Video Games Are The Perfect Way To Teach Math, Says Stanford Mathematician
By Jordan Shapiro, Contributer, 29 August 2013
Wuzzit Trouble, from InnerTube games, is new in the app store this week.
Innertube Games is a learning-games studio founded by four enthusiasts, including the world famous Dr. Keith Devlin: the NPR Math Guy and Stanford Mathmetician. It has taken InnerTube two years from forming the company to release their first game: Wuzzit Trouble.
Although they consider it a soft release, I’m excited to let my kids play Wuzzit Trouble in its current iteration (and to play it myself!). The game fulfills one of the great promises of game based learning: the ability for a game to teach multiple skills simultaneously. That is not to say that everyone who plays will walk away having learned a multiplicity of skills, but rather that the game offers puzzles that work on multiple levels. Therefore, players are able to practice and develop math skills and comprehension appropriate to their particular age and skill level. Innertube puts it this way:
InnerTube Games does not build video games to ‘teach mathematics.’ Rather, we build instruments which you can play, and we design them so that when you play them, you cannot fail to learn about mathematics. Moreover, each single game can be used to deliver mathematical challenges of increasing sophistication.
Wuzzit Trouble has a unique interface that’s based on turning gears. Devlin describes it as an “instrument on which to play mathematics.” He likens it to piano keyboard: you can’t help but learn something about music if you sit down and tinker. Manipulating the Wuzzit Trouble’s game mechanics is enacting the functions of arithmetic, in the same way that pressing a piano’s key creates tone. Put those functions together and you’re doing math. Put those tones together and you’ve made music.
I love the instrument analogy because I’m often explaining to my students why the Ancient Greeks saw math and music as part of the same realm–that area of experience that belonged to the god Apollo. Of course, the relationship has to do with intervals. But both math and music are also related to Apollo’s other domains, such as light, prophecy, healing, etc. The connection has been hard to understand from the rigidly measured viewpoint that has dominated Western thinking since Nietzsche inadvertently cemented the Apollonian into strict opposition with the Dionysian in The Birth Of Tragedy. From Apollo’s standpoint, space and interval reign. And where we focus on distance, it is hard to see the way things touch, or blend into one another. Unfortunately, this dichotomy is pervasive in education. As Cathy Davidson writes in her book, Now You See It:
Everything about school and work in the twentieth century was designed to create and reinforce separate subjects, separate cultures, separate grades, separate functions, separate spaces for personal life, work, private life, public life, and all the other divisions.
Then the internet came along. Now work increasingly means desktop computer. Fifteen years into the digital revolution, one machine has reconnected the very things–personal life, social life, work life, and even sexual life–that we’d spent the last hundred years putting into neatly separated categories, cordoned off in their separate spaces with as little overlap as possible.
Game based learning will lay the foundation for new ways of thinking, encouraging us to look at the process of learning traditionally Apollonian subjects from a Dionysian perspective.
I asked Keith Devlin to explain some of the great thinking that underlies Wuzzit Trouble, and the pedagogical thinking that permeates the InnerTube vision.
Your book, Mathematics Education For a New Era, argues that video games are the best way to teach math to middle school kids. Can you briefly explain why you feel that way?
Mathematics is an activity. It’s not stuff you know, it’s things you DO (and can do). Natural selection equipped us supremely well to learn actions by actually doing them. In fact, any other way is hopelessly inefficient. eg. Try learning to ride a bike by sitting in a lecture or reading a book – or even watching a video! It doesn’t work.
The studies of Street Mathematics show that pretty much anyone can become proficient at mathematics if they pick it up in the course of actions relevant to them. If designed suitably, video games are activity simulators with a dopamine reward system. When someone plays ANY game, they are learning something. The challenge for the math educator is to make that learning be about DOING mathematics.
You’ve related math games to a musical instrument, imagining a platform on which you play mathematics. Share some thoughts about how you think about the relationship between a math game and a musical instrument?
What I think is truly unique about Innertube’s games in the current landscape of math ed video games, is that our games are literally just instruments designed and built to act as representations of parts of mathematics. The mathematics itself is separate. Just as a piano, say, is not music, but can be used to play music. For instance, DragonBox, which you and I both love, is super for helping people master the solution of linear equations. But it cannot go beyond that. (At least, I don’t see how it could.) It’s locked in to that one specific part of algebra.
With Wuzzit Trouble, in contrast, we can add another room of 25 puzzles as often as we want, aiming them at 8-year old learners or 80 year old former Nobel Prize winners. Designing the game as an instrument on which certain mathematics can be “played” means our games are very versatile. As we build our games out we intend to add a feature where players can design their own challenge problems to share with their friends. Teachers too could prepare problem sets that load into our game. I expect that people will come up with ways to embed other parts of number theory into the game.
Why did you decide to build Wuzzit Trouble around Integer partitions?
The goal was to design the game so that any action in the game was a direct action on numbers: adding, subtracting, or multiplying them, in increasingly sophisticated, algorithmic ways. (Acting on the abstract numbers themselves, that is, NOT by way of a symbolic hindu-Arabic representation. We bypass the standard notation just as a piano can bypass musical notation.)
The challenge then was to do so in a way that yielded a fun and challenging GAME, that in its playing required the player to develop and use those increasingly sophisticated thought processes. Integer partitions was simply the best option we could think of. It asks you to look at ways a given integer can be obtained from others using the three basic arithmetical operations.
