James Tanton: We want to bring a joyous experience of mathematics to the world and we want to prove that curriculum mathematics, the mathematics of the curriculum, the math that kids actually experience in classrooms, is its own joyous portal to all wonder, intrigue, delight and human connection. We brought together about 300 people from across the planet just on social media saying we want to be ambassadors to this project, spread the word, and our first year 1.7 million students across the planet [crosstalk 00:00:27].

Kyle Pearce: Today we bring back one of our very first guest, James Tanton, back onto the Making Math Moments That Matter podcast. We love talking to James because he is so passionate about the discipline of mathematics and he has some exciting, timely news to share with all of you.

Jon Orr: We chatted with James way back in episode number six where we discussed his math background, his memorable moment and his passionate views on mathematics. If you haven’t got a chance to listen to episode six, you should jump over to that episode right now and give that a listen. Then, come on back here to hear James talk more about exploding dots, how teaching polynomial division is the same as multiplying in grade five and vice versa, and he fills us in on Global Math Week and how you can get involved.

Kyle Pearce: Let’s get going.

Kyle Pearce: Welcome to the Making the Math Moments That Matter podcast. I’m Kyle Pearce from tapintoteenminds.com.

Jon Orr: And I’m John Orr from mrorr-isageek.com. We are two math teachers who together…

Kyle Pearce: … with you the community of educators worldwide who want to build and deliver math lessons that spark engagement.

Jon Orr: Fuel that learning.

Kyle Pearce: And ignite teacher action.

Kyle Pearce: John, I am super excited for this episode with James. It’s round two with Mr. James Tanton. Are you ready to go?

Jon Orr: Of course, Kyle. But before we get to our chat with James, we want to give a quick shout out to one of you Math Moment Makers. That’s right. This listener left us a five star-review on Apple Podcasts.

Kyle Pearce: Whoa, that’s pretty spectacular. This one was left to us by USMC who says, “Thought provoking. Must-listen for math educators.”

Jon Orr: “I love listening each week along with my daughter who’s in kindergarten. This show offers insight into the classroom experience of many teachers, and the interviews always leave me with something to ponder over the week. Kyle and John have inspired me and I often borrow ideas, tweaking them for my elementary classroom. This podcast is a must-listen for any teacher of mathematics.”

Kyle Pearce: Wow, thanks so much to USMC for posting this five-star review and for hitting that subscribe button. Where are you listening in from? It looks like we’ve got some great reviews from both Canada and the United States, but how about you over in Australia, Great Britain? Represent your part of the globe by writing a review on Apple Podcasts or whatever podcast platform you’re listening from.

Jon Orr: Before we get to the interview, we also want to let you know that last week’s guest, Christina Tondevold from Build Math Minds, is running a free webinar training called, Math is Not a Worksheet. Registration is open now until October 12th, 2019. You can register by visiting makemathmoments.com/buildmathminds. Again, that’s makemathmoments.com/buildmathminds. If you’re listening to this after October 12th, 2019, then that link will either bring you to the webinar replay or a wait-list for the next webinar.

Kyle Pearce: All right . That’s it for now. Let’s dive into the chat with Mr. James Tanton.

Jon Orr: Hey there, James. Welcome back to the Making Math Moments That Matter podcast. We’ve had a number of guests since you. We usually have our guests tell us a little bit of something about themselves, but you’ve been here before. You were back with us in the beginning in episode number six, but before we get into that, how are you doing tonight?

James Tanton: Oh, my goodness, I’m doing so well. First of all, thank you for having me back. I’m honored to be back. What a joy, what a pleasure, and what a real honor. So, thank you.

Kyle Pearce: Oh, it’s so awesome to have you back. It’s great hearing that fabulous voice of yours. I know people at home probably are thinking, oh, James is back, all the way from episode number six. We are super excited to have you here. As Jon was mentioning, we’ve already heard your memorable math moments.

James Tanton: That’s true.

Kyle Pearce: So, we’re going to ask you something a little bit different and it’s going to be based on something that John likes to do during his Math Fight presentations. Jon, you want to queue James up for what you have in store?

James Tanton: Uh-oh. What’s in store for me? What’s going on? All right.

Jon Orr: Sure. We’re going to put him on the spot here. Actually, he’s probably going to put us on the spot a little bit. You have probably heard, people listening and James, about this game, Two Truths and One Lie. Most people play it as an ice-breaker game, but in my class I have used it many times to talk about different concepts, like say quadratics or linear relations, and the kids make two true statements.

James Tanton: As one naturally does.

Jon Orr: Right, this is just natural in a math class.

Kyle Pearce: This in their spare time.

Jon Orr: Kids would create two truths and one lie about, say an equation or a graph, and then their classmates have to try to figure out the truths and the lie. We’re going to ask James to give us one run through here. James, would you tell our audience and us two true statements and one lie about yourself, but do not tell us which one is the truths or lie and Kyle and I will try and figure that out. The people at home will also try to figure this out. Do you have something up, James? Can you give us a challenge here?

James Tanton: Okay. On zero notice, here it goes. I, James Tanton of Planet Earth, have climbed the highest peak of two continents on this planet. I have appeared on the game show Wheel of Fortune. Everything is say is the truth.

