Math Ed? Sometimes It Takes a Team

In last month’s column, I reflected on how modern technology enables one person—in my case an academic—to launch enterprises with (potential) global reach without (i) money and (ii) giving up his day job. That is true, but technology does not replace expertise and its feeder, experience.

In the case of my MOOC, now well into its third offering, I’ve been teaching transition courses on mathematical thinking since the late 1970s, and am able to draw on a lot of experience as to the difficulties most students have with what for most of them is a completely new side to mathematics.

Right now, as we get into elementary, discrete number theory, the class (the 9,000 of 53,000 registrants still active) is struggling to distinguish between division—a binary operation on rationals that yields a rational number for a given pair of integers or rationals—and divisibility—a relation between pairs of integers that is either true or false for any given pair of integers. Unused to distinguishing between different number systems, they suddenly find themselves lost with what they felt they knew well, namely elementary arithmetic.

Anyone who has taught a transition course will be familiar with this problematic rite of passage. I suspect I am not alone in having vivid memories of when I myself went through it, even though it was many decades ago!

As a result of all those years teaching this kind of material, I pretty well know what to expect in terms of student difficulties and responses, so can focus my attention on figuring out how to make it work in a MOOC. I know how to filter and interpret the comments on the discussion forum, having watched up close many generations of students go through it. As a result, doing it in a MOOC format with a class spread across the globe is a fascinating experiment, when it could so easily have been a disaster.

My one fear is that, because the course pedagogy is based on Inquiry-Based Learning, it may be more successful with experienced professionals (of whom I have many in the class), rather than the course’s original target audience of recent high school graduates. In particular, I suspect it is the latter who constantly request that I show them how to solve a problem before expecting them to do so. If all students have been exposed to is instructional teaching, and they have never experienced having to solve a novel problem—to figure it out for themselves—it is probably unrealistic to expect them to make that leap in a Web-based course. But maybe it can be made to work. Time will tell.

The other startup I wrote about was my video game company. That is a very different experience, since almost everything about this is new to me. Sure, I’ve been studying and writing about video game learning for many years, and have been playing video games for the same length of time. But designing and producing a video game, and founding a company to do it, are all new. Although we describe InnerTube Games as “Dr. Keith Devlin’s video game company,” and most of the reviews of our first release referred to Wuzzit Trouble as “Keith Devlin’s mathematics video game,” that was like referring to The Rolling Stones as “Mick Jagger’s rock group.” Sure he was out in front, but it was the entire band that gave us all those great performances.

In reality, I brought just three new things to our video game design. The first is our strong focus on mathematical thinking (the topic of my MOOC) rather than the mastery of symbolic skills (which is what 99% of current math ed video games provide). The second is that the game should embed at least one piece of deep, conceptual mathematics. (Not because I wanted the players to learn that particular piece of mathematics. Rather that its presence would ensure a genuine mathematical experience.) The third is the design principle that the video game should be thought of as an instrument on which you “play math,” analogous to the piano, an instrument on which you play music.

In fact, I was not alone among the company co-founders in favoring the mathematical thinking approach. One of us, Pamela, is a former middle-school mathematics teacher and an award winning producer of educational television shows, and she too was not interested in producing the 500^th animated-flash-card, skills-mastery app. (Nothing wrong with that approach, by the way. It’s just that the skills-mastery sector is already well served, and we wanted to go instead for something that is woefully under-served.) I may know a fair amount about mathematics and education, and I use technology, but that does not mean I'm an expert in the use of various media in education. But Pamela is.

And this is what this month’s column is really about: the need for an experienced and talented team to undertake anything as challenging as designing and creating a good educational learning app. Though I use my own case as an example, the message I want to get across is that if, like me, you think it is worthwhile adding learning apps and video games to the arsenal of media that can be used to provide good mathematics learning, then you need to realize that one smart person with a good idea is not going to be anything like enough. We need to work in teams with people who bring different expertise.

I’ve written extensively in my blog profkeithdevlin.org about the problems that must be overcome to build good learning apps. In fact, because of the history behind my company, we set our bar even higher. We decided to create video games that had all the features of good commercial games developed for entertainment. Games like Angry Birds or Cut the Rope, to name two of my favorites. Okay, we knew that, with a mathematics-based game, we are unlikely to achieve the dizzying download figures of those industry-leading titles. But they provided excellent exemplars in game structure, game mechanics, graphics, sounds, game characters, etc. In the end, it all comes down to engagement, whether the goal is entertainment and making money or providing good learning.

In other words, we saw (and see) ourselves not as an “educational video game company” but as a “video game company.” But one that creates video games  built around important mathematical concepts. (In the case of Wuzzit Trouble, those concepts are integer arithmetic, integer partitions, and Diophantine equations.)

Going after that goal requires many different talents. I’ve already mentioned Pamela, our Chief Learning Officer. I met her, together with my other two co-founders, when I worked with them for several years on an educational video game project at a large commercial studio. That project never led to a released product, but it provided all four of us with the opportunity to learn a great deal about the various crucial components of good video game design that embeds good learning. Enough to realize, first, that we all needed one another, and second that we could work well together. (Don’t underestimate that last condition.)

By working alongside video game legend John Romero, I learned a lot about what it takes to create a game that players will want to play. Not enough to do so myself. But enough to be able to work with a good game developer to inject good mathematics into such a game. That’s Anthony, the guy on our team who takes a mathematical concept and turns it into a compelling game activity. (The guy who can give me three good reasons why my “really cool idea” really won’t work in a game!) Pamela, Anthony, and I work closely together to produce fun game activities that embed solid mathematical learning, each bringing different perspectives. Take any one of us out of the picture, and the resulting game would not come close to getting those great release reviews we did.

And without Randy, there would not even be a game to get reviewed! Video games are, after all, a business. (At some point, we will have to bring in revenue to continue!) The only way to create and distribute quality games is to create a company. And yes, that company has to create and market a product—something that’s notoriously difficult. (Google “why video game companies fail.”) Randy (also a former teacher) was the overall production manager of the project we all worked on together, having already spent many years in the educational technology world. He’s the one who keeps everything moving.

Like it or not, the world around us is changing rapidly, and with so many things pulling on our students’ time, it’s no longer adequate to sit back on our institutional reputations and expect students to come to us and switch off the other things in their lives while they take our courses.

One case: I cannot see MOOCs replacing physical classes with real professors, but they sure are already changing the balance. And you don’t have to spend long in a MOOC to see the similarities with MMOs (massively multiplayer online games).

We math professoriate long ago recognized we needed to acquire the skills to prepare documents using word processing packages and LaTeX, and to prepare Keynote or PowerPoint slides. Now we are having to learn the rudiments of learning management systems (LMSs), video editing, the creation of applets, and the use of online learning platforms.

Creating video games is perhaps more unusual, since it requires so many different kinds of expertise, and I am only doing that because a particular professional history brought me into contact with the gaming industry. But plenty of mathematical types have created engaging math learning apps, and some of them are really very good.

Technology not only makes all of these developments possible, it makes it imperative that, as a community, we get involved. But in the end, it’s people, not the technology, that make it happen. And to be successful, those people may have to work in collaborative teams.