say we had a big piece of bread and then we just wrapped it on top like that? Wouldn't you think that if I had a big piece of bread and I wrapped the top like that, isn't that a sandwich?

Talia: Well, it could be, but if that would be basically like a sub.

Jon Orr: Yeah, that's true, is a sub sandwich.

Talia: Technically.

Jon Orr: I want to keep going here. Yeah, there's like a... Because a hotdog bun is just the wrap, it's wrapped, right?

Talia: Yeah, but it has...

Jon Orr: The hotdog buns is wrapped around the hotdog.

Talia: It has a hotdog in it.

Jon Orr: When you put it inaudible hotdog side ways then you have a top and a bottom.

Talia: Yeah, but if you put a hotdog in a sandwich, usually you would be like, that's different. Usually, if you go to a hotdog vendor and you say, give me a sandwich, they're going to look at you like you're crazy.

Jon Orr: True.

Talia: Because they wouldn't know what you mean.

Kyle Pearce: This is just it. It's interesting though, I feel like you're going down to first principles of sandwich making, Jon, which I think is fantastic, right? Like going all the way back to the loaf before it was cut and sort of making it work that way, but I think I'm almost getting more clear on our characteristics of a sandwich or a hotdog. For us, it's that oneness versus that twoness like a wrap is like one, typically like one piece of bread or pita and it's wrapped together and the hotdog has its own one bun unless you rip it apart as Jon had mentioned, and the same could be said for a sandwich.
But typically it's like, when I go to fill up my sandwich, I take that top. I make it an open-faced sandwich temporarily, right, Jon? Just like your hot turkey. Then we load everything on there and you could get so much on there. crosstalk. Then just toss the top right back on there, and with a hotdog, that is just awfully hard to do and I just feel like it would just be so unfair to say that you could load up a hotdog with crosstalk.

Jon Orr: I would keenly have the bun and the bun is still attached to the... I just do this and then I load it up.

Rob Baier: Lucy, I'm going to come to you, Lucy. I know you're writing stuff down. You're doing such a good job of writing it down, because I know you're about to come out with some more great stuff. With you talking about like a meat and some bread, right? What about taco? Would a taco be considered a sandwich. I mean, with your definition, you said that it would be Kyle's...

Kyle Pearce: That's what she wrote.

Rob Baier: For everybody who is listening on the podcast, you definitely want to jump over to YouTube to see this because they held up a sign that Talia wrote that said no. Based on your definition, Lucy, would a taco be a sandwich?

Jon Orr: No or yes? No. Oh, she's saying no. Why not? Why not?

Lucy: Because the meat's broken up.

Jon Orr: The meat's broken up.

Rob Baier: Well, okay. Well, let's see crosstalk.

Jon Orr: It's not a sandwich because it's like, because it's meats broken up?

Lucy: No.

Jon Orr: Okay, the meat's broken up, it's not a sandwich.

Lucy: But yes, because I have all the same toppings.

Rob Baier: So yes but no?

Jon Orr: They have the same types of toppings. Yeah.

Rob Baier: Okay. So then the...

Jon Orr: What she's saying yes and no, it would be yes or no.

Rob Baier: She is saying yes or no.

Lucy: Yes.

Rob Baier: Then the question I have would be...

Lucy: It's a special sandwich.

Jon Orr: It's a special sandwich. Just like a hotdog is a special sandwich. It's still a sandwich though.

Rob Baier: Chris, you have some questions?

Chris Luzniak: Yeah. Sorry. Let me go over to Talia here. Your dad seemed to think that a sandwich has to have like two parts, like two pieces of bread or something. So then would you call things like a s'more a sandwich?

Talia: It could be, but a special sandwich.

Kyle Pearce: Personally, we never discussed this, but I would call it a special sandwich. That is...

Talia: Because it has two crackers and then all this thing is inside, like the chocolate marshmallows.

Lucy: Except there's no meat.

Jon Orr: Ooh, there's no meat.

Talia: But it doesn't have to have a meat, because sometimes I have a sandwich that has butter and mustard.

Kyle Pearce: Yeah. Well, and I was going to ask, are vegetarians allowed to eat sandwiches?

Jon Orr: Yeah.