Kyle Pearce: Oh, man.

Jon Orr: Oh, my goodness.

Kyle Pearce: This is fantastic. Well, I feel like Wheel of Fortune should be the lie because I’ve seen every episode of Wheel of Fortune and I would have remembered you. I know it.

Kyle Pearce: Jon, what do you think?

Jon Orr: The Wheel of Fortune one, I’m not sure. I’m going to say true on the climbed the highest peak. James is always posting his mini-hikes and his hikes on his Facebook page, and I see him hike every single day. I’m going to say true on that. Now, he threw a monkey wrench into this, Kyle. You’ve got to do some logic right now.

Kyle Pearce: I know.

Jon Orr: “Everything I say is the truth,” which means one of the other two is a lie. Then, what does that mean? Isn’t that the lie? Oh, man. Min blown.

Kyle Pearce: Oh, this is tough.

James Tanton: Oh, my goodness. There’s nothing mathematical in that whatsoever.

Kyle Pearce: Jon, do you think he’s trying to pay us back for putting him on the spot?

Jon Orr: Mm-hmm (affirmative).

Kyle Pearce: With two truths and a lie?

Jon Orr: I think so.

Kyle Pearce: I think we might have an issue here. Yeah. What have you got?

James Tanton: Which you is that you? Is that me?

Jon Orr: No. Kyle, what are you leaning towards here?

Kyle Pearce: I think, unless he’s just not playing the game appropriately, “everything I say is the truth” has to be the lie, so I’m going to go with that one. Jon, I liked your logic here. It’s going to be really embarrassing if we’re reading into that completely inappropriately.

Jon Orr: Mm-hmm (affirmative).

Kyle Pearce: James, everything you say is the truth is your lie. What do you think?

James Tanton: Well, it has to be, does it not?

Kyle Pearce: Yes.

Kyle Pearce: Tricking us. That’s where he’s tricking.

James Tanton: [inaudible 00:07:55].

Kyle Pearce: Right.

James Tanton: By pure logic, that had to be the lie from playing a game that must include one lie.

Kyle Pearce: Right.

James Tanton: Well done.

Kyle Pearce: Oh, my gosh. Before we move on I need to know: James Tanton do you have any episode information about this Wheel of Fortune because I am just… now I’m curious.

Jon Orr: We’re going to put it in the show notes right now.

James Tanton: Okay.

Jon Orr: We’ll even embed if it’s on YouTube, for sure.

James Tanton: Okay. The fact is when I was 18, turned old enough to appear on a game show, I did appear on Wheel of Fortune, the Australian version, way back, gosh, 20-odd, 30-odd years ago, so a crazy amount of time ago in another continent. Yes, it was the cheaper version. I did not… whoever the host is of thingy. But here’s the thing, I actually did not know how the game worked. I never actually watched an episode. It was just complete luck that I signed up for this thing, waited for the interview, and got on. So, I just did it. It was a blast.

Kyle Pearce: That is fantastic.

Jon Orr: You know what we’re going to do? I’m going to search that up on the internet as soon as we’re over here.

James Tanton: No way.

Jon Orr: I don’t know if we can find it, but I’m going to search it and I want to, like Kyle, I want to put it right here on the site if we can.

James Tanton: Hang on, but one thing. I have to call Kyle on one thing.

Jon Orr: Okay.

James Tanton: I’m not actually an athletic person. That mountain climbing business, that’s very recent in my life. I am not at all an exercise person, whatsoever. The fact is, I happened to climb the highest peak in Australia, which is pretty darn small [inaudible 00:09:15]. Then, I was lucky enough to climb Mount Kilimanjaro at one time. It took me nine days to go up.

Kyle Pearce: Wow.

James Tanton: It was fabulous and fantastic, but again, it didn’t involve anything about pointy things on one’s boots or bits of rope or anything like that. It was just a nice gentle hike all the way up. It was pretty darn easy to climb the highest peaks of two continents.

Kyle Pearce: Wow.

James Tanton: Any others? No, because I’m not athletic.

Kyle Pearce: You’re still lapping me on climbing mountain peaks. Like Jon was saying earlier, you’re getting out there in Arizona and you’re climbing whatever is out there. I know they’re not too tall where you’re from, but you know what? I’m sure it’s a good afternoon hike there for you.

James Tanton: Correct. Exactly. I’ve hit my 50’s, so I figured I better start exercising in my life, so what I do is I go climb a little bumpy thing in Phoenix, Arizona. There’s so many bumpy things around. I had to climb to the top of it and I’m done.

Kyle Pearce: Awesome. Fantastic. Awesome.

Jon Orr: Well, James, we wanted to have you back on the show for two reasons. One is your enthusiasm and joy for mathematics is so contagious. You always share with us how human mathematics is and you always give us new insights into thinking about mathematics. Two, we wanted to talk to you about the Global Math Project and Exploding Dots all over again. We didn’t get to talk a ton of time about those kinds of things on your last podcast, so we wanted to dive into Exploding Dots and the Global Math Project.

James Tanton: Oh, that sounds brilliant. I’m in. Yes is the answer. What would you like to know?

