Author and educator Ben Orlin joins the podcast to talk about his latest book, Math Games with Bad Drawings, and if our students can really learn meaningful math through comics, puzzles, and games.
There’s a peculiar trend when it comes to math taught in classrooms: It’s innately competitive. When a student scores lower than the student sitting next to them, they will feel less proficient. And what’s worse: They might stop pursuing math altogether, thinking it’s just not for them.
There’s a scarcity of mathematical understanding and excellence today. One way to reverse the trend is to eliminate the competitive nature and focus on collaboration instead. Math games can help do that.
In this episode, Ben Orlin describes the difference between puzzles and games, showing us that pursuing math can be much more than a tournament.
Games can help math become more about exploring the space of possibilities, Ben says.
Rigorous Math Through Puzzles and Games
Often clumped together, both puzzles and games can be highly beneficial for students when it comes to learning math — and not just for the fun factor either.
First, it’s important to understand how the two are different from each other:
Puzzles can be fun, challenging, and full of reasoning for a student. However, they’re limited by the fact that once you’ve solved one, it’s done. Puzzles are carefully sculpted to be solved once, says Ben. To redo one is usually boring.
Games can provide a similar kind of challenge as a puzzle, but with the added bonus of being re-playable. Each game will bring new decision points and trade offs, as well as collaboration with whoever you’re playing with or against.
If two students sit down to a game of chess, and one student wins, they haven’t won chess forever right? The students will likely play again, with every game they play having slightly different circumstances.
Games Strategically Sculpted for Learning
So is there really a place within math education for games? Do these fun exercises truly make a difference for our problem solvers of tomorrow? Yes, says Ben. But the puzzle and game choices must be well thought out.
There is a long tradition of using puzzles in math. They provide a nice wrapper for mathematical ideas. Games, on the other hand, are a relatively new concept in the world of mathematics. They can be broken into two types:
1. Gamification: This is the idea of taking a traditional math concept and turning it into a game. Think of it as a worksheet with a scoreboard. This can add some fun to the classroom, but it won’t make a huge difference.
“It’s taking the kind of practice you would normally do in a classroom and turning it into a game,” Ben says.
2. Open-ended games: This concept is less about the curriculum and more about dealing with strategic situations. Open-ended games lay out a set of rules and then let the student explore, probe possibilities, and develop heuristics that capture the situation.
“The games that excite me more are less about curriculum,” Ben says. “They’re less about teaching you to add fractions or to divide polynomials, and more about open-ended strategic situations.”
With open-ended games, students can tap into the same skills that a good math education taps into.
Overlap of Math and Humor
If you look at the selection of math books at a store, you’ll see many options for math puzzles. Games … not so much. After recognizing this gap, Ben went to work on his book Math Games with Bad Drawings.
Originally intended for adult game players, Ben felt that most of his readers enjoyed games but not math, despite how similar in structure the two are. What Ben found was that when you write a colorful, playful paper-and-pen gamebook, younger audiences want to get involved too — making his book more of a family book that parents and students can both enjoy.
Math as Community
Most games are collaborative in nature. By playing a game, two students can discuss tactics and gain a deeper understanding of how to play the game better next time.
Most games will have a winner and loser, and that can add somewhat to the excitement. But too much focus on winning can stop a student in their tracks before they ever realize their place within mathematics.
Tournament Atmosphere of Math Classrooms
Many students that could go on to be incredible mathematicians will never get there because of current classroom settings. The structure is just too competitive. Student A might think math just isn’t for them because they never score as high on math tests as Student B.
While the idea of tailoring a student's individual coursework is outside the realm of possibility when one teacher must teach 20–30 students, games can pick up the slack. They can dispel the idea that only the top-scoring students are worthy of pursuing a career in mathematics.
Guest Links and resource recommendations
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Ben Orlin Q&A [2:12]
Eric Olsen: On today's episode, Ben Orlin, author and educator, as well as creator of all the wonderful math comics you see on AoPS' social media channels, joins the podcast to talk about his latest book, Math Games with Bad Drawings, and if our students can really learn meaningful math through comics, puzzles, and games.
Ben, talk about the difference between puzzles and games when learning math concepts.
