Every now and then the rewards for a relatively small amount of labor are disproportionately high. I just managed such a time and I'm still pretty high over it myself. As a result of helping to organize a Roundtable for Project EXTEND I got to be in on a really lively exchange of ideas among a highly articulate collection of people. It would have been worth it for some of the turns of phrase alone, let alone the content. Only snag was that I kept getting so tied up in listening that my note taking sputtered out, so this will definitely not be comprehensive. But then again, you might not be enthralled by a comprehensive report of a three hour conversation!
So what is EXTEND? It's an effort sponsored by the Exxon Education Foundation to promote communication between the community that provides mathematical education from kindergarten up (and up and up) and the community that hires the recipients of that education. Ultimately, it is envisioned as a nationwide electronic conversation, but for a start the organizers are setting up a few real time face-to-face conversations so as to get a feeling for what the crucial questions are. Our perspectives were many, ranging from the ed biz (lots of us, from colleges and universities and K-12) to the Boeing biz (two, but they held their own just fine!), with sundry layers of business between.
The conversation got off to what for me was a somewhat harrowing start when the opening remarks of a K-12 math curriculum specialist elicited from one of the Boeing people a response of "You're prioritizing WHAT?!?" Turned out to be very useful, though, not only because the ensuing efforts produced a lot of clarification about the difference between diminishing the domination of arithmetic skills and jettisoning them altogether, and about the motivation and strategies involved in the reallocation of emphasis, but because by the time we had bushwhacked our way through that morass the ice was well and truly broken.
With that ground cleared, we were ready for the opening salvo from the industry side, which was duly supplied by a Boeing manager. "The era of the Lone Gunman", said he, "is over!" In his line of work, he doesn't need--in fact, has no use whatever for--the isolated genius who looks over the situation and produces, "Voila!!", a Solution. He works with teams of people, each with his or her own strengths and areas of expertise. There are some definite requirements for the union of the set of skills possessed by the team, but no specific mathematical skill is uniformly indispensible. What is indispensible is the ability to be part of a team--to communicate one's own ideas clearly and convincingly and listen with attention and respect to other people's ideas. A team like that can build on all of the strengths of all of its members and work wonders.
At this point someone noted a significant language difference between the cultures. All the folks from K-16 education were referring to teaching in groups, and all the folks from business were talking about working in teams. I think we can deal with that one!
As the afternoon wore on, a number of people discussed the mathematical needs in their branches of work, and a fascinating variety they were. Some were highly numeric (mental computation of profit margins on negociated discounts), some highly analytic (where in this process could the item that we had at the beginning have disappeared from the inventory?). Most involved at one level or another the ability to communicate. In many cases it was a matter of communicating with the rest of a team. Other times the issue was convincing an outsider of the validity of a process. That one struck me, though I didn't manage to say it at the time, as highly related to the ability to produce a really good proof--not a formalized sequence of equations, but a convincing piece of mathematical prose. Or is that a warped view of a proof?
One recurrent theme was a problem which exists most visibly for mathematics educators, but by transitivity has a definite impact for business. A community college mathematics instructor said it far the best: "We need to deal with the fact that society in general has such an emaciated view of mathematics." How many times have you heard "I always loved mathematics because every problem has a single right answer"--and known that that was a person who, confronted with a calculus problem with more than one step and more than one available approach, would have been among those railing at you for not having shown them how to do it? I think the comment runs second only to "I never could do mathematics"--and the two together point loudly and clearly to what may well be our ultimate challenge: the challenge to the inhabitants both of the world where mathematics is taught and the one where it is used to communicate to the rest of the world just what mathematics is and is good for.
The Boeing manager summed that one up at the end, taking the thoughts we had been percolating and generalizing them to cover all of education: what we have got to do is not just agree among ourselves that certain things are important and worthy of support, but take that agreement, package it and convince the world of its value--convince not just the parents, but the government and the voters. Then we could get the financial support needed to make a real difference. We should, in short, take our knowledge that education is essential and sell the world on the idea. Not a bad image at all--and not one which leaps readily to the academic mind. I think this conversation could have a lot to offer.
Ginger Warfield is a member of the Department of Mathematics of the University of Washington in Seattle.