Jon Orr: Let’s start with Exploding Dots. We talked a little bit on the last podcast, episode six. People, if you have not listened to episode six, you’re welcome to go back and listen to episode six, but James is going to talk a little bit about Exploding Dots right now. James, where does Exploding Dots come from? What is this all about because…

Kyle Pearce: It sounds dangerous.

Jon Orr: We’ve heard about this before and we’ve talked about it before, but let’s get the lowdown on Exploding Dots.

James Tanton: Okay. Let’s see. How can I begin? Hopefully, I’m consistent with whatever I said back in episode six. The story begins this way. As you said, I do believe that mathematics is a fundamentally human enterprise. We’ve been doing this thing for thousands and thousands of years, not because it’s just practically useful, though it actually is, but also because it’s enjoyable. It brings us joy and uplift to our hearts and to our minds, and mathematics is just an uplifting experience.

James Tanton: Then, in my wayward career, which I must have talked about last time, I found myself being a high school teacher, which I absolutely enjoyed, but also found it the most difficult and challenging job I’ve ever had in my life. You know, school teaching is just undervalued because it’s such hard work. It’s such important and valuable work. I chose to go to the high school arena because I actually felt at the time it was one of the most joyless arenas, 20 years ago, so I think things have changed significantly since then, but it’s all about passing exams. That was the goal of high school teaching.Get those kids into college. I was like, that get extra mentality that I was really struggling with. How can I bring a sense of joy?

James Tanton: I found myself teaching these 10th graders, 11th graders, polynomial division. Polynomials. Okay. First of all, like why? Why? When was the last time I used them in my everyday life?

Kyle Pearce: Never.

James Tanton: Never. My background is actually research mathematics. As a research mathematician, whenever did I divide polynomials? Actually, you know what? Never.

Jon Orr: You’ve taken all those math all the way up to the top.

James Tanton: Exactly. I’ve been all the way through it. Okay. It’s not that this is not a worthwhile enterprise. I do know that it comes up in some interesting fields of mathematics. [inaudible 00:12:33] how to work with polynomials and all the rest, but that’s not of interest to 10th graders, 11th graders, so why are we doing this? I realized back then as a high school teacher, okay, I’ve got to do something here. I’ve got to get my kids to pass those exams. I had no control over that, but really teach what I think is valuable. Not getting the answers to dividing polynomials, but actually understanding an interesting experience in mathematics that did fasciate mankind and humankind, but actually teaches the art of problem-solving.

James Tanton: I had to think deeply about this, and I said, “Well, really polynomials are all about repeating everything you did in grade school, which was base 10.” Just be a little bit looser about it. Let’s just do it at a general base, an abstract base, call it base x, and walla? Everything you do in how school math about polynomials is just a repeat of grade five and no one tells you. It just has to be base x rather than base 10. In fact, if you let x equal 10, because people forget that x could actually be a number in algebra, that actually you are doing base 10 arithmatics.

James Tanton: I realized that Exploding Dots was, excuse me, polynomial divisions and polynomial algebra in high school really was about taking what you think you know or do know about base 10 arithmatics, which was a very human experience because we humans love base 10 because of our physiology. We have 10 fingers. We think 10 is [inaudible 00:13:46] accounting, but just being a little more loose about that and doing other bases as well. In fact, all bases, infinite many bases, all in one hit. It’s the story of place value and the power of place value and how that abstraction actually gives a place of power to think through problems and how to solve problems. Again, it’s one of these things I’ve always say, upper school mathematics is not about the content. No one actually needs to divide polynomials in everyday life. It’s actually about using the content as a vehicle for teaching and thinking. The thinking here is the wonderful story of place value and the power that brings.

James Tanton: So, I just thought, okay, I’m going to teach polynomial division to the story of place value. That made me think about, okay, how do we think about and how do we write numbers? Again, it’s back to our humanness. We love to think base 10. Two hundred and seventy three is literally how we say it. Two hundreds seventy and the T-Y is short for ten, and three. Then I realized, actually, if you draw a picture of that, and this is where this dots and boxes idea comes in, actually draw boxes for the different place values of 10 and actually draw two dots in the tens place, draw seven dots in the tens place, sorry. Two dots in the hundredths place, seven dots in the tens place, three dots in the ones place. You can actually see the number 273. Then all the grade school algorithms you do of long addition, long subtraction, long multiplication, long division make perfect sense if you just draw the picture. I’m not going to say you have to draw the picture each and every time you do a computation problem, but once that picture’s in your mind once, it’s forever in your mind and everything makes perfect, good sense.

James Tanton: Then, suddenly everything makes the same perfect good sense for high school polynomial algebra. To be base 10, being 100 and 10 and one, you can be x with x and one and it’s exactly the same work. Suddenly, these kids had a connected story of a human experience, which is you start with kindergarten math knowing nothing. We learn how to count, we know about the counting numbers. We learn how we humans obsess with number 10 because we have 10 digits. I don’t know if you ever noticed we call individual numbers in a number digits and we call our fingers and hands digits because we are literally being human right there. Then all that stuff is about working powers of 10, and just say, “Okay, martians might have four fingers per hand. I’ll do powers of eight.” Computers actually only have on/off switches. They like powers of two. It’s all the same mathematics. Let’s be abstract. Let’s not be locked into our cumulous and do powers of x. That’s the story of upper school mathematics is doing powers of x and all the work is done in the same exact way.