Talia: They do. You could have lettuce and mustard for vegans.

Jon Orr: For vegans. Okay.

Chris Luzniak: And then maybe back to Lucy, so your definition was its bread with some kind of filling inside. I'm guessing, would you kind of a s'mores as a sandwich? Because there's no bread involved.

Jon Orr: Yeah, it's a sandwich.

Chris Luzniak: What about two pieces of bread with nothing in the middle? Is that a sandwich?

Kyle Pearce: That sounds like an almost depleted loaf of bread.

Jon Orr: That's just bread. Yeah, I don't think that's a sandwich.

Kyle Pearce: That's just a really used loaf of bread, right?

Jon Orr: I have a question about the... You guys brought up.

Lucy: It's just toast.

Jon Orr: Yeah, it's a toast. One of your warrants, I think, it was warrants that you said that I think you were implying that a hotdog only has a limited amount of topping for a hotdog, but a sandwich could have a lot of toppings.

Talia: Yeah, because if you put a lot of toppings in a hotdog, then the hotdog bun will break and everything will fall out. But then it won't make... Like then, it will just spill out.

Kyle Pearce: It's like kind of like a gravitational pull that I think is working against you with a hotdog, right?

Talia: Yeah.

Kyle Pearce: Like if I throw on...

Jon Orr: I think you have a better luck of holding more stuff in a hotdog bun than in a sandwich with the two pieces of bread with all of the sides. This is like a little carrying case for a sandwich.

Talia: But if you have two pieces of bread, then the top and bottom, you could put as much as you want, couldn't even be that thick. But then...

Kyle Pearce: I agree.

Jon Orr: Sure.

Talia: But if you put a lot of sauces, just sauces, then that will fall out. But if you put actual toppings then it won't fall out.

Rob Baier: Talia, I want to ask you a question. We keep talking about having two pieces of bread or lettuce and that would be a sandwich. What if two people give you a hug? If two people give you a hug, is it Talia sandwich?

Talia: Yeah.

Lucy: There's no filling inside.

Rob Baier: She's the filling.

Talia: Yeah, I'm the filling.

Kyle Pearce: Now, I guess here's my question and this is for our friends the pro hotdog is a sandwich friends. If I came and gave Jon a hug, is that a sandwich? Because I mean, if a hotdog is a sandwich, then me just hugging Jon should be a sandwich, should it not?

Chris Luzniak: An open-face hug?

Kyle Pearce: An open-faced hug. That's exactly what it is.

Jon Orr: Yeah, it's an open-face hug. That's all that is. That's all that is. It's an open-face hug. It's totally a sandwich. Yeah.

Kyle Pearce: Okay.

Jon Orr: It's a Jon Kyle sandwich.

Kyle Pearce: I love it.

Chris Luzniak: For both of you then, does it have to be food to be a sandwich?

Talia: No.

Kyle Pearce: Wow. This has gotten very deep.

Jon Orr: Lucy, she had this epiphany. Go ahead.

Lucy: Hotdog is the same thing as bologna and you put bologna on a sandwich.

Kyle Pearce: Interesting, the ingredients.

Jon Orr: Just a bologna sandwich. That's all we're talking about here.

Talia: Yeah, but then why did they call it bologna instead of a hotdog?

Jon Orr: Made of bologna, it's the ingredient.

Talia: I'm so confused.

Kyle Pearce: A question I have then is, would you say if you went and you ordered a bologna sandwich and someone gave you a hotdog, would you walk away feeling like you received what you had ordered?

Jon Orr: If you say, hey, can I have a bologna sandwich and they gave you hotdog, what do you think about that? I'd be pleasantly surprised myself.

Lucy: But you don't get bologna sandwiches at restaurants.

Jon Orr: No.

Talia: But if you ask for a hotdog, they'll give you a hotdog. They won't give you a bologna sandwich because if you say, can I have a bologna sandwich? They'll give you a bologna sandwich. If you say...

Jon Orr: You're right.

Talia: ... can I have a hotdog? They'll give you a hotdog.

Jon Orr: I think that's definitely right. I think we're not saying that a hotdog isn't a hotdog. We're just saying it's a special type of sandwich.

