Digital Games Promise to Improve Math Skills
An excerpt from Greg Toppo’s The Game Believes in You
Greg Toppo is USA Today’s national education and demographics reporter. Raising children in a world “driven by images, media, and interactive technologies” gave him a different perspective on education reform and aroused his curiosity in video games and the role they could play in learning. In this excerpt from his book, The Game Believes in You: How digital play can make our kids smarter, Toppo focuses on math instruction and the success of the games Wuzzit Trouble and DragonBox.
When he was in high school, Keith Devlin had a revelation: Math is not a spectator sport. It’s not body of knowledge, it’s not symbols on a page. It’s something you play with, something you do. He remembered reading Martin Gardner’s legendary “Mathematical Games” column in Scientific American, which ran for twenty-five years, from 1956 to 1981. “Pretty much anyone in my generation who became a mathematician will say that one of the influences that made them do it was reading that column … because it was an incredible antidote to the drudgery of school mathematics that we had been subjected to.”
Devlin, who would go on to teach math at Stanford University, realized that, like Gardner, all great mathematicians spend much of their time playing with ideas. Actually, he realized, it’s very similar to what musicians do. In both music and mathematics, the symbols on a page are merely static representations of mental processes, laid out on a flat surface for easy reference. Representing math symbolically makes it easy to record and pass on to others, but it’s not the actual math.
Because so many of us have intimate experiences listening to and even playing music, we know this instinctively. Twentieth-century technology, from the gramophone to the cassette tape to the MP3 player, has taken music off the page. But most of us believe that math is flat, that doing it involves nothing more than manipulation of symbols. Partly this is due to the lousy math education we received in school and partly to the image of mathematicians in popular culture. When most movies or TV shows want to show that a character is a mathematician, Devlin realized, they show him or her writing symbols on a piece of paper, on a blackboard, “or, quite likely, on a window or a bathroom mirror.” Never mind that real mathematicians never write on glass. People identify doing math with writing symbols, often obscure ones. This “symbol barrier,” as he dubbed it, being unable to get beyond the symbols to the math behind them, prevents most of us from going further than we could.
But just as no self-respecting pianist would have you believe that his musical education ended with the ability to read the notes in a score, no self-respecting mathematician would say the symbols on the page are the actual math. Devlin remembered research from the early 1990s that looked at the math skills of young street vendors in the markets of Recife, Brazil. Faced with complex arithmetic, the children in the study, aged eight to fourteen, mastered it, in their heads, to 98 percent accuracy. But when researchers asked them to solve the same problems with paper and pencil, their accuracy dropped to less than 40 percent.They were experiencing the math in their heads, free from symbols, almost perfectly. Subsequent experiments found that Americans in a southern California supermarket did much the same. Asked to perform similarly complex math in the aisles, they did fine. But their performance suffered if they were asked to sit at a table and take a “test” with exactly the same math. Devlin, the British-born author of thirty-two books and National Public Radio’s longtime “Math Guy,” wondered if there was some way to break free from the symbols. It was, he realized, an interface problem, one that music didn’t have. He began to consider perhaps the most perfect musical interface of all: the piano.
Though it has become a naturalized part of music-making since the first one was built in 1710, the pianoforte (its name means “soft-loud”) was a technical marvel for its time, a machine that changed music in ways that are hard to imagine. Computer pioneer Alan Kay once observed that any technological advance is “technology only for people who are born before it was invented,” and in the case of the piano, this applies to no one alive today. Seymour Papert, the MIT researcher, concluded, “That’s why we don’t argue about whether the piano is corrupting music with technology.” Four hundred years later, few can play the piano well, but just about anybody can sit down at a piano, pluck out a simple tune and perhaps even sing along. Devlin realized that foremost among the piano’s virtues was its ability to enable just about anyone to play real music from day one, on the same instrument that professionals use. You could go from absolute beginner to Carnegie Hall soloist on exactly the same instrument, sitting in the same room, over the course of a decade or two. The piano delivers instant feedback on your performance, allowing you to easily gauge your progress.You must touch the piano to play music, but the more you do, the more you’ll learn, naturally, about melody, harmony, consonance, and dissonance. It is, in a word, immersive.