James Tanton: Now, it’s very hard for me to talk about this on an audio thing because it’s all about the power of the picture, but suddenly, as soon as you draw a single picture, everything falls into place. I called this Exploding Dots because, A, who doesn’t live explosions. They seem to be a very popular thing. The idea is that if you put, if I’m working base 10, as soon as I’ve put ten ones in one box, I’ll realize, well, ten ones we humans like to call one ten. Actually, ten dots are like boom, disappear and replaced by one dot one place left in the tens box. Ten tens we tend to call a hundred. Kaboom. They can disappear and be replaced by one dot on place left in the hundreds box. That powerful mechanism actually is just astoundingly power. We use the word right there. It unlocks all the mysteries of those grade school algorithms [inaudible 00:16:57] as a high school teacher.

James Tanton: Actually, what I love about this is that if we can teach fifth grade, fourth grade, sixth grade mathematics as the visual power of place value, then those fabulous grade school teachers done all my work as a high school teacher, because that is actually the same work as polynomial algebra, which is all the work I did as a college professor, because actually polynomials taken to another level. Infinite polynomials are called series and it’s kind of the same work all over again. It connects all of mathematics in wondrous ways.

James Tanton: Exploding Dots is the story of seeing mathematics of place value as one connective story from kindergarten and how we write numbers, how we manipulate numbers through grade school, how we actually work with polynomials all through high school, how we deal with infinite series, and beyond in university of above and you can get quirky and get into fractional bases and negative bases and irrational bases by just playing the same game that any kindergartner could play. It’s just drawing a picture and then you see what happens and you get into this really quirky wondrous things. Actually, there are unsolved problems still baffling mathematicians to this day. No one understands the mechanics of base one and a half. It’s full of mystery. Any third grader could actually play what a call a three, two machine, discover patterns, try to explain the patterns, if the patterns are true, they probably would discover something brand new to the entire world of mathematics. It is just wondrous and amazing. Check out Exploding Dots is what I’m really saying here. Check them out. Try them out.

Kyle Pearce: I think you did such a great job, even though it is such a visual experience, I want to even go a step further and say, I’m picturing back as you were talking, back to your Oye M-E talk, you did a keynote and this must have been three years ago, four years ago and you were using a document camera and you were doing the experience on printed slides so that you could actually do the experience live. There is just something about actually doing the work of Exploding Dots that allows you to make some of those connections. Right? I know for me, even when I try to show it a teacher I’m like, “No, no. We can’t just show you. You’ve got to do the work.” I find that once people do it’s like they’re just sucked right in and they don’t want to stop.

James Tanton: Kyle, you actually gave me more sophistication than I have. I didn’t even use printed slide.

Kyle Pearce: It was white paper and marker.

James Tanton: I used nothing. It’s just let the math be itself. No technology. No bells and whistles. I’m not techno in any way. Just let the math shine itself. Use nothing.

Kyle Pearce: I remember nudging Jon next to me and going, “There’s no way I could pull anything off like that.” I like having my slides and this stuff and you’re up there just giving her in front of a thousand people. As you go, obviously, you had it all worked on in your mind, but it was like making it as you go, which was fantastic.

James Tanton: I do run into this problem. When people ask me to give talks, they ask me, “So, what equipment do I need?” I say, “Can I have a whiteboard? No. Can I have a chalkboard? No. Can I have a bit of paper and a document camera?” That’s hard. We live this age now where everything has to be technology. Me to, I’m just like, just do it. Actually have a hands on experience. I’ll have the hands on experience on stage. That’s really hard. That’s really unusual in this day and age.

Kyle Pearce: The other thing, too, that was popping into my mind I couldn’t help, but when you had said going all the way down to when we’re counting, something that’s sort of, I guess, sad to me is that most young children know about the numbers in the teens and they know what it looks like. My kids knew what the number 12 looked like with digits, symbolically, way before they understood why there was two digits and all these other numbers from zero to nine, they all had one digit and then all of a sudden this one just has two and it was like, nobody mentions it, nobody shows why. Kids just accept it that that’s just the way it is. Almost like when they see 12 they see a one and a two, but it doesn’t look like a one and two. It looks like that. That is 12. They don’t even have this understanding of place value and we work through school and then we talk about place value a little bit more later on, but now it’s like trying to go backwards and really try to unpack what’s happening.

Kyle Pearce: I’m wondering, as you’re teaching the secondary classroom and you run into this issue with trying to divide polynomials, where did your Exploding Dots experience begin? Did it begin way down in playing with the base two machine or the two one machine? Was it way up there with polynomials and working your way backwards? How did this come to be? Was it just little bits and pieces over time and you just, over time, filled in the middle? I’m just curious for my own wondering. How did that develop over time?

