2007 : WHAT ARE YOU OPTIMISTIC ABOUT?

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Executive Director, H-STAR Institute, Stanford University; Author, The Man of Numbers: Fibonacci's Arithmetic Revolution
Mathematician; Executive Director, Center for the Study of Language and Information, Stanford; Author, The Millennium Problems

We Will Finally Get Mathematics Education Right

For the first time since Euclid started the mathematics education ball rolling over two thousand years ago, we are within a generation of eradicating innumeracy and being able to bring out the mathematical ability that research has demonstrated conclusively is within (almost) everyone's reach. The key to this development (actually two developments, one in the developing world, the other in affluent, technology-rich societies) is technology (actually two technologies).

First the developing world. Forget the $100 laptop, which I think has garnered the support it has only because of the track record and charisma of its principal advocate (Nicholas Negroponte), the ubiquitous computing device that will soon be in every home on the planet is the mobile phone. Despite the obvious limitations of a small screen and minimal input capability, with well-crafted instructional materials it will provide the developing world with accessible education in the basic numerical and quantitative reasoning skills that will enable them to escape from the poverty trap by becoming economically self-sufficient. Such a limited delivery system would not work for an affluent consumer who has choices, but for someone highly motivated by the basic desires of survival and betterment, who has no other choice, it will be life transforming.

At the other end of the economic spectrum, the immersive, three-dimensional virtual environments developed by the gaming industry make it possible to provide basic mathematical education in a form that practically everyone can benefit from.

We have grown so accustomed to the fact that for over two thousand years, mathematics had to be communicated, learned, and carried out through written symbols, that we may have lost sight of the fact that mathematics is no more about symbols than music is about musical notation. In both cases, specially developed, highly abstract, stylized notations enable us to capture on a page certain patterns of the mind, but in both cases what is actually captured in symbols is a dreadfully meager representation of the real thing, meaningful only to those who master the arcane notation and are able to recreate from the symbols the often profound beauty they represent. Never before in the history of mathematics have we had a technology that is ideally suited to representing and communicating basic mathematics. But now, with the development of manufactured, immersive, 3D environments, we do.

For sure, not all mathematics lends itself to this medium. But by good fortune (actually, it's not luck, but that would be too great a digression to explain) the medium will work, and work well, for the more basic mathematical life-skills that are of the most value to people living in modern developed societies.

Given the current cost of developing these digital environments (budgets run into the millions of dollars), it will take some years before this happens. We can also expect resistance from mathematics textbook publishers (who currently make a large fortune selling a product that has demonstrably failed to work) and from school boards who still think the universe was created by an old guy with a white beard (no, not Daniel Dennett) 6,000 years ago. But as massive sales of videogames drives their production costs down, the technology will soon come within reach of the educational world.

This is not about making the learning of mathematics "fun." Doing math will always be hard work, and not everyone will like it; its aficionados may remain a minority. But everyone will achieve a level of competency adequate for their lives.

Incidentally, I don't think I am being swayed or seduced by the newest technology. Certainly, I never thought that television, or the computer, or even artificial intelligence, offered a path to effective math learning. What makes immersive 3D virtual environments the perfect medium for learning basic math skills is not that they are created digitally on computers. Nor is it that they are the medium of highly seductive videogames. Rather, it is because they provide a means for simulating the real world we live in, and out of which mathematics arises, and of doing so in a way that brings out and confronts the player (i.e., learner) with the underlying mathematical structure of our world. If Euclid were alive today, this is how he would teach math.