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How to design video games that support good math learning: Level 2.

The educational goal
Part 2 of a series.

Anyone setting out to design a video game to help students learn mathematics should start out by reading – several times, from cover to cover – the current “bible” on K-12 mathematics education. It is called Adding it Up: Helping Children Learn Mathematics, and was published by the National Academies Press in 2001. The result of several years work by the National Research Council’s Mathematics Learning Study Committee, a blue-ribbon panel of experts assembled to carry out that crucial millennial task, this invaluable volume sets out to codify the mathematical knowledge and skills that are thought to be important in today’s society. As such, it provides the best single source currently available for guidelines on good mathematics instruction.

The report’s authors use the phrase mathematical proficiency to refer to the aggregate of mathematical knowledge, skills, developed abilities, habits of mind, and attitudes that are essential ingredients for life in the twenty-first century. They then break this aggregate down to what they describe as “five tightly interwoven” threads:

Conceptual understanding – the comprehension of mathematical concepts, operations, and relations

Procedural fluency – skill in carrying out arithmetical procedures accurately, efficiently, flexibly, and appropriately

Strategic competence – the ability to formulate, represent, and solve mathematical problems arising in real-world situations

Adaptive reasoning – the capacity for logical thought, reflection, explanation, and justification

Productive disposition – a habitual inclination to see mathematics as sensible, useful, and worthwhile, combined with a confidence in one’s own ability to master the material.

The authors stress that it is important not to view these five goals as a checklist to be dealt with one by one. Rather, they are different aspects of what should be an integrated whole. On page 116 of the report, they say [emphasis in the original, image reproduced with permission]:

The most important observation we make here, one stressed throughout this report, is that the five strands are interwoven and interdependent in the development of proficiency in mathematics. Mathematical proficiency is not a one-dimensional trait, and it cannot be achieved by focusing on just one or two of these strands. … [W]e argue that helping children acquire mathematical proficiency calls for instructional programs that address all its strands. As they go from pre-kindergarten to eighth grade, all students should become increasingly proficient in mathematics.

In my book, I describe in some detail how to incorporate these educational goals (actually, to be faithful to the NRC Committee’s recommendation, I should say “educational goal”, in the singular) into good game design for a video game that seeks to help children learn mathematics. In this post, I’ll simply distill from that discussion eight important things to avoid. Try using this list to evaluate any math ed video game on the market. Very few – and I mean VERY few – pass through this filter.

  • AVOID: Confusing mathematics (a way of thinking) with its (symbolic) representation on a static, flat surface. (cf. music and music notation.)
  • AVOID: Presenting the mathematical activities as separate from the game action and game mechanics.
  • AVOID: Relegating the mathematics to a secondary activity when it should be the main focus.
  • AVOID: Reinforcing the perception that math is an obstacle that gets in the way of doing more enjoyable things.
  • AVOID: Reinforcing the perception that math is an arbitrary hurdle to be overcome, or circumvented, in order to progress .
  • AVOID: Encouraging the student to try to answer quickly, without reflection.
  • AVOID: Reinforcing the belief that math is just a large bag of isolated facts and tricks.
  • AVOID: Reinforcing the perception that math is so intrinsically uninteresting it has to be sugar coated.

I’ll be referring to Adding It Up a lot in this series. I shall also discuss many things TO DO when designing a good video game that support good learning, not just what to avoid. As you might (and for sure should) realize, with two challenging goals, good game and good learning, designing a successful math ed video game is difficult. Very difficult. If you do not have an experienced and knowledgable mathematics education specialist on your team, you are not going to succeed. Period.

Game programmers who think that because they were good at basic math (and they have to have been to become successful programmers) they can design a video game that will provide good learning are deluding themselves.

It’s easy to underestimate the depth of expertise of professionals in areas other than our own. Let me stress this point from the perspective of a hypothetical math educator who knows how to program in html5 and decides to create the next Angry Birds.

S/he might well think, “I can write code that produces screen action like that.” Indeed s/he probably can; it’s not hard. But as any experienced game developer will attest, the coding is the easiest part. The huge success of Angry Birds is not an accident. It is a result of brilliant design on many levels. (See this article for an initial, eye-opening summary of some of what went in to making that success.) The expertise it took to be able to create that game was acquired over many years. The Helsinki, Finland based Rovio game studio built ten other games, picking up a ton of increased expertise and insights along the way, before they reached the design heights of Angry Birds.

To build a successful game, you have to understand, at a deep level, what constitutes a game, how and why people play games, what keeps them engaged, and how they interact with the different platforms on which the game will be played. That is a lot of deep knowledge. On its own, being able to code is not enough.

To build a game that supports good mathematics learning, requires a whole lot more.  You have to understand, at a deep level, what mathematics is, how and why people learn and do mathematics, how to get and keep them engaged in their learning, and how to represent the mathematics on the different platforms on which the game will be played. That too is a lot of deep knowledge. On its own, being “good at math”, or at least the relevant math, is not enough.