James Tanton: Okay. You mentioned the number 12 a number of times. Before I actually answer your real question, let me talk about this. We, in society, are somewhat strange. We do allow ourselves to say 12 hundred. That sounds normal for us. We don’t let ourselves 12 teen; 12 tens. We are fickle in society. We are allowed to have 12 dots in the one hundreds box. We won’t allow us to have 12 dots in the tens box, which is inconsistent. Even if we say a number like 112. We are literally saying one hundred and 12 units. We don’t write one zero, then the symbol 12. We actually write one, one, two. We are terribly inconsistent in society. The wonderful thing about Exploding Dots, it says, actually, the number one, zero, twelve is fine mathematically. One hundred and twelve units is actually nothing wrong with it mathematically, just society prefers to write one, one, two, no 110 over two. It just has a predelection for reasons of making no sense. I can say the number twelve thousand twelve hundred and twelvty twelve and some of that sounds okay to you and some of it doesn’t sound okay to you. Why is society so inconsistent?

James Tanton: What we do to young kids is actually kind of bizarre and strange and kind of cruel. The thing is, we need to get the true story of the mathematics behind this. The math doesn’t care about societal convention. Twelve thousand twelve hundred and twelvety twelve is actually fine mathematically. Society prefers, yes, twelve thousand, feel free to say that. Twelve hundred, feel free to say that. Twelvety, no. Please make that one hundred and two tens, so one hundred and twenty. Twelve, we are allowed to say, but don’t write that twelve there. Put another one in the tens place and two in the singles places. Very very confusing.

James Tanton: When I was a high school teacher, this Exploding Dots story. What made me really think about this, actually it was percolating in my mind before then because I was doing some work in some math circle work [inaudible 00:23:27] place where you came up in different contexts as well. This is really subtle and confusing story. I realized we do confuse students all the way through K through seven and K through eight and just make them conform without really thinking deeply about it. What I decided to do when I did polynomial work with schoolers was that, do you know what, we’ve never had the actual story of place value. We spilled out. These kids have some mathematical sophistication. They are ready to look back at all that they thought they knew and see it in a brand new light. Yes, when I work with high school students on polynomial division, I do not start with polynomial division. That’s kind of absurd to me.

James Tanton: Let’s talk about place value. I do go back to the very beginning of my classic story. If you Google Exploding Dots you’ll see me say, “When I was a child I invented a machine.” Not true. All this machine was you put dots and boxes. It was called a two, one machine, blah, blah, blah. We learned about this thing called binary, but don’t even say the word binary, just doing it for the sake of doing it. We’re doing three, one machine. We’ll just do it for the sake of doing it. Don’t say [inaudible 00:24:25]. Then we’ll just go wild and get up to ten, one machines and we realized everything you do in a ten, one machine is how we speak about numbers. We realized, oh, these machines are place value and actually that two, one machine is binary, which is actually used in every day life in computers. Computers are based on the two switches that are on or off. They only like two fingers, if you like. The three, one machines are ternary. The ten machine is base ten. There it is. These kids have never actually had the chance to take stock of what they have allegedly mastered and learned in the past.

James Tanton: What is this learning process? We seem to have a curriculum that pushes kids through. Of course, think about when you first learn a subject. You’ve become familiar with the mechanics of the subject. You just develop some facility as mechanics, which is fine. You can do it, but you never had a chance to then reflect on what you’re actually doing. The curriculum says, oh no, you can do it now. Moved on. Check, your first exam. Move on. There’s going to become a time when you realize, even though I’m familiar with the mechanics of it, I haven’t really understood it yet. I haven’t really internalized it. That’s the next process. What am I really doing, because I have to question it? All sorts of interesting questions will come up and you realize you had no opportunity to reflect on what you’ve been doing.

James Tanton: We so really equate familiarity with understanding. It’s one of my favorite things to say because it’s so true. We’re so familiar with it in the algorithm because we can do it, but doesn’t mean we have yet internalized it and really understood it. I really felt it was absolutely important my high schools kids to have a chance to say, “Okay. You’re just gone through the last ten, eleven years of your schooling life about this place value stuff and haven’t actually had a chance to now reflect upon what you’re actually doing.” Actually going back to the beginnings was essential. Absolutely viable. Developing deep understanding, in which case, by the time we get to the point of doing x, one machines, base x, why are things trivial. Okay. We get the story. What’s the big deal? There’s no big deal.

James Tanton: If my colleagues assigned me in this algebra two or pre-calculus class, I can’t remember what level I was at, three weeks to do polynomial division, I’ll spend one entire lesson just talking about two, one machines, three, ones machines and the light. I’ll spend another lesson talking about four, one minutes and then ten, one machines and place value. Then, by the time we get to x, one machines, the end of lesson two, we are kind of done. What’s there to learn? It’s all kind of trivial. We have a complete understanding, it’s like, well, duh. Of course the match makes sense.

Jon Orr: I completely agree here. I did this lesson today. I had on the docket that we were going to get into polynomial division today with my grade 12 class and for the last four years I’ve been spending that lesson going back and redoing grades five, four, almost like a history lesson on how you did division and multiplication and how they’re linked. Then how that relates to the Exploding Dots, but how that also relates to the ariel model and how you’re getting the algorithms out of that. No one probably told you that these things are linked this way or that you can represent them in this way. The eyes of the kids are just like, really. This ariel model, which they have touched on being in grade 12 back in grades 10 and 11, depending on which teacher they had, actually. You can just see them starting to connect the dots that the algorithms that they were shown back in the grades five and six for multiplying and dividing are these exact same representations and they’re coming out. The algorithms come out of the work that Exploding Dots does, but also the ariel model is showing.

