Keith Devlin
Keith Devlin

Part 8 of MindShift’s Guide to Games and Learning.

Keith Devlin is a well-known mathematician and the author of many popular math books. He is co-founder and Executive Director of Stanford University’s Human-Sciences and Technologies Advanced Research Institute and is well known as the “NPR Math Guy.” He’s also a big fan of using video games as a teaching tool and the founder of an education technology company called BrainQuake.

Devlin believes the future demands a substantial change in the way we think about math education. “So many people in the U.S. have never experienced good mathematics teaching. They have a totally false impression of what mathematics is,” he says.

In this conversation, he explains why we now need different mathematical skills than we once did, and points out that the math curriculum of the 20th century did not equip today’s adults to mentor children in the math skills of the 21st century.

Devlin argues that video games are the perfect tool for teaching math. He also sheds some light on those Common Core math problems that are so controversial.

Jordan Shapiro: In 2011, you published a book entitled Mathematics Education For A New Era: Video Games As A Medium For Learning. What inspired you to write that book? Do you play video games?

Keith Devlin: I not only play video games, I actually wrote one, way back in the early 1980s when personal home computers were just starting to appear. I wrote a math game where you use trigonometry to find buried pirates’ treasure on a desert island. I did it for use in the math class at the local elementary school my daughters attended. When I saw how my daughters were totally engaged by video games (professional ones, much better than mine!), I recognized at once their potential in mathematics education.

I wrote the book to try to give teachers some sense of what it would take to build a good video game for mathematics learning and to explain to game designers what it would take to embed good mathematics learning into a game. I was not thinking about building a video game myself (back then).

JS: In the book, you argue that video games are the best way to teach math to middle school kids. We’ve spoken about this before and you’ve talked about the importance of learning through doing. Why is context so important? And how can thinking of video games as math simulations help to move the typical math class from an product based pedagogy to a process based pedagogy?

KD: Video games are an ideal medium for developing mathematical thinking. It’s a classic case where a technology that renders old skills less relevant actually provides their replacement. Many people outside of the worlds of mathematics (particularly math as used in the world) and mathematics education are simply not aware of the dramatic shift that both disciplines have undergone as a result of digital technologies.

When today’s parents were going through schools, the main focus in mathematics was on mastery of a collection of standard procedures for solving well-defined problems that have unique right answers. If you did well at that, you were pretty well guaranteed a good job. Learning mathematics had been that way for several thousand years. Math textbooks were essentially recipe books.

But now all those math recipes have been coded into devices, some of which we carry round in our pockets. Suddenly, in a single generation, mastery of the procedural math skills that had ruled supreme for three thousand years has become largely irrelevant. In my book, I used the term “mathematical thinking” to distinguish the kind of math that is relevant today from the (procedural) “mathematics” most people are familiar with.

The skill that is in great demand today, and will continue to grow, is the ability to take a novel problem, possibly not well-defined, and likely not having a single “right” answer, and make progress on it, in some cases (but not all!) “solving” it (whatever that turns out to mean). The problems we need mathematics for today come in a messy, real-world context, and part of making progress is to figure out just what you need from that context.

Books and lectures (in a room or on a screen) are useful resources for mathematical thinking, but they are no longer at the heart of math learning. The only way to acquire mathematical thinking ability is by a process of exploration – lots of trial-and-error and reflection. This is exactly what video games can deliver. They can provide small scale simulations of the kinds of open-ended, context-influenced, project-based, problem solving that is at such a premium in today’s world.

JS: I wrote about your game Wuzzit Trouble earlier in this series. I also sometimes show it when I’m doing workshops or public speaking. I’ve used your metaphor often: learning games should work like musical instruments. What does it mean to create a mathematical instrument? Can we do the equivalent for other subjects?

KD: Yes, it’s fortunate that the word “play” applies both to musical instruments and video games. Everyone knows that the best way to learn an instrument is to start to play it. We don’t ask someone to learn to read music before they sit at a piano or pick up a guitar. But that’s exactly what we do in mathematics! The reason we do is that through most of its history, mathematics did not have any instruments. Video games can provide math instruments you can use to learn mathematics. Take a look at the twenty-minute video of the talk I gave recently. In it, I use Wuzzit Trouble to explain how this can be done.

We can do the same kind of thing in other subjects, but many of them already have instruments (e.g. laboratory equipment in the natural sciences). Before video game technologies, however, all we had for math were paper and pencil, augmented with ruler and compass for geometry.

JS: So, are you saying that kids don’t need to learn how to scribble numbers and equations on paper? Does that mean the symbolic Hindu-Arabic representation of mathematics is obsolete?

Keith: No, kids need to master Hindu-Arithmetic representation of numbers far more today than in the past. What they don’t need to do – and I think this is what you’re getting at with your question – is train themselves to do long computations, as was necessary when I was a child. No one calculates that way any more! What they (we) need in today’s world is a deeper understanding of how and why Hindu-Arabic arithmetic works.

