Devlin's Angle

Ten Years On

Welcome to the new MAA on-line information service, and to my own particular corner - though the corner metaphor does not transfer well from the paper page to the scrolling screen. In fact, the vocabulary we use is just one of a number of things that have to change as we move to ever greater use of electronic media in our daily business.

If you are reading these words, then you have already taken the plunge and made at least the first tentative steps into the strange new world of the World Wide Web. And it really is a different world, with different rules, different advantages, and different dangers.

The principal "dangers" I was referring to were computer viruses spread by email. Back then, ten years ago, spam, Internet pornography, and children's Websites that provide a stalking ground for pedophiles were still way in the future.

Several of my early columns were based on, or related to, my then-new book Goodbye Descartes, which described Humankind's quest to develop a mathematics of human thought, starting from the ancient Greeks' attempts to develop a mathematical logic, moving on through the medieval scholars, on to Boole, and then into the computer era, in particular the push to develop artificial intelligence.

I've always been a fan of AI, indeed on one occasion I nominated (successfully) AI founder John McCarthy for an honorary degree. Yet I have always felt that AI's importance was as much in what we learned about human thought from the enterprise's failures (to produce intelligent behavior) as from the technologies that AI led to, and Goodbye Descartes argued that there are definite limits to the degree to which human thought can be captured or modeled by mathematics. (Hence the book's title.)

The other two themes that the column addressed in its first year were (i) the (changing) role of mathematics in society and the ever greater need for mathematicians to work with people from other disciplines, and (ii) the changing nature of mathematics itself, as the community reflected on the evolving concept of mathematical proof.

There was also one column (September 1996) addressed to students, in particular incoming university students. Education has, of course, been changed by new information and communication technologies at least as much as the rest of our lives. And I'm not just thinking about the use of technology in the educational process. As a result of growing up in a world of computers, mobile phones, instant messaging, graphing calculators, and videogames, today's students are simply different from their predecessors when it comes to learning.

To take one example, in their book Got Game, How the Gamer Generation is Reshaping Business Forever, John Beck & Michael Wade list some of the principal cognitive features that you find among young people who have grown up playing computer games:

1. Failure doesn't hurt
2. Risk is part of the game
3. Feedback needs to be immediate
4. Used to being the "star"
5. Trial and error is almost always the best plan
6. There's always an answer
7. I can figure it out
8. Competition is fun and familiar
9. Bosses and rules are less important
10. Used to group action and conflict

Got Game is aimed at the business world. It focuses on the managerial skills many games develop. Those skills include problem solving, resource management, decision making under uncertainty, decision making under pressure, multitasking, and (particularly the multi-player online games) interpersonal skills and organizational ability. (The US Army was one of the first large organizations to spot these positive learning outcomes from videogames and has invested many millions of dollars into their development and use. Many large corporations also use them to train their managers.)

Clearly, however, Beck and Wade's list is highly relevant to those of us in the business of teaching mathematics, for the very obvious reason that it describes the approach to learning of many of our students. How many? Close to 100 percent according to recent surveys, such as a recent study of 524 fifth- through eighth-graders in Michigan and California, which found that 93 percent of girls and 97 percent of boys play video games on a regular basis.

Most leading mathematics educational thinkers would argue that all but one of the features that Beck and Wade list are precisely the characteristics of a good learner and a desirable learning environment. The one exception would surely be number 5, but that is more a feature of the simplistic way the authors state the principle. Successful game play almost always requires guided trial and error, where the player learns from previous experience in the game what attempts to avoid and what is best to try first. (It is possible to argue that 6 is also not in tune with the real world, including real world applications of mathematics, but confinement to problems that have answers does seem to be a universal feature of our entire educational system, and maybe there is a good educational reason for that.)

Item number 9 may worry some educators, but if all those recent studies of gamers are correct, it's now an unavoidable fact of educational life. Those nine characteristics describe features of the students we are actually faced with teaching.

It seems to me that those of us in the math ed biz need to try as best we can to see the world through the same eyes as the gamer students in our classrooms, and adjust our instructional methods accordingly. That may involve providing learning experiences that are suited to their instinctive, experimental approach. Or, if we feel that learning mathematics is best done in a rule-based way, it may require that we accept that part of our job is to help them learn how to survive and prosper in a more rule dominated environment. In any event, I don't think that we are anything like yet done with the changes in our lives resulting from new developments in information and communications technologies. The next ten years will, I believe, be every bit as interesting as the last.