If you’re hoping to someday play Chopin polonaises, you should probably learn a few notes, scales, sharps, and flats, but none of these obstacles by necessity stands in the way of you playing real music. But let’s say you learn the symbols and decide to tackle a Chopin polonaise. Faced with a section you can’t play, you’d break it down into smaller bits and master each one at a slower tempo. No teacher on earth would suggest you practice on a simpler piano or, heaven forbid, just work it out with paper and pencil. If anything, a good teacher would double down on the real music. She’d play the passage for you, suggest you listen to a few recordings and urge you to practice the tricky parts over and over again. You’d live in the world of the music, your hands on the keys of the machine to give you access to the music and reproduce what’s in your head.
Devlin realized that a good digital game could do the same thing, helping kids “play” mathematics in much the same way. At their heart, video games are “activity simulators with a dopamine reward system” that could help kids strip problems down, analyze their underlying patterns, try out solutions and practice these skills repeatedly. “Video game worlds are not paper-and-pencil symbolic representations,” he wrote, “they are imaginary worlds. They are meant to be lived in and experienced.” Because they bypass symbols, he realized, they could give kids direct access to the math. They weren’t just a good medium for math education – they were probably the ideal medium. What the printing press was to reading and mass literacy in the fifteenth century, he decided, video games are to math literacy in the twenty-first century. For a math teacher to not know how to use them, he decided, would someday be akin to teaching English without being able to read.
“If video games had been around in 350 BC, Euclid would have made a video game,” Devlin told me. The thirteen books of Euclid’s Elements would have been the supplemental material, a PDF file that you could read if you wanted to. “People think I’m joking – I absolutely mean that. Euclid would not have written a textbook, he would have designed a video game.” Peek at any of his proofs, Devlin said, and you’ll quickly find that the great Greek mathematician, often called the father of geometry, is asking the reader to do things. “He says, ‘Draw this arc,’ ‘Drop this perpendicular.’ ‘Bisect that line.’ These are actions, and actions are what you get in video games.”
But when he looked at the popular math video games on the market, he found the same thing that Matthew Peterson, co-founder and CEO of the MIND Research Institute, did: most were “forced marriages of video games with traditional instruction of basic skills,” rat-race wheels built around repetitive practice, or digital flash cards that delivered traditional pedagogy onscreen, “a new canvas on which to pour symbols.” They were, he realized, no better than the textbooks they sought to replace. “If you look at the vast majority of the games – and there are hundreds and hundreds and hundreds of them – you don’t learn much, but you practice what you’ve already learned.” They reminded him of the first early motion pictures. When people first started making movies, they essentially just filmed stage plays because that’s what they knew how to do. “But then they realized that making a movie meant something very different from doing a play on the stage.” Actually, a better model might be those disastrous turn-of-the-century flying machines that tried to recreate the flapping of birds’ wings. The early aviators, he thought, confused the larger, more complex phenomenon of flying with the simpler act of flapping, the one activity they’d observed. He realized that to create a good math game, you had to separate the activity from its familiar representations.
In 2010, a mutual friend got Devlin in touch with John Romero, one of the legendary group of video game designers who had essentially created the first-person shooter genre in the early 1990s with the groundbreaking Doom and Quake games. Romero and his former id Software partner John Carmack were once called “the Lennon and McCartney of video games,” but a decade after he left the company, Romero was interested in finding out if it would be possible to embed high-quality mathematics instruction into a genuinely engaging game. He took on Devlin as a kind of informal math advisor, and for four years the two talked regularly, the Stanford math professor and the rock-star father of Wolfenstein 3D. The “stealth project” generated no new products, but Devlin cut his teeth throwing out ideas for games he thought would be fun, only to have them “destroyed within two minutes” by Romero. “There were good reasons why these things wouldn’t work,” he said with a laugh. “The simple one was that kids aren’t going to play it unless you stand over them with a whip.”