Ben Orlin: Yeah. So a puzzle has a single solution, right? I think it's something like a Sodoku, where you solve the Sodoku, it's tricky while you're doing it. You're doing lots of fun thinking. Maybe you have some insight in the middle where you solve the one tough square that needed a different kind of reasoning. And then once you've solved, it's done. You don't go back. I mean, I guess you could go back and erase your Sudoku and then solve it again. It's a little boring though, right? You've got the solution. You had that aha moment. So puzzles aren't reusable. Puzzles are these one time experiences. They're good puzzles. You hear it and then you tell it to a friend. You kind of get to relive it that way, but you never get to solve it yourself again.
Games are different. Games are replayable. So when you sit down and learn chess for the first time, we play, you beat me, that isn't the end. You haven't won chess forever, right? If we sit down and play another game, there will be new decisions. There will be new circumstances. You'll always be facing new difficult choices and trade offs anytime you play the game. So that's the basic difference, I think, is that puzzles are these one off experiences, kind of carefully sculpted for you to go through once. And then games are renewable games, are these generators of new questions.
Eric Olsen: You say, you can play games more than once. But my first week here at Art of Problem Solving, a lot of the math curriculum folks invited me to their weekly holdem tournament. And I think they saw me as a mark, the marketing guy. Got really, really lucky with the cards the first night, won the tournament, have never showed back. I just like being this like legend that they just talk about so I'm never playing that game again. Then when we talk about this concept of puzzles and games, I think of this concept of like, let's maximize engagement, let's try to make learning educational. But can our students really learn meaningful, deep, rigorous math through comics, puzzles, games?
Ben Orlin: Yeah, it's a good question. I think not through all comics, puzzles and games, right? I would love to say that you can just give your kids Calvin and Hobbes and they'll learn math. They'll learn some fun life lessons maybe, but... So you've got to sculpt these things carefully. There's a long tradition of using puzzles in math education. And by long, I mean like millennial old. If you go back and look at the oldest algebra problems we have, those funny find the person's age puzzles where it's like. "Today I am half my brother's age. And in five years, he will be 50% older than I am" things like that which are very artificial, they're very puzzle like. But puzzles can be very nice kind of wrappers for mathematical ideas. So puzzles have a very long tradition.
I think games, that's maybe more of kind of an exciting new last few decades thing where people have been trying to make games a central part of math education. I see two basic kinds of games. There's taking math content and gamifying it, which the word gamification is a somewhat clunky word. And these are somewhat clunky games sometimes. I've done this with my students. It's like, "Oh, today we're playing trigonometry jeopardy." It's like, "Well, what is that?" That's we're playing jeopardy, but the questions are about trigonometry. It's taking the kind of practice you would normally do in a classroom and turning it into a game. Essentially, it's a worksheet with a scoreboard. That's fine. I think that can add a little pleasure sometimes to a classroom activity.
The games that interest me more and excite me more are ones that maybe don't hit curricular content quite as clearly. So games that aren't going to teach you how to simplify trigonometric expressions or how to plug a value into an algebraic expression. The games that excite me more are less about curriculum. So less about teaching you to add fractions or to divide polynomials, and more about open-ended strategic situations. A game kind of lays out a set of rules, and then you're free from that point to kind of explore and make deductions and probe possibilities and develop heuristic that capture the underlying truth of the situation.
And that's exactly what we do in math, right? You lay out some assumptions, axioms if you're building a whole system, or just some kind of geometric assumptions, a geometric puzzle where you draw this shape and that shape, and then you think, "What can I figure out? What can I deduce? What's possible? What's impossible?" And so to me, those open ended games, those games for game's sake, they can build really lovely mathematical thinking and they tap into some of the same skills that good math education taps into.
Math Games with Bad Drawings [7:17]
Eric Olsen: You've written some amazing books that overlap math and humor and comic design. Your most recent book is Math Games with Bad Drawings. Who did you write this book for? And what was your primary goal in writing it?
Ben Orlin: Yeah, I think the genesis of the book was, if you look at a shelf of mathematical books in a store, you go to Barnes & Noble and look at the math section, you'll find a dozen or a hundred lovely books of mathematical puzzles. There're just great collections out there, brain teasers and puzzles. There weren't collections of games I could find, like Sid Sackson wrote this book. He's a board game designer who wrote this book in the late 1960s that was a fun collection of math games. There's a few other more recent collections of pencil, paper, mathematical games. But basically that was missing from the shelf, the idea of a collection of games that provoked mathematical thought. So it just seemed like it was missing. It seemed like it should already be there and someone needed to write it. So that was one reason for writing it.