In all four offerings of my mathematical thinking MOOC to date, I have had as students, engineers with years of experience who suddenly found themselves out of a job when their employers replaced them with software systems (or sometimes overseas outsource services). Those engineers are now having to retool to learn this other skill of creative problem solving – mathematical thinking.

Incidentally, the Common Core State Standards that are so much in the news were designed to guide the shift to this new kind of mathematics, as I’ve tried to explain before. Many of the parents who object to the basic goal of Common Core appear do so because they too have not realized how much the world has changed in its demands for mathematical skills. (There is a lot to argue about when it comes to the implementation of the Core, but that’s a separate issue.)


JS: In the past, you and I have discussed the “Symbol Barrier.” Now I think I misunderstood the concept. I always thought you meant that Hindu-Arabic representation was an obstacle to mathematical thinking. But clearly that’s not what you meant. Explain the “Symbol Barrier” and how video games can help to circumvent it.

Keith: The Symbol Barrier is the name I gave to a phenomenon first noticed in the early 1990s. If people need to use basic computational mathematics in their everyday lives or careers, they quickly pick it up and are able to perform at a 98 percent accuracy level. That’s not just some people, it’s ALL people (apart from around 3 percent who have a brain condition called dyscalculia). But if you ask those same people to solve the same math problems presented in a traditional, school, paper-and-pencil test format, their performance levels drops from 98 percent accuracy to a mere 37 percent correct. Those people (all of us) don’t have an inherent math problem, they (we) have a language problem! That’s the Symbol Barrier.

The Symbol Barrier is a problem – i.e. a barrier to entry into mathematical thinking – because at the moment, learning mathematics and being tested in mathematics is all done by way of the symbolic representation! It’s as if we taught and tested people’s musical ability by instructing them in musical notation and testing how well they could write music using that notation. We don’t do that. We ask them to sit down and play an instrument!

Same with driving. Would you prefer to be driven by someone who had just passed the written part of the driving test, or would you want to know they had passed the road test?

Or an airline pilot. Which gives you more confidence, someone who has flown successfully in a simulator or a trainee pilot who has just passed a written test on how to fly a plane?

Likewise for mathematics. I would feel much more confident in the arithmetical ability of someone who had scored highly on my own game Wuzzit Trouble than someone who had simply learned how to line up numbers in columns and apply the standard algorithms of arithmetic. The latter just requires rule following, the former makes you think.

JS: What other types of learning products are you working on at your company, BrainQuake? Which mathematical concepts are you trying to tackle?

KD: Our basic platform is mobile games, though we intend to bring out Web-based PC versions for classroom use. The user data we obtained from the release of Wuzzit Trouble, last fall was as good, if not better, than we had hoped. We were ranked highly in many general game categories, not just educational games, and we were appealing to people of all ages.

Once we knew Wuzzit Trouble was succeeding as a general category video game, it made sense to develop that side more, so as to appeal to the widest possible audience. So we have been focusing on embedding that basic gears mechanic into a richer video game.

However, to be honest, Wuzzit Trouble is barely classified as a game. I would (and did) call it an entertaining and engaging math-based mobile app. To reach a much wider audience, we need to incorporate more of the elements of the highly successful video games that attract tens of millions of players. Teaming up with John Romero (the legendary creator of Doom and Quake) as our chief Game designer provided us an exciting opportunity to go after that elusive big audience.

We are also developing the assessment side. Students, parents, and teachers – and adult player-learners – want to know how well they are progressing in terms of math learning. Video-game learning provides extremely powerful mechanisms to track learning – potentially far better than the existing methods used in standardized tests. Doing that requires the development of powerful algorithms that take the raw player data (which goes right down to individual finger actions on the screen) and use it to infer the player’s thought processes behind those actions, so we can see how a player is trying to solve the problem. This will take the old idea of “show your working” to a whole different level.

JS: This sounds great. Should we be trying to do this for every part of the mathematics curriculum?

KD: BrainQuake is absolutely not obsessed with trying to achieve “full curriculum coverage,” whatever that might mean. To my mind it makes no sense to try to use video games to provide learning for parts of mathematics where an alternative, interactive representation does not add anything significantly new.

Also, I think it will always be largely up to a good teacher to help learners master the symbolic approach necessary for more advanced mathematics. I think that people who see technology as a way to eliminate the need for good classroom teachers fundamentally misunderstand what it takes to help someone learn how to think a different way – in my case the mathematical way. Technology can help. It can help in significant ways. But it cannot replace a good teacher.

JS: What do teachers and parents need to know about the future of game-based learning, the future of pedagogy, and the future of education in general?

KD: Game-based learning is the future. Games are just simulators with an internal incentive structure (often dopamine based). That means they tap into the way humans, and all living creatures, are hard-wired to learn: by doing.

But people are not machines. We are social creatures. If you want a child to develop into a useful citizen who can have a good life and contribute to society, you need to develop that child fully as a human being. That requires good parenting and great teaching. Doing it right requires close integration of the technologies with the human interactions.