Devlin wasn’t sure if Romero ever got anything out of the conversations, but they must have lit a fire, because when Devlin formed a small startup to create math games, Romero volunteered to help. The company’s first game, which debuted for iPhone and iPad in August 2013, invites players to pick a series of locks by spinning little number dials that add, subtract, or multiply increasingly complex number combinations, all without any of the calculation symbols present in math exercises. Wuzzit Trouble presents players with a dial that looks much like a sixty-minute clock face, only it goes up to sixty-five (remember that number!). Each level asks you to figure out the most efficient way to hit a series of target numbers etched into the dial face using little cogs turned to multiples of smaller numbers. You spin the dial forward or backward by generating multiples of these smaller numbers, in the process using one, two, and sometimes all three mathematical operations. For instance, one early level asks you to pick the lock by hitting three targets – six, eighteen, and fifty-four – using multiples of six. Easy enough. But the following level presents three new targets – thirty-five, forty-seven, and fifty-nine – none of which is a multiple of six. You soon realize that the only way to hit these is to dial backward from sixty-five (sixty-five minus six is fifty-nine … fifty-nine minus eighteen is forty-seven, and so on). As the game gets increasingly harder, the carefree playing around with numbers turns more purposeful. What for many levels had been a kind of practiced plucking of low-hanging mental fruit starts to demand a ladder. Pretty soon you’ve got five targets to hit and three different cogs with which to hit them, all in six moves or less. Where to begin?
Inevitably, if you have any hope of beating these levels, you must start thinking strategically, looking at the big dial and little cogs as a system. You may even ask yourself, “How did the level designer decide that I could do this in six moves or less?” Then, as the levels get progressively harder – at some point, the game adds a fourth cog, opening up the possibility of millions of sequences – something remarkable happens. Trial and error, while they were fun for a while, are no longer good enough. Getting the dial to turn just so takes on a strange urgency that can only be satisfied by a precise, clever solution. But you can’t be precise and clever unless you’re immersed in the numbers, intimately familiar with them and the intervals between them. They’re like notes on a scale and you’re playing a chord.
As the intervals become more complex and the need to keep track of them becomes more urgent, arithmetic turns to algebra. You may even pull out a sheet of paper and a pencil and start scribbling figures down (please, no writing on glass). But in the end, you must translate the paper-and-pencil figures into action to make the dials turn. You’re living in the world of the numbers, your hands on the keys of the machine to give you access to the math and reproduce what’s in your head. To succeed in Wuzzit Trouble, you have to practice. But when it works it is elegant. When you come up with a complex solution, all you really want to do is see it again and show to your friends. Watch this, you say. It is a performance.
Forty-year-old Jean Baptiste Huynh, the Vietnamese Frenchman living in Oslo who persuaded the entire country of Norway to spend a week solving algebra problems, looks quite a bit younger than he really is. He has a shock of dark hair, white teeth, a big smile, an athletic frame, and nearly boundless energy, and when I met him at a tiny café near Dupont Circle in Washington, D.C., during one of his visits to the United States, he could have passed for someone just a few years out of college. I wanted to ask him about his popular iPad algebra application DragonBox. It had been in Apple’s App Store for several months by then, and everyone I knew was asking me if I’d played it. One friend had breathlessly told me I had to get it. It teaches algebra to preschoolers, he said. It’s amazing! But as soon as I sat down, Huynh pulled a travel-worn iPad from his bag and he said he wanted to get one thing straight about DragonBox. “It’s not an algebra app,” he said, swiping the glass touchscreen to bring up the game. “It’s not about algebra.”
By the time we met in the spring of 2013, DragonBox had already been downloaded about 85,000 times, mostly by parents, and Huynh had become convinced that the iPad’s ability to let children access the material directly, as well as the app’s straightforward pedagogy, made them “the single best resource I can use” to teach children. I soon learned that Huynh had that trifecta of a great teacher’s personality: a passion for his students and his subject, a bit of a foul mouth, and a dry, balancing wit. During our conversation, I made the mistake of asking what he thought of the school system he’d attended in France as a young man. It had gotten him pretty far, I thought. “You know what? This is a f***ing prison,” he said. “Your brain is dead when you’re in prison. You don’t want to be there.” He may have sensed my shock, so he smiled and said, “I come with very strong words because I am French. I can do that.”
Huynh explained that he and his colleagues at We Want To Know, the Norwegian game company he’d co-founded with French cognitive scientist Patrick Marchal, had been trying to decide whether to sell the game to schools, which were beginning to buy iPads at a steady clip. “That’s the natural place to play this game,” he said. “And we decided, ‘No, we don’t do that,’ because teachers are going to say, ‘You do that, you do that.’” In other words, he said, teachers would find a way to take the fun out of his fun little game.