The audience I had in mind was basically adult game players. I thought so many grownups love games. Not so many grownups love math. That is a rare passion, but they're so similar. There's so much common structure there between games and mathematics. They're isomorphic as a mathematician would say, although as a game player might not. And so I thought I'll just write a book that kind of reveals the underlying structure, teaches a bunch of fun games with some cool mathematics to them, and then explains the mathematics that's lurking inside those games and kind of build that bridge. And this will be something if you're hosting a board game night, these games are mostly shorter games, but this would be the ones you would play while you're waiting for people to show up, or maybe the intermission between two longer games.
But what I found out is that if you write a colorful playful book about pencil and paper games that's accessible to anyone, nine year olds are going to gobble it up. Actually your audience becomes nine year olds. So although I've gotten some nice emails from adults who've read the book too, I'd say the overwhelming majority of people I'm hearing from are parents or the kids themselves who will send me really great questions about the ins and outs of particular games, or they'll show me their game boards. So it's become more of a family book even though I wasn't necessarily picturing the nine and 10 year old reader when I wrote it.
Eric Olsen: I had emailed Ben previously about a real life bookstore interaction I saw in a local bookstore in San Diego when I walked in. I saw a nine year old, maybe 10, maybe 11, see this gorgeous comic-based cover Math Games with Bad Drawings, which a clerk obviously hand selected to be in the primary site of view site when you walk into the store, ran up to it, grabbed it and said, "Dad, look, can I get this?" And he showed it to the dad. The dad didn't say much, but I think the dad obviously saw, "All right, math, this seems good. The kid's interested in math." And the dad went and bought it for him. So, yes, I think you see this kind of parallel in the purchase decision of this looks interesting for kids and the parents are like, "All right. Yeah. If you're going to learn from it, that sounds great."
Ben Orlin: Yeah. Yeah. Yeah. I hope it goes both ways where the kids says, "Oh, that looks like fun" and can sell it to the parent, because, "Hey, the first word in the title is math. That's got to be useful." And then similarly, if the parent's looking for something fun for the kid, fun but enriching, fun but educational, hopefully it doesn't... I don't think it'll taste too much like medicine. It should taste pretty good. It's like that rare... It's like grapes or something, right? It's at once sweet and healthy. I assume grapes are healthy. I actually have no idea. I let my three year old eat a lot of grapes so I'm hoping they're okay for her.
Why collaboration and community within math is so important [10:50]
Eric Olsen: You mentioned this hole in the market that you found. I'm so glad you did it. It's such an amazing book. I think what's most interesting about it is that it specifically designed to be a book that facilitates playing games with one another. It is more than a single person book in the majority of use cases. Talk about your belief in math as community and why collaboration within math is so important.
Ben Orlin: Yeah. I think you're exactly right. It's sort of funny to have a book of games that aren't collaborative games for the most part, right? There are games usually where someone wins and someone loses. But you're exactly right. I was thinking of it as a collaborative book as I wrote it. To me, the most important part maybe is the conversation you have after the game. You play, somebody wins, somebody loses. Somebody makes a great move, somebody makes a mistake. And that's all fun as a self-contained experience. But what really builds deeper understandings is that conversation afterwards, is the chance to dissect and step back and connect and just think it through together. And that's totally a collaborative process.
And so I wanted the book to give both of those things, the direct, like, "Here's the game here are the rules. Go play. Have fun. And then come back and let's talk about the math. Let's talk about the strategy. Let's basically play it with our hands open, cards up on the table." Most games are actually pencil and paper games, not card games. But same idea, right? Like, let's just look at it from both players' sides stand outside this game for a second and have that larger conversation.
Why failure is a critical part of the problem solving process [12:22]
Eric Olsen: Is failure a necessary part of this collaborative nature as well? You've spoken a lot about how it's really important that we teach our kids, that we train our kids to not see failure as failure, but a critical and essential part of the learning and discovery process. Is that easier to facilitate in a collaborative setting?