Rob Baier: Now, I guess my next question be is this would... I'm going to start with Lucy on this. What about a pop-tart? Is a pop-tart a sandwich?

Lucy: No.

Rob Baier: Maybe a dessert sandwich or a breakfast sandwich?

Jon Orr: Yeah, what do you think?

Rob Baier: There's stuff inside, right?

Lucy: It doesn't have another cracker on top.

Jon Orr: Well, it's like pastry and then there's like the jelly or whatever, the filling in the inside of the pop-tart. Lucy doesn't have a lot of pop-tarts.

Lucy: I had one.

Jon Orr: She's had one before.

Rob Baier: Well, at least, you know what they are. All right. Well, let's go over to Talia.

Jon Orr: Wait, wait, wait. Do we think so? I think so. Based on our definition, right? It's got this surrounding and it's got a filling in the inside. That's a sandwich.

Rob Baier: And Talia?

Talia: I don't think it is because a pop-tart has like, basically like filling inside. But if you wanted to open it, you would have to cut it in half or do all that stuff, but for a sandwich you could easily just go take the...

Jon Orr: Right. inaudible.

Talia: ... two pieces of bread and open it.

Jon Orr: Yeah.

Talia: That's why I don't think it's a sandwich. I just think it's a bit, it's like kind of like a cookie, but...

Kyle Pearce: Then we're coming back to like the open-face pop-tart again, holy smokes.

Chris Luzniak: We're going to have to call this the open-face episode.

Rob Baier: All right. Now, coming back to you Talia because based on what you just said, what about like peanuts that are still in the shell that you have to like crack open? Would those be considered a sandwich based on your definition?

Talia: No, because you basically have to crack it open. Then if you wanted to like, if we had crack and then you can eat the peanuts.

Rob Baier: Right.

Talia: But then for a normal sandwich, you just go open, because you have to crack it open. Then it's like, no.

Jon Orr: Do you eat the shell?

Rob Baier: Unless you eat the shell, at least you do whole. So the act of cracking where it gets us with our sandwich so we can't crack it to open it up, correct?

Jon Orr: I think it's more about the eating of the shell. You don't eat the shell. Yeah.

Rob Baier: Some do.

Kyle Pearce: That would be like, if you don't eat the shell, then that would be like a double open-faced sandwich. Like that would be now, we're really getting carried away.

Jon Orr: Yeah.

Chris Luzniak: Well, okay. Let's take this a little bit away from food for a moment. I think it was Talia that you said, if you asked for a sandwich, no one's going to ever bring you a hotdog, right? I'm just curious for both of you to weigh in, how much does it matter what other people think or what, like the community tells us is a sandwich or people just seem to know as a sandwich, how much does that matter?

Talia: It doesn't matter that much. It just matters what you think. But a lot of people, I'm not saying everyone, but a lot of people think if you ask for a sandwich, they'll give you a piece of bread toppings in it and then another piece of bread, because if I even ask my parents, I say, can I have a sandwich? They'll give me a sandwich, they wouldn't give me a hotdog.

Kyle Pearce: Something that was interesting to us, now that you're asking Chris about what other people think we were curious to actually look up the definition and try to understand, what is the accepted definition? And the accepted definition says that a hotdog is a sandwich.

Talia: But then I also...

Kyle Pearce: At least in the dictionary we were looking at.

Talia: ... I looked more.

Kyle Pearce: Yeah.

Talia: And that's where I got another thing. It was like, if you went to a hotdog vendor and asked for a hotdog, they wouldn't give, or you ask for a sandwich, they're going to think you're crazy. Because if you ask for a hotdog, they're going to give you a hotdog. But if you ask for a sandwich, they're going to be confused because they only sell hotdogs.

Kyle Pearce: Yeah. We were, I guess kind of maybe shocked that it was actually formally in the definition, but then we started to think about that and sometimes definitions aren't necessarily maybe widely either known or accepted. This was one that when we started to think about some of these scenarios, we were like, well, if that's the true definition and that's for real, at least here in our experience, it doesn't seem to be the case. At least everyone we know doesn't seem to abide by that rule. We found that kind of into interesting as we were just kind of brainstorming on this, I was actually shocked. I was like, why don't we look at the definition? That might be good support for us. And we're like, oh, we don't want to talk about the definition when we bring this up.