If you are a game developer who happens to have both kinds of expertise, then go ahead and build a game on your own. But I have yet to meet such a person. For the rest of us, the answer is clear. You need a team, and that team must have all the expertise you will require to do a good job. If that team does not include, in particular, an experienced, knowledgable, math education specialist, then you are not a good engineer. You are an amateur.

How to design video games that support good math learning: Level 1.

Cut scene

Most designers of video games to support mathematics learning make a number of fundamental mistakes. That does not mean they don’t create a game that gets played, and it may be that the game helps some children develop better mathematical ability, or at least memorize or master some basic skills. But minimal results like that are like justifying the creation of the piano because it supports the playing of a two-fingered rendering of Twinkle, twinkle, little star.

The fact is (and I know this is a fact because I have seen hard evidence that was obtained as part of a four-year project I took part in to develop and test elements of video games to support middle-school mathematics learning), the medium offers huge potential to completely revolutionize mathematics education at the K-8 levels, and to enhance it at the high school and university levels. But to date, that potential has at best been sniffed at.

Last year, I published a book outlining some of the factors that need to be taken into consideration when deciding whether to incorporate video games into schooling, including purchases made by parents to assist their children. Though I did include some tips for game developers on ways to incorporate mathematical learning activities into a video game, my main audience was the mathematics teaching community and my primary focus was (therefore) on the pedagogic issues. In this series of articles, my focus will be different. I’ll lay out some of the principles that I believe game developers should follow to create video games that support good learning. In particular, I’ll describe how video games can overcome the single biggest obstacle to mastery of mathematical thinking ability.

But that’s all for the future. Many video games begins with a “cut scene” or “cut sequence” that explains the background a player needs to know in order to play. Likewise for the series of articles I’m starting here. How did we get to be where we are now? In particular, how did I, an older university professor with graying hair, get to be both a gamer and a video game advocate? [The remainder of this introductory discussion is abridged from my 2011 book. I’ll pull material from that source throughout this series of articles, but much of what I say will be new.]

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 to perfect it, 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.

This was in the mid 1980s when I was living in the United Kingdom. Soon after small personal computers appeared, so too did video games to play on them. My two (then very young) daughters particularly liked a fast-action game called Wizard’s Lair, which they played on our first personal computer, an inexpensive machine called the Sinclair Spectrum. Wizard’s Lair offered a two-dimensional, bird’s eye view of a subterranean world. My daughters spent hours playing that game. (A new version of the game, using three-dimensional graphics, was developed and released recently by IGN Entertainment.)

Meanwhile, the brand new computer in their elementary school was sitting largely unused. About the same time that Clive Sinclair (in due course, Sir Clive) introduced the Spectrum computer, the British government mandated that every elementary school in the nation be supplied with a computer. (That’s right, one per school—the early 1980s were the Stone Age of personal computers.) But when my daughters’ school received delivery of its shiny new machine, there was no software to run on it. Apparently no one thought of that. Mindful of what I had observed my daughters doing at home, I wrote a simple mathematics education game, 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 Wizard’s Lair, the children at the school seemed to enjoy playing it. 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.

After that one brief foray into the game development world, computer games remained for me a parental observation activity until 2003, by which time I was living in the United States and working at Stanford University. The previous year, Stanford communication Professor Byron Reeves and I started a new interdisciplinary research program at Stanford called Media X. Media X carries out research in collaboration with industries, mostly large high tech companies, and one early focus of Media X research was the growing interest in using video-game technology in education. In the fall of 2003, Media X organized a two-day workshop on the Stanford campus called Gaming-2-Learn, to which we invited roughly equal numbers of leading commercial game developers and education specialists from universities interested in developing educational games.

The main take-home message from the Gaming-2-Learn conference was that it took a lot of money and effort to design and build a good video game, and no one knew for sure it would be successful until it was finished and released. Both the cost and the uncertainties increase significantly when you try to incorporate mathematics learning into the game in a meaningful way. That perhaps explains why the vast majority of math-ed games that come out look like forced marriages of video games with traditional instruction of basic skills. It’s hard enough just getting a game out, without trying to integrate mathematical thinking into the gameplay.

Still, I was hooked on the promise, if not the then actuality. Following the Gaming-2-Learn event, I decided to take advantage of my location in the heart of Silicon Valley, and started to have conversations with, and in due course collaborate with, professional video game designers. That gave me insights into the organizational and engineering complexities involved in commercial video game production, leading eventually to my partnering with some colleagues from the commercial video game industry to form a video game company last year. More on that as the series develops.

Meanwhile, for all those skeptics out there who believe video games have little to offer education, I’ll leave you with a challenge. Find one – that’s right, just one – video game that is not about learning.


I'm Dr. Keith Devlin, a mathematician at Stanford University, an author, the Math Guy on NPR's Weekend Edition, and an avid cyclist. (Yes, that's me cycling on the Marin Headland.)

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