Devlin's Angle

March 2011

Learning Math with a Video Game

According to 2008 figures from the Pew Research Center, 97% of today's K-12 students spend many hours each week playing video games. By the time they graduate from high school they will have spent some 10,000 hours doing so. During the course of that game play, they will acquire a vast amount of knowledge about the imaginary worlds portrayed in the games, they will often practice a skill many times until they are fluent in it, and they will attempt to solve a particular challenge many times in order to advance in a game. Would that they devoted some of that time and effort to their schoolwork!

Since video games first began to appear, many educators have expressed the opinion that they offer huge potential for education. The most obvious feature of video games driving this conclusion is the degree to which games engage their players. Any parent who has watched a child spend hours deeply engrossed in a video game, often repeating a particular action many times, will at some time have thought, "Gee, I wish my child would put just one tenth of the same time and effort into their math homework." That sentiment was certainly what first got me thinking about educational uses of video games 25 years ago. "Why not make the challenges the player faces in the game mathematical ones?" I wondered at the time.

In fact, I did more than wonder; I did something about it, although on a small scale. I wrote a simple mathematics education game for my children's elementary school, in which the player had to use the basic ideas of coordinate geometry in order to discover buried treasure on an island, viewed in two dimensions from directly above.  While it did not offer the excitement of the commercial entertainment games my own children were playing, the children at the school seemed to enjoy playing my more modest effort. Perhaps offering a prelude of things to come, the game even made a financial profit. I wrote it for free, and the school PTA sold copies to other local schools. I think we sold five or six copies in total, each one on an audiocassette tape. I did not give up my day job.

And that was about the extent of my foray into the world of video games until around 2003, when, as a result of my location in the heart of Silicon Valley, I got to know some professional video game designers. Talking with them, and with video game scholars, over the years not only aroused in me once again the huge educational potential of the medium, but also gave me insights into the organizational and engineering complexities involved in commercial video game production.

Yet whenever I have tried some of the math ed video games being produced, I have been significantly underwhelmed. For the most part, they do not teach mathematics at all, rather they test what has already been learned elsewhere. Moreover, that testing is largely restricted to automatic recall of basic number facts and rapid use of arithmetic skills. Nothing wrong in that. I wish I'd had access to an enjoyable video game to help me practice my multiplication tables when I was in elementary school. What has left me unsatisfied is that those games (and we are really still talking about first-generation mathematics education video games here), while succeeding in achieving their (modest) educational design goals, fall way short of the potential I, and many other, are sure the medium offers.

One problem with the majority of math ed video games on the market today that will quickly strike anyone who takes a look, is that they are little more than a forced marriage of video game technology and traditional mathematics pedagogy. In particular, the player of such a game generally encounters the math in symbolic form, often by way of a transparent screen overlay on top of the gameworld.

But video-game worlds are not paper-and-pencil symbolic representations; they are imaginary worlds. They are meant to be lived in and experienced. Putting symbolic expressions in a math ed game environment is to confuse mathematical thinking with its static, symbolic representation on a sheet of paper. It's like the early would-be aviators who tried to fly by building ornithopters - machines that added flapping wings to four-wheeled cycles. Those pioneers confused flying with the only instances of flying which they had observed - birds and insects. Humans achieved flying only when they went back to basics and analyzed the notion of flying separately from the one particular implementation they were familiar with. Similarly, to build truly successful math ed video games, we have to separate the activity of doing mathematics, which is a form of thinking, from its familiar representation in terms of symbolic expressions.

Mathematical symbols were introduced to represent mathematics first on parchment and slate, and still later on paper and blackboards. Video games provide an entirely different representational medium. As an interactive, dynamic medium, video games are far better suited in many ways to representing and doing middle-school mathematics than are symbolic expressions on a page. We need to get beyond thinking of video games as an environment that delivers traditional pedagogy - a new canvas on which to pour symbols - and see them as an entirely new medium to represent mathematics.

This will not be easy. I know that from personal experience, having spent a large part of the past five years working on a well-funded project trying to do it. But I am convinced it can be done - though to what extent and how well remains to be discovered. Sadly, I cannot describe the particular project I worked on, which had proprietary elements, but my new book, just published, summarizes my current thinking on the subject. I'll come back to the topic of mathematics education video games in future columns.

In the meantime, if you want to get a good background into the educational potential of video games, I highly recommend the book What Video Games Have to Teach Us About Learning and Literacy by Prof James Paul Gee of Arizona State University. And if you want to experience a video game that will really challenge your (logical, not mathematical) problem solving ability, try the free demo version of Portal. If you are like me, you will willingly pay the $14.99 price to convert your free demo into the full version. (BTW, the little animation you see on the demo website is not the game; rather it is an "instructional video within the game". The game itself has high production values.)

Devlin's Angle is updated at the beginning of each month. Find more columns here. Follow Keith Devlin on Twitter at @nprmathguy.
Mathematician Keith Devlin (email: is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute (H-STAR) at Stanford University and The Math Guy on NPR's Weekend Edition. His most recent book is Mathematics Education for a New Era: Video Games as a Medium for Learning, published by AK Peters/CRC Press.