Chris Luzniak: And so then Lucy, same to you, though, how much does it matter what other people believe is a sandwich or you think they would believe? Does that matter in your definition?

Jon Orr: No. Do you want to elaborate on that? Does it matter what other people think?

Lucy: Mm-mm (negative).

Jon Orr: Why not?

Lucy: Because everybody has their own opinion.

Jon Orr: Everybody has their own opinion. Okay. And it's okay that we have our own?

Lucy: Mm-hmm (affirmative).

Jon Orr: Okay.

Rob Baier: This last question from me is actually going to go directly to Jon and Kyle. This question, this hotdog is a sandwich question. How is this question useful to math teachers? And I'll actually start with Kyle and then we'll go over the Jon right after. Kyle, how is this question useful for math teachers?

Kyle Pearce: Yeah, I think it's great. Actually, I think it's a great follow up to your discussion around the trapezoid debate, right? That in a math class, I think what's most important is less about it being the definition and more about the math community, having at least seeing eye to eye on what the definition is. For example, if Talia and Lucy are in the same class and let's say it's not a hotdog were discussing, maybe it's something in math and they are able to at least voice their beliefs, their current understandings or what they believe to be true, and they can articulate that. That thinking I think is the piece, which again is why both of you are doing this podcast, right? That thinking is really what we're after. It's less about being "accurate", whatever that really even means, right?
Some person or some group decided that this is what it is. I look at it as all of the thinking I learned through the process of planning with Talia. I thought it was going to be an easy for us to prepare for this, but I didn't realize how hard it actually is. Especially working with a younger student to sort of understand like what is a debate? Like what are we trying to achieve here? Through this process, I just think as long as you're able to sort of, you have some rules and I realize that some of what we thought our rules were, weren't quite what they appeared to be based on the questioning that both of you had given us. It's like, oh wait a second, I didn't really think about that. It kind of forces us to kind of go back to the drawing board and sort of go wait a second. Maybe we need to redefine our definition a little bit. I think the process just at least lets you think more deeply about it and involve that thinking.

Rob Baier: And Jon, what about you?

Jon Orr: Yeah, no, I echo all the things that Kyle has just said. If I toss in the say content piece to this, if you think about like this, knowing the definitions and knowing the properties in of certain elements in mathematics, like we talk, let's talk geometry, like just screaming at me to talk about the definitions between a rectangle and a square or where like how do I define a particular type of triangle or when we're talking about, say the distance between a point and a line and there's a lot of geometrical ideas that are rooted in definitions.
And when we talk about proofs in geometric proofs, all in there, and so an activity like this, like what Kyle is saying is like really great to bring out the discussion and whether it's right or wrong. But I think it's also really great because it's such a low floor activity, like this activity itself to debate a hotdog is like I feel like a necessary first entry level into this realm of looking at definitions to help prove things or also to help justify things. And so such a low floor thing to get your kids in your classroom, talking, sharing, debating, you know that they're all going to have opinions about this and you shaping it like you guys did in this debate, shaping it.

Kyle Pearce: Yeah, I was going to say that facilitator moves was key to keep this discussion going.

Jon Orr: Right. You shaped it to talk about like certain pieces that would say, well, this work, would this work like that's such a pro move there. If you think of a teachers doing that too, kind of shaping that discussion and then all of a sudden going, okay, well, we talked about this definition, now let's talk about this other one over here. It's now like this, hey, we already did this, now we easily could start talking about something else. I feel like a really nice low floor activity as an entry level into talking about definitions, proofs, that kind of thing in whatever class.

Chris Luzniak: Awesome.

Rob Baier: Well, and to add on that real quick, before I let Chris go, you talked about this being a very low floor. Chris actually has a lot of resources that are very low for on his website to Luzniak.com website. And one particular that we have started with as a low floor is like, what's better, cats are better than dogs or dogs are better than cats? That's another one that though. crosstalk.

Kyle Pearce: Let's answer again, I mean.

Rob Baier: Yeah, right.

Jon Orr: We should have debated that, Kyle.

