Guest Blog: Keith Devlin on Math and Video Games
I recently reached out to Keith Devlin, the co-founder and Executive Director of Stanford University’s H-STAR institute, a research center that focuses on the application and innovation of technology for research, education, entertainment, commerce, and other areas of life. Mr. Devlin agreed to contribute a guest blog entry detailing some of the ideas in his recent book, Mathematics Education for a New Era: Video Games as a Medium for Learning. What follows in this post is his entry. I’d like to thank Mr. Devlin for taking the time to write and share his thoughts with us.
There are a fair number of video games available that claim to teach mathematics, many of them free, some for sale. If you include the casual games in the App Store, they number in the hundreds. But it does not require more than a cursory look to see that the vast majority do not teach mathematics at all; rather they provide an opportunity to practice basic math skills that have already been learned. That is a useful contribution to math learning, and if it can be achieved in a fun way without the student becoming discouraged or learning to hate math, then all to the good.
But video games offer far more than that. A good video game is about exploration, (genuine) learning, and problem solving. That makes them an ideal medium for real, conceptual mathematics learning. So why are there so few games that do just that? Part of the reason appears to be that the people designing them do not really understand mathematics education. With the best of intentions, they focus on the most obvious part of mathematics learning, namely mastery of basic number and algebra skills (mostly just the former), and within that highly restricted range they go for the low hanging fruit, such as automatic recall of the basic multiplication bonds (“multiplication tables,” in old terminology).
I suspect that in most cases (and in a few cases know for a fact) the development team did not include either a qualified, classroom-experienced mathematics educator, nor a mathematician. From a math ed perspective, that is like setting out to build a house by assembling a group of bricklayers and carpenters, but not thinking to hire an architect. Basic math skills are the bricks you need to build the mathematical house. But what today’s society needs (in numbers far larger than our schools are currently supplying) are mathematical architects – people who can think mathematically. Video games can help develop mathematical thinking, but they are a lot more difficult to design than a simple skills-tester.
Examples of such games are those by Dreambox Learning and Mind Research Institute. Both of those products are aimed at fairly young children. When you look at middle school and upwards, you have to look outside mathematics to find a really good example of a video game that develops sophisticated thinking – namely the wonderful game Portal, a game sold as an entertainment game, as it happens, not developed for the education market.
The first thing you need to do when setting out to design a math ed video game – and this is something that hardly any math ed game designers appear to have done – is decide on your underlying pedagogy.
In broad terms, there are two approaches to mathematics teaching and learning: instructional and discovery. In the former, instruction and demonstration are typically provided by a teacher, a textbook, a video, or an instructional computer program. After which the student attempts to answer questions and solve problems. With discovery learning, the student is presented with a series of questions or challenges that guide a process of discovery. Though these are sometimes viewed as being in opposition, they need not be, and in fact good teachers use a combination of both, most commonly adopting a global discovery approach supported by on-demand instruction when the student is unable to move ahead.
While teachers can, and in many cases do, use elements of both pedagogic approaches as they think appropriate, educational media tend to be suited to one or the other. Traditional textbooks and educational videos (such as Kahn Academy) are essentially instructional media. They have to be, since they are unidirectional — pure delivery media that cannot react to the student’s actions. Educational computer programs can, of course, respond to the student’s actions, which offers some degree for discovery, but only to the extent that the student acts in a way that the programmer has anticipated and has scripted an appropriate response. Of course, there is nothing to stop a teacher using textbooks, videos, and computer programs as resources for discovery learning, and many do just that.
With video games, however, things are clear cut. By their very nature, they are all about exploration, discovery, and student-driven (i.e., player-driven) problem solving. This does not preclude instruction being given within the game, but unless it is done well, it can destroy the very game in which it occurs. The exploratory learning approach is where we should be directing our efforts. Having worked for almost five years on a stealth, math ed project in a large commercial video game company, taking the inquiry-based learning approach, I learned two things. One: it is definitely possible to design and build quality video games that are fun to play and help develop genuine mathematical reasoning skills. Two: it is extremely labor intensive and time consuming – hence expensive, which is why the project I worked on was cancelled before we had a releasable product.
On the other hand, we set out to build a game that (in its initial release) covered the entire mathematics curriculum at a particular grade level (with other grade levels to follow). With hindsight, we bit off far more than we could chew. We came away knowing that in these early days of designing quality math ed video games, it makes sense to do it piecewise, one curriculum topic at a time. Along with some colleagues from that project, I am now trying to do just that.
In my recent book Mathematics Education for a New Era: Video Games as a Medium for Learning, I discuss many of the fundamental educational issues that should be addressed if we are to take full advantage of the huge educational potential of video games. Though I do talk a bit about game design issues, most of my focus is on pedagogy. For one thing I am convinced of, after eight years thinking about these issues, is that it is not enough to simply combine traditional instructional pedagogy with video game technology. You have to design your pedagogy around the medium. Video games are not going to deliver much of a benefit if we view them as simply supplementary add-ons to the educational system we already have. They offer such great potential, we have to rethink the entire educational process.
Keith Devlin, Stanford University.
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