Ben Orlin: Yeah, definitely, I think. Yeah. Why don't students accept failure as part of the learning process? I think it comes back largely to the weird tournament atmosphere that we've set up in math classrooms in school. Some of this is hard to avoid, but you have 25 students all about the same age. For bureaucratic reasons, it's just more efficient to put them all in one classroom, one teacher teaching them the same thing pretty much day in and day out. Whether that's the right lesson for this kid on this particular day, we don't really have the latitude to customize those lessons or give you this close one-on-one mentorship. It's like, "All right, you're in this class of 25 kids, you're getting this lesson today."
And what winds up happening is it feels like a tournament. It feels like a race. It feels like whoever finishes the work that day first is the best. We often give similar kinds of work, a lot of skills practice because that's easy for the teacher to assess and easy to give grades on that feel "fair." And so we wind up with this very narrow and peculiar experience of mathematics in school. It just makes it so easy to look at the kid to your left and look at the kid to your right and feel like, "Oh, okay, I guess I'm in the middle because I'm faster than the kid on the left, but I'm slower than the kid on the right." And it's a totally artificial scarcity, right? It's this feeling of like, "Oh, well, there are A math students and B math students. And then the students who are getting C are students who are struggling."
And it's completely artificial. You get students who could be wonderful mathematicians who just like, "Eh, it's not my subject. I'm not one of the math kids" and sort of get scared off of it or put off of it, I should say. They may or may not be feeling scared. And it's totally artificial, because then you get into the adult world and there's this absolute scarcity of mathematical understanding and mathematical excellence. Every organization would love to have more people around who know mathematics and can do mathematical modeling and do modeling that's sensitive to context and help solve problems and harness data.
Eric Olsen: We're hiring.
Ben Orlin: Yeah, exactly. Exactly. Yeah. Everybody's hiring good mathematicians. So the scarcity is totally artificial. And I think it comes from that tournament atmosphere, that sense of a competition. The way adults talk about their own math education, it's weird. It's like they're describing the NCAA Tournament for basketball and they're like, "Well, I made it to the tournament, but I lost in the first round." And that's like, "I took trigonometry, but I never quite got calculus," or something like that. And then people will say, "Oh I made it to the final four," like a good team, which would be like, "Oh, I took multivariable calculus in college, but then I took an abstract course. And it didn't make sense to me so I stopped." It's as though math is the thing you progress in until you hit a wall and then you drop, then you've lost. Then you've even knocked out of the tournament. Which is so just such a silly way to experience things. Not to blame the people who are having that experience, but it's a silly system we've backed into.
So that's a long way of saying that yeah, games break the mold a little bit. And especially that conversation after the game where you've won or you've lost, but now you can step back and realize it wasn't about the winning or the losing. It was about exploring the space of possibilities.
Eric Olsen: Man, it's really great stuff. Leave us with some next steps advice. Perhaps some of our listeners saw this book in the bookstore and said, "Well, this isn't serious math." Listeners who may have a skepticism toward puzzles and games because we've seen our kids say, "No, no, no. It's a math game." And you see them play a bad version of Zelda for 20 minutes and have to answer two plus two to get over a bridge once every 20 minutes, like this nonsense. So there's some inherent skepticism toward you. You try to cloak nonsense math as a math game to make us all feel better about it, but it's silly. And the real math, the abstract math, the rigorous math is wholly separate from puzzles and games. Remind us why that's not quite right.
Ben Orlin: Yeah. I think the... Right. The Zelda game where it's, "Oh, don't worry. I had to add two plus three. And so I'm learning math." That's definitely coming from gamification. And in particularly, that's gamification done poorly. So I guess the best case scenario would be you're playing Zelda and you're being asked questions, but the questions are actually at a good intellectual level for you. And that's fine. That could be a fine experience. That's not what my book is going for though. The games aren't curricular. They're not about particular arithmetical or algebraic skills. They're structures, right? They're interesting mathematical structures that you would climb inside, you play with the rules for a little while and then you climb outside and you think, "Okay, cool. What was going on in there? What was that all about?"
And importantly, a question I sort of ask in almost every chapter of the book is what if we tweaked the rules? What if instead of the point being scored by connecting the two lines, you've got a point when you broke a connection? Or what if you were, instead of trying to maximize the length of this path, you were trying to minimize the length of the path and make sure there are no long paths? Those kinds of questions I think are very mathematical. It's not the exact math you're going to be doing in your Algebra I class, but it's a different path to the same kind of thinking.