Rob Baier: We should have. Even with like kindergarten students and first grade students, like you're able to access that with students to get them to kind of not just state a claim, but also have reasoning of why. That's kind of like why we did this low floor debate, but it's a much grander thing. Go ahead, Chris.

Chris Luzniak: Yeah. I have one last question for the girls here, Lucy and Talia. Kind of like what we just asked your dads, I wonder, can you say, what do you think would be the benefits or what good would it be for students to have a debate like this in math class?

Kyle Pearce: Do you think that you learned something through this experience? Feel good? I wonder do you feel more confident in what you were thinking before? Like even though we prepared after doing the debate, do you feel like you could talk about this with somebody else? Like even more deeply next time? I know I do. I've got tons of ammo now.

Jon Orr: Lucy was, I think just thinking about what we just did here, as would you say, group work and you like group work? It's your favorite? And this is an element of group work. We did some group work here and we discussed, why do you like group work so much?

Lucy: Because you get to work with your friends.

Jon Orr: You get to work with your friends. Yeah. If you don't do group work, you don't get to work with your friends. Is that the case? Okay. Why is it fun to work with your friends?

Lucy: Everyone has different ideas that we can put together.

Jon Orr: Everyone has different ideas that can put together. Okay. I like it. I like it.

Kyle Pearce: I'm wondering too, for both the girls, we had very different opinions, but yet did you feel like we were ever in an argument or in like anyone was raising their voice or even though we were disagreeing, do you feel like how Rob and Chris were helping us facilitate this? Do you feel like this could also be helpful outside of math in just everyday life when you're maybe not agreeing with something? Do you think Luz?

Lucy: You were talking very loud.

Jon Orr: I was talking loud?

Chris Luzniak: She called you out, dad.

Jon Orr: I guess so.

Kyle Pearce: The whole family can hear him from upstairs. Look at this.

Jon Orr: Yeah.

Chris Luzniak: Jon was too loud.

Jon Orr: I was raising my voice.

Chris Luzniak: All right. I think we can stop there. This concludes our questioning round and will now end by giving each side a final minute or two to make their final argument.

Rob Baier: We're going to begin with Jon and Lucy. You have two minutes.

Jon Orr: Awesome. Thanks so much guys. We are going to reiterate that we believe a hotdog is a sandwich. We've got a couple points to make about that one. Mostly kind of making sure that we comment on your guys points about why it was not a sandwich, but one we're going to start with, Lucy's going to talk about the idea that you guys thought that there was a limited amount of toppings you could put on a hotdog. We disagree. Lucy?

Lucy: The toppings that you could put on a hotdog are chili, cheese, tomatoes, lettuce.

Jon Orr: Anything else?

Lucy: No.

Kyle Pearce: See, that feels pretty limiting to me. I don't know.

Jon Orr: Lucy, are you sure?

Lucy: Ketchup.

Jon Orr: Ketchup, yeah. I think...

Lucy: Mustard and relish.

Jon Orr: Well, we had talked about that pretty much.

Lucy: Pickles, onions.

Jon Orr: Yeah, pickles, onions, anything you can put on a sandwich, you can put on a hotdog, right?

Lucy: You can't put mayonnaise on a hotdog.

Jon Orr: I always put mayonnaise on a hotdog.

Lucy: No, you don't.

Talia: It's disgusting though.

Kyle Pearce: It is.

Talia: Just saying.

Kyle Pearce: Agreed.

Jon Orr: I put everything, though. You also talked about that there's two pieces of bread. You were really fixated on that. We still disagree with that in the sense that two pieces of bread is still one piece of bread cut. That's really the saints of bread, which is a hotdog. It's really the same piece of bread folded. And then the last piece you guys were talking about this restaurant idea. If you go to a restaurant and you order a hotdog and you get a sandwich that would be heartbreaking or in vice versa. I think we agree with that piece. Our point there is, we're not saying that it is not a sandwich, we're saying it's a special type of sandwich. Yes, you wouldn't get that if you ordered it, but it's still a sandwich. This is a specialty.

Chris Luzniak: Awesome. Thank you both. With a final word, we have Kyle and Talia and your two minutes begins now.