So if DragonBox wasn’t about algebra, I asked, what was it about?
Speed and imagination, he said.
“Mathematics is creativity. It’s play. You take an object and you ask, ‘What if?’” But that’s not how it’s taught in schools. “We teach it as a dead subject – like Latin. A dead language. You have fantastic texts, but it’s a dead thing.”
He remembered a conversation he had had recently with his four-year-old son, Paul. They’d gone out for the day and Huynh was carrying him on his shoulders as they arrived back at their Oslo apartment building. Paul said he wanted to push the buttons for the building’s security code, so Huynh told him: “It’s ‘ten-ten’ – ‘one-zero-one-zero.’”
His son leaned in and pressed “two-three-two-three.”
“I have a lot of time,” Huynh told me. “As a parent, I think it’s important to have a lot of time. I say, ‘Paul, why did you enter this code? The code is “one-zero-one-zero.”’ And then I realized: the way you learn is by experiencing all the possibilities. And it’s quite natural and sensible to [press] ‘two-three-two-three.’ Why shouldn’t it work?”
He thought about it and smiled. “This is extraordinary!”
Huynh is as responsible as anyone for the recent surge in interest, here and abroad, in high-quality, imaginative math games for children. For a while, before several equally offbeat competitors began appearing in the App Store, DragonBox was the go-to app that smart parents with iPads were recommending to their friends. After it was released in mid-2012, Wired magazine’s “Geek Dad” blogger Jonathan Liu played the game with his daughters and said he was impressed that it “doesn’t give you the answers, but it enforces the rules.” DragonBox, he wrote, “is making me reconsider all the times I’ve called an educational app ‘innovative.’”Which is all very surprising when you consider that Huynh, growing up, wasn’t a gamer. He remembers playing a PC version of Romero’s early first-person shooter game Doom and thinking, What a waste of time! “I don’t know anything about games still,” he said. “I don’t play.”
Huynh has already had at least three careers: he’d started out as a stock portfolio manager, but then he and his wife, a child psychiatrist, began having kids – when I met him, their children were four, nine, and twelve. “I guess I got this crisis that any people working in finance hit at some point,” he said. “You want really to use your energy on something really useful. So I decided that I would do something for children.” He quit his job and started a children’s magazine, but after a few years decided he should really be teaching. He sold the magazine and took a job teaching high school math and economics in Spain.
He was a miserable failure.
Huynh remembers spending twenty-eight hours one time preparing for a two-hour lesson. The results showed that his students afterward were performing only “marginally better.” He decided, much like Devlin, that the tools were holding him back. He needed something interactive that would give students control of the experience, that could help them access the math quickly and without fuss. “My own children, I want them to learn as fast as possible,” he said. Years earlier, he’d read two books that had a profound effect on his thinking: tennis coach Tim Gallwey’s 1974 book The Inner Game of Tennis and Betty Edwards’s 1979 book Drawing on the Right Side of the Brain. Both focused on what it takes to improve at a craft, separating the analytic parts of our brain from those that get the work done. Both suggested a new approach to teaching, Huynh said: “The more words you use, the less impactful you are.”
He began to investigate games, but at a kind of arms-length distance. “I’m not a fanatic, you know, ‘Games, gamers, game-based learning.’ I hate this. I consider it more like Montessori of the twenty-first century.” All he really cared about, he said, was putting the child at the center of the learning process. “It’s about experiences and not games.”
Huynh basically had to get his wife’s permission to develop the app. “I’m married to a child psychiatrist,” he said. “No screens at home! No TV. No Nintendo, PlayStation, name it – nothing. Nothing. When I say to my wife, ‘Well, I think I’m going to design some games because that’s the best way to teach,’ she says, ‘No!’ I have to argue. I say, ‘You know I’m doing that because that’s the best way – you have the prison which is school. Please, let me do that!’ She says, ‘Well, OK, show me what you have.’”
Huynh made her a promise: Whatever he created, he told her, it would get the job done quickly, with a minimum of screen time. When the game finally appeared, many users said the same thing, both in praise and complaint: DragonBox was strange, lovely, and engaging. It got their kids thinking algebraically in six minutes, five minutes, four minutes! And it was over way too fast. In a way, Huynh was the victim of his own success.