Enroll in AoPS Academy Math and Language Arts Summer Camps [18:11]
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Ben Orlin Rapid Fire [18:55]
Eric Olsen: It's now time for our rapid fire segment called Problem Solved where we ask the guest to solve incredibly complex and difficult education issues in single soundbites. Ben, what's one thing about K-12 education you wish you could snap your fingers and problem solved, it's fixed?
Ben Orlin: Yeah, I think the simple, boring, but correct answer for me is funding. We fund schools locally. So it distorts the housing market on top of messing up education and making it so that you've got well funded districts and poorly funded districts. I don't think anyone thinks that a kid's education should depend on how wealthy their parents are. We understand that wealthy parents want a great education for their kids. I don't begrudge them spending money to ensure it. But everyone should get a great education. So funding should happen at the state or the federal level. It should not be based on local property taxes. That's a little bit of a technical answer.
So my more interesting, my weirder answer, my fantasy would be to snap my fingers and somehow separate the evaluative aspects of school, the sorting aspects of school from the learning and teaching aspects of school. I think this is kind of impossible so it's really just a fantasy. But if you could somehow have like... I guess what I want is the sorting hat. If the sorting hat was going to be placed on children, it tends to tell them what kind of college they would go to, where they'd go to college and it would always get the answer right, it would completely free up teachers and students to stop worrying about grades and stop worrying about the economic future of the students, which understandably kind of weighs on the whole process and just say what is going to build your skills and your passion and your curiosity to make you able to go out in the world and do excellent things.
Yeah, because there's scarcity in... Harvard only has so many beds in the freshman dorms, so there's just scarcity there. But there's not scarcity in excellent people doing excellent things. We all want more great people out there who are passionate and curious and have lots of skills and can solve problems in the world. Yeah. We got to work on the R&D for the sorting hat as the first step.
Eric Olsen: Ben, if you could go back and give your kid-self advice on their educational journey, what would it be?
Ben Orlin: Yeah. Some of your other guests have said similar things, which is just worry less about the grades and get more things wrong, take more weird risks. I think what I would probably do is... To my high school self, I would give him a quota and say, "You have to talk at least once in every class." I was a very weirdly silent student, which is funny for a guy who now writes books and has podcast. I was just very quiet. I think it was the same as you with having won that first time at poker. And you're just like, "Drop the mic." You're like, "All right, I'm done. I'm out of here." People thought highly of me in high school and I didn't want to say things and ruin that impression, right? Say silly things, say something wrong and ruin it. Which I think is a very typical fear of high performing students or students who've been told that they're clever.
And so I would say like, "No, you have to say something in every class. Ideally something kind of dumb and just do it." I'm giving you that quota. And then to my college self, I would give the quota of, "You have to get at least one B every term. If you get all As, you messed up. You didn't take classes that were hard enough. You didn't go explore a subject you didn't know enough." And the reason I give such specific quotas is I think, as a student that's what I did, was that just telling me, "Oh yes, you should value learning and creativity and trying new things." It's too easy to side step that. Whereas if I gave myself a rule, like, "No, no, if you get straight As, you've done it wrong. That makes you a bad student. A good student is you're going to get a mix of grades and you're going to try things you might not succeed at." Anyway, that is the advice I would give my student self.
Eric Olsen: That's a good one, Ben. And I also appreciate the free psychological evaluation this morning on my reason of not poker playing again.
Ben Orlin: Yeah, no problem. Right. The difference being that, I think it's okay to walk away from poker. You're not going to have missed out on important life experiences because you're not playing poker. Whereas like, if I walked away from literature classes, literature may be more important to one's overall wellbeing than Texas holdem. Or maybe not. I shouldn't…
Eric Olsen: I just like leaving as a legend, leaving as a ghost, being the guy at your Christmas party where they said, "Boy, that Eric, there's something weird about him."
Ben, what part of education do you think or hope looks the most different 10 years from now?