Jon Orr: Like you said, it’s almost like a no-brainer once you go through that process and then you just say, “Okay. Now we’re going to use a quadratic and factor a quadratic.” Then we say, “Now we’re going to use a cub and we’re going to divide it by a linear model or a linear equation.” It’s a no brainer. By the time we got to the polynomials, there was 20 minutes left of class and I didn’t have to do anymore examples. It was like one and it was done. I totally agree that you can just do it with numbers and show them it’s the same. It’s beautiful. It’s just beautiful.

James Tanton: What is the scariest thing, though. We are so locked into base 10, let me say, twelve thousand twelve hundred and twelvety twelve. We always insist on carrying those terms out. In polynomial algebra, you don’t care what base you’re in. Have a coefficient of 12. It’s fine. Have a coefficient of eight. It’s fine. Have a coefficient of 102. It’s fine. The fact is this no borrowing in carrying in polynomial work, which actually makes it so much easier. It’s a fussiness of our society that says the base 10 never have digits bigger than nine in any one position, which is just actually annoying. It makes it so hard. It’s time that you reveal the true story of the mathematics by going to polynomials, the big three of the whole notion of borrowing and carrying.

Kyle Pearce: That’s fantastic. Just like both James, you had said, and Jon has said about how useful this is. Sure. Exploding Dots, it’s useful, definitely do it, but there’s a reason we wanted to bring you on to talk specifically about the Exploding Dot’s experience and joyous math and that’s because coming up real soon, like this week, when this episode goes live, we are going to be days away from this little thing that is known as Global Math Week. I’m not sure, but I think you might have something to do with Global Math Week, so I’m wondering, can you help us get, for those who don’t know about Global Math Week, what’s going on during Global Math Week? Tell us a little bit about it.

James Tanton: Okay. Here’s another story. My colleague, Phil Denees, just loved Exploding Dots. He said to me about three or four years ago, “James, have you heard this thing called code.org?” This hour os code business where they brought an hour of coding to the world back in 2013 or something like that, which has been tremendously successful, but actually for computer science to class us all around the planet. I think they’ve declared a special week in October as well, actually, to be our Code Week and they just invited us students to have a coding experience of some kind. Whatever level they’re at. If they know C++, go and do a C++ experience on their website. Have a grand time. If you know nothing, just play with bits of paper and learn about binary and wait, have an experience. They’ve been tremendously successful, something like a quarter of a billion students at this point. Jewel said to me, “You know what? We need to have something like this as well. We need like a global math week. Something that is dedicated to mathematics; the joy of mathematics and it should be Exploding Dots.” I said, “Yes. Let’s make it happen.” I can’t so no to that.

James Tanton: We just declared October 10th to be the start of Global Math Week. It was a team of seven of us that I put together to say, “Let’s bring a joyous math experience to the world”, this was back in 2017. It was our first Global Math Week. We chose October 10th, the start date, because I happened to be in Australia, living in America right now, married to an American, as well, and I’m very confused about dates. In Australia, I always said, “Day and month” and in America you month and day, therefore we chose the date that was palindromic, tenth of tenth. Tenth of October. October tenth. No matter how you read it you get it right. I have to say, we did try all the math versus math things, so we have Global Math Week. We want to bring a joyous experience of mathematics to the world. We wanted to prove that curriculum mathematics, the mathematics in the curriculum, the math that kids actually experience in classrooms, is it’s own joyous portal to all wonder, intrigue, delight, and human connection. It was clear Exploding Dots is the story we should bring to the world that actually is that K through five through eight through twelve beyond experience.

James Tanton: We declared we are going to bring Exploding Dot’s to the world. Based on nothing, we are actually hopeless at public relations and hopeless at fundraising. We’re based on nothing as all grass roots. We brought together about 300 people from across the planet, just on social media saying we want to be ambassadors to this project. Spread the word and our first year, 1.7 million students across the planet had an Exploding Dots experience with their teachers in the classroom. It just proved to us that having an option to do joyous, genuine mathematics is a yes to our fabulous teachers throughout the planet.

James Tanton: We did begin last year, last October. We’re not at 5.5 million students, which is ridiculous. These are just people, again, volunteering their own time and their own absolute passion and joy of mathematics to bring a joyous, passionate experience of math with their fabulous kids. It’s just all grass root. It’s just beautiful, beautiful teachers on our planet.

James Tanton: We’re doing it again this year, 2019. October 10th to start our Global Math Week. We have one little pickle that a lot of people think, okay, just have an Exploding Dots experience during Global Math Week and they stop, but actually Global Math experience is a year long thing. Exploding Dots is a year long enterprise. We’re going to try to bring the story this time around that it’s not something during this week. Have a wonderful experience. Share it on social media. Celebrate being part of a global community of teachers all across this planet who just celebrate joyous mathematics. Do something on social media, share your wondrous thoughts, photos, videos, whatever you have that shows kids can love math, too, during that week, but make it a year long experience.

