We think this debate is important. We think this debate is interesting. We think this debate is loud. And, more to the point, we think the debate is incomplete.
To be sure, there are a plethora of issues on the table. How can we teach so that people with different levels of ability and different learning styles can all benefit? How can we close the gaps in achievement between students of different race, gender, and economic groups? What method(s) of teaching are most appropriate in light of what we know about how people learn mathematics? How much drill should be used? How many real world applications? Which technologies should be used, and how, and when? Any one of these questions could be the subject of a lifetime of debate, and they are all important and appropriately included. However, there seems to be something left out of all of this, an issue that touches not only school mathematics, college entrance, and career choice, but our overall quality of life.
What YAMPOD is concerned with is that, although people are discussing ways to teach mathematics better, there doesn't seem to be too much talk about teaching better mathematics. True, a special topic or interesting problem of the week gets thrown in here and there, but by and large we are talking about teaching the same fairly dull collection of topics in more interesting and effective ways. That is a step in the right direction, but It would be nice to have at least some of the debate centered on whether there might be a better (and possibly very different) choice for subject matter, or at least a plan for letting people know that there is other subject matter out there that is interesting, wonderful, challenging, and intriguing in its own right.
Mathematicians characterize their field of study as a source of profound beauty, symmetry, and power, an endless playground for the mind, full of fresh and interesting challenges and wonderful rewards. Nearly everyone else sees mathematics as a tool for accountants and scientists, and among the tools in those professions, math is seen as the most austere, dry, and utterly uninteresting, except for its utility. Even among those that use mathematics on a daily basis, comparatively little is known about mathematics and what its practitioners spend their time doing, much less why they are so enamored with it.
Our desire is to build the bridges necessary to close this information gap. The fact is that there are a wealth of topics in mathematics which, if presented well, have the power to move, inspire, challenge the intellect and enrich people's lives in the same way that knowledge of art, music, science, and literature do.
What are these wonderfully fascinating areas of mathematics that the public has been deprived of? In general, it is probably true that every field of mathematics has something fascinating and wonderful to offer the general public. Part of the problem is that very few people work on the problem of "how can I explain what is exciting about what I'm doing to people who don't have an extensive mathematics background?". It may be true that some things are just so esoteric that few people are ever going to be able to appreciate them. But there are many, many examples of "advanced" topics which lend themselves very naturally (although not effortlessly) to understandable and interest-capturing exposition. Knot theory, graph theory, topology, abstract algebra, set theory, and dynamical systems all have excellent examples of concepts, problems, puzzles, and applications that have repeatedly demonstrated the ability to capture the interest and fuel the imagination of the non-mathematician. There have been numerous isolated cases ("random acts of mathematics" as Nancy Casey of the MegaMath project put it) in which these topics have been shown to young people or random adults with varied amounts of previous mathematical training. The results of these incidents are very encouraging--the isolation is not. And the obstacles to overcoming this isolation are nontrivial.
Suppose, for example, that we decide that some of these topics ought to find their way into the school mathematics curriculum. How many people on a school board or textbook committee would even know what we were talking about when we said that these topics ought to be considered for inclusion? How do you get the flow of information started?
Questions to explore include (some thoughts on possible answers or avenues for further study, (if any occurred during writing) are included in parentheses after the question):
(mail msouth@shodor.org with comments, questions, offers for funding, etc.)