Kyle Pearce: All right. So Talia wanted, she had something she wanted to mention earlier and she's wants to take this opportunity to bring up, once again, another sort of additional point, which I don't know if it is against the rules, but we're going to go for it T like another scenario that again, just might sway people a little. What do you think?

Talia: If you had a hotdog day at school, you would obviously get a hotdog, not a sandwich, but if you had a sandwich day at school, you would get a sandwich, not a hotdog. If you got a hotdog on the sandwich day, everyone would be confused. But if you got a sandwich on a hotdog day, everyone would still be confused.

Kyle Pearce: Right. It kind of removes this idea that it's a special sandwich, which I thought was a very interesting point to think of through here.

Talia: They're two different things. It might seem like they're the same thing, but to me, it's like two totally different things.

Kyle Pearce: Yeah. Based on what we've heard, a lot of different examples have been given and we thought long and hard about this hotdog being a special sandwich. For us, we feel like the one of that definitive characteristic for us, we said that we didn't call it a property. What we call that a feature, right? You had said the feature of a sandwich that a hotdog doesn't have is that twoness to it. So like there being two things kind of holding it together. When you modify, when you mess with that, when you want to... You have to name it something different, like an open-face sandwich, so like a hotdog...

Jon Orr: crosstalk.

Kyle Pearce: It's almost like a hotdog is a...

Jon Orr: inaudible hotdog anymore.

Kyle Pearce: Hotdog is a permanently open-faced sandwich.

Talia: I said this earlier, I don't know if I kept it in, but I remember putting this, I put a hotdog. If someone said like, people usually say, pass me hotdog bun, because it's usually you would have like, it's usually considered one bun just cut in half, but not all the way down. But then I said, it's considered one bun unless it breaks, because people usually say pass me two pieces of bread so I can make a sandwich or pass me a bun so I can make a hotdog.

Kyle Pearce: In summary, and this will be the last before our very... That got bigger summary here. We're going to say that a hotdog is like a mono meal and a sandwich is like a bino meal. They're similar, but they're very distinctly different, so the Pearce family will say that a hotdog is not a sandwich.

Talia: Yes. It is not.

Chris Luzniak: A wonderful mathematical comparison, and thank you all. That conclude our debate while you've given us so much to think about, and also, that was a ton of fun. Thank you.

Rob Baier: Now, it is up to our listeners to take a moment, partner all these amazing arguments from both sides and consider what resonated with you and which side you stand on.

Chris Luzniak: We'll pause for a moment here to give you a chance to think, feel free to pause the podcast and think out loud with a friend. We want to hear from you. What did you think of this? Which side are you on? Go to our Twitter at Debatemathpod to vote for who you think was more convincing in this debate.

Rob Baier: We will leave it up for one week and tally the results for the following Wednesday night.

Chris Luzniak: And huge thanks to all four of our guests. You were very thoughtful and respectful in this debate. No one was too loud, even though you got called out for it, Jon. It was brilliant and cooperative. I think we got into lots of good nitty gritty ideas here.

Rob Baier: Real quick, there's a few people we want to shout out to kind of help bring this to light. First, I want to shout out Justin Aion and Shelby Strong. They revive this debate at the NCTM Regional Conference in New Orleans and upcoming, depending on when you're listening to this, the upcoming NCTM Indianapolis Conference, they are going to be reviving it again. If you're in Indianapolis, definitely check that out. It's a ton of fun and they go even deeper into this whole of a hotdog is a sandwich or is a tuna melt in pizza?

Chris Luzniak: We can't do this debate without the help, so I'm recognizing Christopher Danielson and Megan Schmidt and the whole sandwich chat, hashtag sandwich chat on Twitter.

Rob Baier: Also, thanks to all of you who are listening and have been listening to the podcast. We appreciate all of you. We hope that each time that you listen to us, that you enjoy it, that you learn from us. Also, don't forget to vote, it's our very scientific way to make sure we know who won.

Chris Luzniak: For zero prizes. As a wrap up, Jon, where can listeners find you?