Ben Orlin: Yeah, I'm a big believer in weird idiosyncratic education. So if I could cast a wish or cast a spell on education for 10 years in the future, I just want lots weird quirky teachers helping weird quirky students find their own way. I see the bureaucratic need for a certain level of standardization and I see where standardized curricula and standardized tests come from. But I think great education always comes from someone with a singular vision for a subject and a belief of how it can fit into one's life, really working hard to help students connect with that vision. And that vision is just always at a more granular level. It's always more personal than something written by a big curriculum company, even a great curriculum company. And so, yeah, just quirky, personal, weird education is my vision for the past, present, and future.
Eric Olsen: I'm not sure you can win the rapid fire Ben, but boy, this is coming pretty close today.
Ben Orlin: See, my belief is everything boils down to victory and defeat. And I hate fantasy. So I hope I'm winning.
Eric Olsen: Let's see if you fumble on the last one. Ben, and this is the most important one, your best advice for parents looking to raise future problem solvers?
Ben Orlin: Yeah. Whenever I talk to parents, I'll be at a book event or something and I'll get some questions from parents, I always need to spend the first five minutes asking about their kid and what they do together and how are they enjoying school and what subjects are they excited about and what do they love outside of the classroom. So it's always so particular. It's hard to give very general advice, but I realize my victory in the rapid fire is on the line here. So I would say if I had to break it down, I guess the two things I look for are joy and skills. So to be an excellent mathematician, you need to have joy in it and you need to have the concrete skills. Skill is construed broadly. But the concrete understanding and knowledge and skills that allow you to solve mathematical problems and perform mathematical tasks.
And even one without the other can be okay. So joy without skills, that's me with basketball, right? Love the sport. It's beautiful. Love to watch it. I love to play it too, although I don't play it well. What it means is it leaves you in the position of kind of a fan, right? Like I'm a spectator when it comes to basketball. I'm not a practitioner of basketball. And you can go the other way. I see students who have lots of skills and not much joy in the subject. And often, those students can get As in my classes or they can often succeed. You can sort of work a job that way. But I think it's not going to bring out your very best. You're not going to achieve excellence if you don't have some joy in the subject.
So my advice for parents tends to be, where's your kid at right now? Do they have tons and tons of joy and energy and excitement about this subject and they just need a channel for it? Well, then like buy a book of puzzles and/or get some interesting curricular content and have them dive into deep problem solving because they're excited and ready for it. And often you'll see the other thing, which is you'll see students with very precocious skills, seven year olds who are solving problems usually assigned to 10 year olds, and they love being good at it, but it's not clear there's a lot of intrinsic love for the subject. It's, they love being good at something. I think all kids love that.
And when that's the case, then I tend to tell parents to try to channel that excitement or that skill into some joy. So that's when you start watching number file videos. And that's when you get a book like mine with the games and try to find experiences of mathematics that will develop a real love of the subject itself, not just of being good at something. Which is of course fun, but then the moment you feel not good at it, you've lost your love. And so developing the joy, that's more robust. That'll last longer and get them through hard times in a way that just feeling really good at something that that's just a more fragile self image.
Eric Olsen: BZZZ. Oh, I’m so sorry, Ben.
Ben Orlin: Oh man. What was it? What was the correct answer?
Eric Olsen: Nope, that is not how this works. So you'll just have to come back for another try when your next book gets released.
Ben Orlin: Very good. Very good. All right. Failed on the last level of the video game, but hit continue and try again.
Eric Olsen: And listeners, we'd love to hear your answers as well. So email us at firstname.lastname@example.org with your best advice for raising future problem solvers. And we'll read our favorites on future episodes.
Ben, thanks so much for joining us today.
Ben Orlin: Thanks so much, Eric.
Episode Summary & Conclusion [28:24]
Eric Olsen: All right. It's a little annoying when a hysterically gifted comic artist is also super thoughtful too, right? Almost unfair, Ben. But I loved hearing Ben's thoughts on puzzles versus games, about how so much about learning looks like failure, how to make sure our kids don't take the wrong lesson from that experience, and how games at their very best facilitate collaboration, not merely competition. And I love that Ben's games are some of the most engaging ways to drink some really delicious math medicine. So definitely follow our social media channels. If you want to see Ben's math comics that our kids absolutely love, go check out Ben's latest book release Math Games with Bad Drawings. And may you continue your journey alongside us, raising the great problem solvers of the next generation. See you next week.