Having built the game and played it, I know just how engaging and challenging it can be. But even though I always felt confident it would work, I have to admit I was surprised at just how well it works as a game concept.
One of the things I love about Wuzzit Trouble is that it doesn’t dis-empower teachers. Players can learn on their own, but that learning will be enriched with serious instruction. How do you imagine that games like Wuzzit Trouble will change the way math is taught in schools?
For the later puzzles in the game (and even more so for some fiendish puzzles we haven’t dared include in this first release which is aimed as much as anything at helping us raise money to build further), there is no hope of getting a top score without stopping the game and doing some good-old-fashioned paper-and-pencil algebra. I’d love it if kids get sufficiently hooked that they go along to the math teacher for help.
Just think, when there are three cogs, there are 30 choices for each move, so 900 two-move sequences, 27,000 three-move sequences, 810,000 four-move sequences, and 24,300,000 four move sequences, etc. So plain luck is out of the question. A player who wants to solve a three cog puzzle in 4 to 10 moves inescapably has to think mathematically. Trial and error is out of the question.
When we have the money, we’d like to prepare a teacher demo version of the game, probably in HTML5 for Web access, absent the glossy front end but with mathematical annotations, that a teacher can use in class for demonstrations. That would also require providing teachers with support: lesson plans, classroom ideas, etc.
We felt that the game is the game, and should hold its own among all the other games, and teaching is for the teacher. We did not want to try to do in our game what a good teacher can do SO MUCH BETTER in the classroom.
So we see our instruments as resources for teachers, not apps that try to do things for teachers. But we also see them as just plain fun games!
In your view, what does game-based learning mean for the future of learning, or the future of schooling in general?
When the big supertanker that is systemic education finally gets fully on board, and has seen enough examples of good educational video games to be able to separate the wheat from the chaff (currently it’s mostly the latter that is out there), then I think that video games will play a significant role in mathematics education.
Video games are a much better representation system for learning mathematics than are symbolic representations on a static page. If the technology had been available in 350BCE, Euclid’s Elements would have been a video game. All Euclid’s arguments are instructions to perform actions: draw an arc, drop a perpendicular, circumscribe the square, etc. It would be much more efficient, both as a communicative medium and for the student learning, if instead of writing instructions in words, the student was presented with opportunities to perform those ACTIONS.
A change in how we teach math will inevitably also change how we think about math, and therefore, what math is–big picture: how will incorporating games like Wuzzit Trouble into school curricula change math and provide new possibilities for mathematical applications?
Since video games (call them simulators if you prefer) can help people learn mathematics in practical settings, it would make sense to test performance for the majority of students within the games themselves.
Not everyone needs to master symbolic mathematics. And there is good reason to conclude, as I have done in my book that you mentioned above, that many people are unable to get past what I call there the Symbol Barrier. So a rational strategy would be to have everyone learn in videogames (simulators) and evaluate them by their in-game performance, thereby equipping them to use mathematical thinking in the everyday world.
We should reserve study of symbolic mathematics to those intending to be scientists, engineers, etc. When they can use their experience in good video games as a basis on which to ground the symbolic approach. It’s really just replacing one symbol system, the videogame, with another, 15th century symbolic algebra. The latter gained ascendancy when paper was the primary communication medium.
In the era of the digital tablet, that ancient representation system is no longer optimal, at least not uniquely so.
What’s next for InnerTube games?
We have plans to build out Wuzzit Trouble by adding a lot more rooms of puzzles, each aimed at different audiences, from 8 to 80 years old, of different ability levels. (We will charge for some of those. Our basic philosophy is to provide the basic games for free, so everyone can benefit educationally, and make additional puzzle sets available for a fee so those who simply love the puzzles and will buy as many as we can provide).
We will build a data analytics back-end. We designed the game to make that possible, but did not have the financial resources to do it before launch. We will need that back-end for game development, teachers will need it if they want to use our game in class, and education researchers will be able to use it to carry out learning research using our game. (Our super-stellar educational advisory board are eager to start that phase. By being on our board, they have an edge over their colleagues in getting us to put in algorithms to collect the data as they want it!)
We have another twenty or so different games that exist in prototypes of various stages of Flash implementation, many of them kids tested, and we want to start building them. In our first year post-launch, we’d like to bring out two more, one based on algebra, the other on geometry – thereby demonstrating that we can span the three basic food groups of mathematics learning.
But we can’t do any of that without a fairly sizable injection of funding, probably a commercial investment. A video game like ours needs a support staff to handle updates as platforms advance, deal with customer problems, fix bugs, etc., etc. The only way to do that is to generate a revenue stream.
Right now, I think our best way to do that is to sell great puzzle sets to older folks – folks like me actually. I pass many hours on long airplane rides doing math-based puzzles. Because we can target our game — the same instrument — to kids in school and their grandparents, simply by providing different datasets to generate the individual puzzles, we can take money from the latter and use it to provide free games to the former. I call it the Robin Hood business model. No one is going to get rich in this business. But then, if it were about getting rich, none of us would be in education, would we?
Jordan Shapiro is author of FREEPLAY: A Video Game Guide to Maximum Euphoric Bliss and co-editor of Occupy Psyche: Jungian and Archetypal Perspectives on a Movement. For information on his upcoming books and events click here.