James Tanton: Even if you’re not ready to do something this coming week, even though Global Math Week is around the corner, that is fabulous, do something this year. Check out Exploding Dots and have a fabulous, wondrous experience with your kiddos. [inaudible 00:33:32] expands a bit, because many teachers have now done Exploding Dots a couple of times and, of course, it’s fine because we all have new round of students each and every year, but we started bringing some Global Math projects short experience as well, as we are starting to expand in other arenas. We’ve got a little thing about geometry, a little thing about probability theory, a little thing about quadratics at high school level that are short experiences, just short of the Exploding Dots in the Exploding Dots mindset. What is the human connective joyous uppity story behind this piece of curriculum that you have for your students and see the math you thought you knew and the brand new astounding light. That’s our goal. Let’s share that with the world.

Kyle Pearce: Awesome. We will definitely share that. That’s why we wanted to have you on is to share that and promote this as widespread as we can. If you’re listening right now, please, please share some information that James was talking about. We want you to get into showing Exploding Dots in your classroom. Now James, I’m wondering, you just talked about having short experiences, more longer experiences. I’m trying to help our teachers see how this could look in their classrooms. What kind of unique experiences have you seen teachers do? You said people are sharing online and social media or maybe they’re writing back to you and saying what they’re doing in a class. Could you give us a couple examples of what it looks like in the class, start, end, for a lesson plan and then also maybe what the short one looks like?

James Tanton: First of all, I understand it can be very intimidating to do something new under very short notice. One thing we do suggest is perhaps, when you have half a class period, that will do it, 20 minutes. Give us 20 minutes with the kids. It will be grand.

James Tanton: If you go to our website, globalmathproject.org, you’ll see a very easy way to start. That is, just go to that website and see there a lovely animation. All it really is is a worthless animation that illustrates something about a two, one machine binary. I shouldn’t say that now because it kind of gives it away, but show this animation for 80 seconds with your kiddos. That all it is, 80 seconds. Purely wordless with cute sound effects and then do the classic, what do you nice? What do you wonder? It actually is intriguing because you can’t not notice something. You can’t not wonder something about it. Have a chat. Have a chat about it.

James Tanton: All I’m going to ask you to do is just please share your students discoveries about this one little 80 second animation. Share it with the world. Just go on social media. What did your fabulous kiddos discover or wonder about? Just so we know about it, please use the hash tag Exploding Dots or hashtag G-M-W-2019 for Global Math Week 2019, so we can recognize it. Then you’ll realize you actually are part of millions of millions of students across this planet doing the same thing. In Serbia, in Japan and Australia and Tanzania. All across the planet. We really are in 170 different countries and territories at this point, which is amazing.

James Tanton: You’re got to admit, this is just stunning and beautiful. This is joyous mathematics transcending borders. This is global community united by the joy and passion of mathematics. Share that too with your students. Know that are actually part of a huge, huge global community united by mathematics. That is just such a powerful profound and beautiful thing. Kids respond to that. Teachers do actually do that and it’s just beautiful. When they see their posts and see other posts of other students doing the same sort of thing, brilliant. What’s best of all, is when students have their own questions or their own puzzles that make up, based on Exploding Dots, they could write them up on the board, they take a photograph of that and then post that and they realize that actually students in other parts of the world start thinking about that too.

James Tanton: This actually is beautiful because it doesn’t matter what resources you have. Some classrooms have the high tech margin, every student has a laptop and they play with a full web app experience, while other classrooms have next to nothing, but just a rickety chalkboard. It doesn’t matter. Whatever you have, you can think and share with the world and have the world see what you’re thinking, see what you’re asking and respond to what you’re asking. You know what? We are a beautiful, global community. It transcends politics, it transcends borders, it just unites us all. That is stunning and beautiful.

Kyle Pearce: James, that is so well said. I was so happy that you addressed the tech piece, because I go online and I look at the globalmathproject.org website and I can see this fantastic, beautifully done, organized tech experience that you can have through the friends at Buzz Math and Sunil and all the crew over there, Luke and many of the people that we know over there, great, great people.

James Tanton: So cool. So cool.

Kyle Pearce: Yeah. It is so cool, but on the other hand, too, I love how you literally have all kinds of great just printable resources that you can pull out and you can literally just run it James Tanton, keynote style, by just getting that rickety chalkboard or whatever it is. If it’s that document camera or whatever they’ll give you, you can run this and the beauty is is that the kids are just as interested, no matter what the method. It’s not the tech, even though it’s a beautiful experience on the web, I’m telling you right now, often times I start just with that one video, that one animation because that animation that notice and wonder, like you said, it leaves kids and right away they’re at. The next part in the video sort of challenges them to try to figure out the code for this other representation of Dots and I think that’s such a cool gateway to get somebody hooked in.

Kyle Pearce: Like Jon and I always say, “Spark curiosity”. Get them to lean in and the next thing you know, kids are fueling their sense making with all of these ideas and literally, like you had said, you could take this as far as you would like to go. If you feel restricted by the curriculum, you don’t have to go all the way to polynomial division, you can go to where you think it’s appropriate. I know there’s going to be kids in your class that are going to keep going whether you like it or not and I think that is a fantastic thing when you have kids going home wanting to continue that.