Shortly after the game appeared, Huynh met University of Washington researcher Zoran Popović, director of the university’s Center for Game Science. Popović had made headlines around the world in 2011, after he and a colleague helped two graduate students design Foldit, an online, crowd-sourced game that challenged players, most of whom had little to no biomedical knowledge and most of whom played the online game across great distances, to learn about the shapes of proteins and compete to fold them into the most efficient shapes. Dubbed “Tetris on steroids” by one player, Foldit took advantage of humans’ puzzle-solving skills, in the process helping researchers make advances in treating cancer, AIDS, and Alzheimer’s disease, among others. In a 2011 paper published in the journal Nature Structural and Molecular Biology, Popović shared authorship with eleven other researchers and two Foldit players’ groups, one calling itself the “Foldit Void Crushers Group.” In one of the game’s more recent challenges, players analyzed a monkey HIV protein whose structure had eluded scientists for fifteen years. One far-flung team of Foldit players figured it out in ten days.
Popović got the idea to use DragonBox to challenge large groups of children to work through thousands of online algebra problems, on deadline. He adapted the game to offer more help to students who needed it while allowing those who understood a concept to move on. In an early trial, 93 percent of students mastered the basic ideas after only ninety minutes of play.In June 2013, he and Huynh persuaded more than 4,000 students in Washington State to spend a five-day work week solving algebra problems. The students continued after Friday rolled around, spending the equivalent of more than seven months doing math. In the end, they solved nearly 391,000 problems.A few months later, students in Wisconsin solved nearly 645,000 problems.In January 2014, in Norway, students solved nearly 8 million equations. Nearly 40 percent of the work, Popović’s team found, was done at home. “To us this is very exciting because it shows the engagement way beyond the brick-and-mortar school day,” he said.
DragonBox has undergone several modifications and expansions since it first appeared – a new version, which tackles geometry, came out in the spring of 2014 – but it is still lovely, mysterious and a bit off center. One critic, Forbes games writer Jordan Shapiro, praised its “avatars that were simultaneously sweet and a little twisted.”And despite what Huynh insists, families are buying it to get their kids – in many cases their preschoolers – thinking algebraically. The game presents players with an odd little scenario: a mysterious box arrives, for no apparent reason, with a wide-eyed, omnivorous baby dragon inside, packed in straw. Also for no apparent reason, the dragon wants to be alone. He must be alone before he’ll eat. Don’t ask, just play.
The game board is divided into two sides, with your little dragon-in-a-box on one side. On both sides are “cards” – random images of lizards, horned beetles, deep-sea fish, and angry tomatoes. Again, don’t ask. To win each level, you must touch and tap and drag the cards to get rid of all of those on the dragon’s side. Once you do, he noisily eats everything that remains on the other side and the level is done. “The box is alone!” the game declares. The game is strange, but you keep playing. Soon you’re encountering “night cards” with darkened versions of the creatures that, you learn, will soon stand in for negative numbers. Pretty soon you’re strategizing which cards to get rid of first – order of operations, anyone? On level twelve, one of the animal cards has mysteriously been replaced by a little black “a.” Five levels later, there’s a “c.” Finally, on level eighteen, the little wooden dragon box is momentarily replaced by a floating letter “x.” You’re doing proto-algebra. It’s been about three minutes since you downloaded the game.
This strange procession continues through 100 levels, with no explanation or elaboration. Addition, multiplication, division, fractions – all of them appear, without fanfare or explanation. You play sixty levels before an “equals” sign appears between the two sides of the board. By game’s end, at level 100, you’ve moved seamlessly, baby step by baby step, from a cute baby dragon eating a spiky two-headed lizard, to this: “2 over x plus d over e equals b over x,” which you solve, fearlessly and perhaps even a bit impatiently, in exactly fourteen steps. You are four years old.
An excerpt from The Game Believes in You: How digital play can make our kids smarter, by Greg Toppo (Palgrave Macmillan: 2015).
Sign Up To Receive Notification
when the latest issue of Education Next is posted
In the meantime check the site regularly for new articles, blog postings, and reader comments