Jon Orr: Yeah, I guess if you are listening, there's a couple places that you can go. Kyle and I, both are the co-host of the Making Math Moments That Matter Podcast. We also have a weekly podcast on math education. Math talked with Chris, we talked with Rob, we talk with teachers in the classroom. We talk with lots of different people, Kyle and I share sometimes our thoughts on certain math education ideas. We put that on Monday morning. If you're listening to this and you want a little bit more, math podcasting in your daily life or in your life, head on over to Makemathmoments.com/podcast, that's where you can find information out about it, or you can just search in your podcast platform. Kyle, I'll let you share the rest.

Kyle Pearce: Yeah. I mean, that's probably where friends were listening to this probably would probably want to hop over to the podcast. We also have a lot of problem based math units. We're really focused in on trying to be really intentional. Again, I had mentioned earlier about how much learning both Jon and I have done in our own content knowledge and things we wish we knew five years ago, 10 years ago, and we're really trying to find ways to get it out into classrooms. If you head over to the Makemathmoments.com website, you can check those out. And yeah, otherwise, we'll be hanging out with you in your ears, hopefully on Monday mornings.

Chris Luzniak: You want to shout out some social media contacts if they want to tweet with you or something.

Kyle Pearce: Yeah. I was going to say the Make Math Moments account, MakeMathMoments. I'm MathletePearce on Twitter, but MakeMathMoments I think is on all the platforms, and then Jon.

Jon Orr: Yeah, I'm MrOrr, I guess, dash or underscore, I think Geek on Twitter. Also, we have a Facebook group, which is Math Moment Makers K-12, so check that out as well.

Chris Luzniak: Awesome. Thank you all and that concludes our podcast.

Kyle Pearce: All right. Thanks for having us.

Chris Luzniak: All right. Thanks.

Jon Orr: I'd say, thank you.

Kyle Pearce: Well, Math Moment Makers, I hope you enjoyed that conversation. I know I did. And Jon, I think you did as well. What an awesome experience. I don't know for those who listen to our podcast quite regularly, I hope that you saw that this is just yet another structure, another way to bring in, again, this ability to get your students communicating, using math discourse, reasoning, and proving. You'll notice we always are saying that we want our students convincing us, right? Like we want them to craft convincing arguments. We want them to be able to stand behind their work. When you bring in this idea, this structure of debate into your classroom, you're really just giving yourself another opportunity for students to engage in that process. That was a big takeaway for me doing the process. Like Jon, they set us up perfectly ahead of time...

Jon Orr: Oh yeah.

Kyle Pearce: ... to give us that framework of what this would look like and sound like. But I was still not exactly sure how it was going to go and I felt like the entire process felt natural to me. I'm picturing my students, if I was to bring this into my classroom. Sure, maybe at first using this structure. I might not be able to do it as well as Chris and Rob did in this conversation. But in time, I see us being able to position students to feel like they are able to debate and actually be able to communicate their thinking and their reasoning to others. I don't know.

Jon Orr: Yeah.

Kyle Pearce: I think it was a great experience for us and hopefully others are going to dive into their podcast a little bit more so that they can potentially bring this into their own classroom.

Jon Orr: Totally. Chris and Rob, like you said, did a great job of facilitating this, imposing the right questions at the right time. I think sometimes that's going to take some practice on our part on the teacher's part to do this in the classroom. That's why they've also dedicated some resources to help you do this in your classroom. I know that you can head on over Luzniak.com/podcast to check the podcast out. But if you just go to Luzniak.com, L-U-Zed-N-I-A-K.com.
If you just go there, Chris's website has a ton of information of how you can get started in your classroom doing debates, examples of some debate topics. He also has a course on grassroots workshops to help you get started in your classroom as well. Check those resources out and we've put all links to resources in our show notes page as always. You can head on over to Makemathmoments.com/episode178. That's Makemathmoments.com/episode178 to find all the links and resources from the episode you just listen to.

Kyle Pearce: Awesome stuff. And friends, listen, we've asked a couple times head over and subscribe to their podcast. Do us a solid, subscribe to ours too, right? Like go ahead, hit that subscribe button over on YouTube. You can actually see us in these discussions each and every week plus you'll get access to our weekly video, which is usually somewhere from like an eight minute to sometimes a 20 or 25 minute, depending if we're doing like a classroom sneak peek or something longer like that, but definitely hit that notification bell, hit that like button, and my friends, we will see you in the next episode. So until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high five for you.