James Tanton: I know this is sounding like wrapping up, but I have to tell one story then because kids will go as far as they go, irrespective of you is a beautiful sentiment because something happened in Zimbabwe. One of the most beautiful stories where, you see, it was a school that had zero resources. I mean, a chalkboard was as rickety as anything. One teacher did actually do an Exploding Dot’s experience and they did the two, one machine, ten, one machine and they worked on how we write numbers as really place value. Those kids were so excited. The teacher went out during recess that day and found his class was digging holes in the ground, I suppose they just dirt in this particular school, and using pebbles they found and his kids were explaining they stood all the other kids at their grade level in the playground during recess. They invented their own way of doing it. They just dug holes, literally, in the ground and used stones they found as the Exploding Dots.

Jon Orr: While you guys were chatting, I went to Twitter and typed in Exploding Dots, the hashtag Exploding Dots and just scrolling and I’ve got this amazing video and the title of the video from Simon and Greg from last year says, “A Video of an Alien Explaining Base Six” and it’s a little boy, he’s got to be maybe five, six years old and he’s using chalk on the ground, out in the play yard, and he is drawing the boxes and using a six to one machine and explaining how they’re counting in base six. Then the teacher kind of just says, “Now, how do we count on Earth?” Then he redesigns it for base ten. It’s pretty awesome to see, just scroll through, like you explained, James, that you’re going to see instances of teachers sharing videos of you explaining it, an area in Twitter and also, there’s lots of info about this year’s Global Math Week on the hashtag GMW 2019. Lots of stuff in there for teachers just to get started. It’s going to be a great, great event.

James Tanton: Excellent. Thank you so much for being such supportive believers in this project. It really is just beautiful. I’m really just stunned that if you set mathematics free, you set the joy of mathematics free to let mathematics shine for itself, it does. It’s embraced by all of humanity. If fabulous teachers across this planet, they believe in mathematics and set them free to just let the mathematics shine with their kiddos, it just shines left right and center for one and all.

Kyle Pearce: Well, James, obviously you are the right person to have at the front of this push to really, it’s not to make mathematics joyful, as you’ve already mentioned, it is. It’s bringing it out and it’s like we’ve hidden it for too long, so I really love that. Like Jon had mentioned earlier, your energy, it’s contagious. We love having chats with you in person, here on the podcast and I want to make sure that those who are listening don’t miss out on this experience. Again, the website is globalmathproject.org. We will link it up in the show notes. Also, don’t limit your experience to your own classroom. Get your colleagues on board. If you’re scared, we’re all scared to try something new. Just like James had said, try with a colleague. Maybe do it at a staff meeting with all of your staff so that you can fumble your way through. I’m telling you right now, it’s such a cool experience and make sure that you’re sharing whatever you do in the classroom with the hashtag Exploding Dots on Twitter. You can also use hashtag GMW 2019 and be sure to tag the Global Math Project team at global math P-R-O-J, so that they can get retweeting and sharing.

Kyle Pearce: At this point, James, I think it’s time for you to go climb a mountain and we will catch up with you for the third episode that you’ll come back on the show, hopefully, in not too distant future.

James Tanton: You’re so on. It’s a real pleasure to chat with you guys. Thank you so much for all you do. It’s incredible work and I really appreciate it.

Jon Orr: Thank you, James. Thanks so much.

Kyle Pearce: Thank you, James, again for spending some time with us again to share the Exploding Dots Global Math Project experience with you, the Math Moment Maker community.

Jon Orr: It was a great conversation. I know that I am going to be participating in the Global Math Week and you, too, should if you haven’t thought about it, get over to globalmathweek.org and get in on that action. Remember that Global Math Week is from October 10th to October 17th this year, 2019. If you’re listening to this in 2020 or maybe you’re listening to this in like 2025. That would be crazy.

Kyle Pearce: Woo hoo.

Jon Orr: I’m sure there’s a math week then in October, too. Get in on that. Before we end here, we want to let you know that last week’s guest, Christina Tondevold from Build Math Minds, is running a free webinar training called Math is Not a Worksheet and I know this is going to be dynamite. Registration is open now until October 12th, 2019. You can register by visiting makemathmoments.com/buildmathminds. Again, that is makemathmoments.com/buildmathminds. If you’re listening to this after October 12th, then that link will either bring you to the webinar replay or the wait list for the next webinar.

Kyle Pearce: In order to ensure you don’t miss out on any new episodes as they come out, each and every week, be sure to hit that subscribe button on iTunes or on your favorite podcast platform. Also, if you like what you’re hearing, please share the podcast with a colleague and help us reach a wider audience by leaving us a review on Apple Podcasts and tweeting us at Make Math Moments on Twitter and Instagram.

Jon Orr: Show note, send links to resources from this episode can be found at makemathmoments.com/episode45. Again, that is makemathmoments.com/episode45.

Kyle Pearce: Well, until next time, I’m Kyle Pearce.

Jon Orr: And I’m Jon Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high hives for you.