The MindShift Guide to Games and Learning is made possible through the generous support of the Joan Ganz Cooney Center and is a project of the Games and Learning Publishing Council.

Digital Games and the Future of Math Class: A Conversation With Keith Devlin 26 June,2014Jordan Shapiro

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  • “Game-based learning” may indeed be the Pavlovian future of K-12 mathematics education in the US, where students need to be entertained and coddled, and where educators are only too willing to offload their workload to devices, but American students will only fall further behind those from top-performing nations, where students from primary school up to high school struggle on a daily basis with lengthy, difficult problems of seemingly infinite variety.

    • I’m pretty sure Keith Devlin doesn’t see games as a replacement for patient, varied, problem solving.

  • darren65

    Why do a problem at all if you’re not going to get the correct (or at least an optimal) answer?

    • Have you ever written an essay? You probably have, and you almost certainly revised your work a lot, if it ended up being a good essay. This is true of mathematics problem solving as well. Far too often we expect kids to get an answer on the first try, and do not value the process through which they get feedback and refine their work.

      • Darren65

        My comment has nothing to do with doing a problem over, but with doing it correctly. It’s OK to take a few times while learning, but to be honest I don’t see how this relates to •my• point at all.

  • barrygarelick

    Routine problems are a requisite for the non-routine (and ill-posed) problems that Devlin and others seem to think are the holy grail of math education. But people like Devlin want to start at the non-routine end, thinking that giving students ill-posed problems creates a problem solving “schema”. It doesn’t; novices have to start at the beginning to become experts. Devlin and others like him don’t see any distinction between novices and experts; they see everything through the expert lens that they have acquired.


    • 4 references? You will have to work harder to convince me than a three page paper that references the work of Sweller, et al.

      • barrygarelick

        I could give you some Willingham references but something tells me you won’t like those either.

  • Guest

    “The only way to acquire mathematical thinking ability is by a process of exploration – lots of trial-and-error and reflection. This is exactly what video games can deliver. They can provide small scale simulations of the kinds of open-ended, context-influenced, project-based, problem solving that is at such a premium in today’s world.”
    “Only?” Clearly, this article is marketing hype for his products. Students do NOT properly master all of the required detailed skills from a top-down, discovery process. This can only be done from the bottom-up individually with daily problem sets that carefully lead students from simple applications of new techniques towards more complex variations. If you learn math properly, then you won’t have to struggle with vague problem solving techniques over and over. That’s what math teaches you. It teaches you about merit functions and what to do when mn.
    What has it been, twenty years or more since K-8 schools have been using fuzzy, discovery techniques in math? Where are the results? There is a common belief that the problem is just lack of engagement or rote learning. No, the problem is that nobody accepts responsibility for ensuring any level of mastery of basic skills. I got to calculus in high school with absolutely no help from my parents. That is an impossibility these days.
    Computer games could be a helpful addition, but too many drink from the discovery (and $$$) Kool-Aid cup and try to make it the “only” basis for learning math, something that plays well with educational pedagogues. Meanwhile, many of us parents cover their asses at home with flash cards and worksheets. We make sure that our kids have the basics to make educators feel warm and fuzzy about all of the group, hands-on work done in class. At least school music teachers acknowledge that much of their top-down concert band or orchestra successes are built on years of individual private lessons – scales, finger exercises, etudes and high expectations.

  • As a game designer, now doing educational games, I enjoyed how Devlin articulated (in his book) some of his points on why well-designed (math) games are the holy grail of learning math. I particularly enjoy his analogy of the bird-like flying machine to modern day educational games. He’s absolutely right when he talks about the importance of integrating math into the game mechanics, something few math ed games do.

    I can see where barry (if he read the book) felt that Devlin placed too much emphasis on mathematical reasoning first, and basic arthimetic skills second. I would like to think that he just meant that mathematical reasoning should be the driving force in a game and that skill acquisition should be the natural result of that direction. That is basically (shameless promotion) what we did in creating, where kids focus on problem solving to build structures, but learn number relationships in the process.

    I’m very curious to see what his next educational game (after Wuzzit Trouble) has to offer.

  • This is a great article. IPMG (iplaymathgames) Publishing is committed to transitioning all of our math game and activity content into interactive games. Out first was called Tic Tac Math (IPMG Publishing) and Apple picked it as New and Noteworthy in 2010. Thanks for the work that you’re doing.

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  • ankita soni

    A good article with full details on math conversation. Yes this type of things must go in the classes. math tutor

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Jordan Shapiro

Jordan Shapiro’s academic work and publishing blend psychology, philosophy, and business in surprising ways. His internationally celebrated writing on education, parenting, and game-based learning can be found on  He teaches in Temple University’s Intellectual Heritage Department where he’s also the Digital Learning Coordinator. He is the parent of two boys (six and eight years old) and the lead administrator at Project Learn School (an independent cooperative K-8 school in Philadephia). His most recent book FREEPLAY: A Video Game Guide To Maximum Euphoric Bliss, considers how the games we play in our youth shape our adult lives.

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