17 April 1997

The following assertions are discussed in more detail in the body ofMathematics and the World Wide Web.If you're feeling part Nostradamus, send me your predictions and I'll add them to mine.This document will be presented as an informal talk at the EPADEL meeting on April 19, after which there will be a panel discussion, the results of which I will summarize and post on the Web.

I see the World Wide Web functioning in three very important ways:

- as a conveyer of mathematics materials for courses and research;

- as a means of personal expression for relating who we are, our interests, and small mathematical and pedagogical triumphs not worth journal publishing but eminently suitable to adorn our Web pages;

- as a means of communication with colleagues, students, and organizations. For this purpose it will eventually far outstrip our current e-mail habits because of how nicely it presents mathematics, and because thanks to the Web we'll know more about each other and the contexts within which we work.

We examine the impact of the WWW on the following:## Good solutions to mathematical typesetting on the Web will arrive within two years, making the Web even more attractive as a conveyer of mathematical information. Stay tuned to the HTML Math Overview page, and for current information see Math Typesetting for the Internet from the Math Forum.

Math Publishing

Mathematics research journals

There will be a furious battle between commercial publishers and new electronic journals spearheaded by desperately poor librarians. Consortia of neighboring institutions will need to try to pool resources; many institutions will be forced to add services to provide rapid turnaround printouts of selected articles. Commercial publishers will fight such solutions by further raising prices. Perhaps there will be incentives to publish in free electronic journals.The crystal ball is occluded and the current standoff, with many journals existing in both electronic and paper form, will continue for some time.

Ancillary course materials

Java-based programs and Web plug-ins such as the Maple-based MathView will capture the imagination of school and college teachers who have enjoyed using computers to construct examples and exercises for their courses. These Web materials will grow in quality and will offer students the opportunity to work in interactive environments where they can explore focused concepts with graphic and symbolic tools. They may even turn out to facilitate good pedagogy as wonderful microworlds are created for students to explore.Such enriched materials in the form of Web pages will of course be independent of platform and everywhere available. The ease of sharing and searching on the Web will make it possible to pull together growing numbers of such pages for use in standard classes, and it may ultimately be possible to weave together entire courses from such pieces.

Courses

Publishers will have to wrestle with the growing possibility that each teacher will be able to build a course from Web resources. They'll go to course-on-demand schemes, whereby it will be possible to order only the desired chapters and sections of a book. Enrichment in the form of associated Web pages of the type just discussed will be available only to book subscribers.Although young people may be able to learn to read and study from computer screens, reaping the advantages of hypertext, interactivity, and colorful design, many of us older folk will cling to paper, subverting hypertext by printing it out till our dying day.

Experts at a distance

What with the national focus on volunteerism, batches of us retiring, and good software and projects like Ask a Topologist, Ask Dr. Math, the Elementary Problem of the Week, and the Geometry Problem of the Week springing up, it may become possible for students at all levels to have direct contact with math experts. Our own projects have shown that this can make a difference. Also, students will benefit from a delightful variety of good mathematics put together by mathematicians. The prospects are exhilarating.

Courses at a distance

Will distance learning developments mean that every tiny school - or home school - will be able to offer a high-quality calculus course? that penurious school boards will be able to offer Algebra II to a thousand students at cut-rate prices? that universities will be able to Rochesterize math departments at will? Wish I knew. Wish I knew where to look. It's evident that we jolly well better keep up with this.## There will be more lively areas like the Topology Atlas, with preprint servers for conveying research information. Classy refereed electronic journals like the Electronic Journal of Combinatorics will be available for tenure and status publishing. Some mathematicians such as Jonathan Borwein believe that along with mathematics changing technology, technology also changes mathematics. Certainly new tools for collaboration will alter how we can work together at a distance (see Section 8).

Research

TeachingCollege teaching

I expect that many faculty members, followed by their colleges and universities, will gravitate to the "Penn" model, putting assignments on the Web along with teaching aids and ancillary course materials as discussed above. Help will include teachers' suggestions and study guides, along with e-mail discussions. Why will this happen? a) it might be helpful, and b) it makes teachers, courses, departments, and colleges look good.

School teaching

Teachers are looking for good problems and exploratory environments. I expect they'll soon become interested in using the Web to individualize instruction.It's been my experience that given a bit of help, enterprising school teachers will jump right in and use good Web-based materials. Some will even create very high-quality Web pages themselves. The second wave of teachers will join up when they see that there are things on the Web that can be easily used for better teaching.

As in the college community, there will be some who will object that they are already excellent teachers and have no need of extraneous technology. They will retire soon. J. B. Priestly reportedly said, "The world will change. It will probably change for the better. It won't seem better to me."

I don't imagine the "Penn" model will soon arrive in the pre-college world, but I'm not sure what other teachers-communicating-with-students models will develop. I imagine that Web-based portfolios will become popular means of assessment.

10-14 teaching

In the next couple of years greater access to the Internet and its splendid possibilities for communication will make it abundantly clear what late high school, early college, and community colleges have in common: they teach many of the same math courses. It would be wonderful if the sharing of information could contribute to discovering new roads to success and better and less redundant routes for students. For example, Doris Schattschneider seems to be making a breakthrough in integrating precalculus with calculus.

The Teaching Community

Many of us will find contacts out there on the Net and won't be nearly as alone as before. At all levels teachers of elementary school math, high school geometry, differential equations, or continuum theory will begin to work together in interest groups - in fact, this is already happening in these areas and many others. The communication possibilities of the Web threaten to be even more important than the Web itself for conveying math materials.For a few years I imagine a thousand flowers will bloom, as each person publishes favorite ideas on how and what to teach, with most folks finding at least a couple of kindred spirits out there. After a while I wouldn't be surprised to see some coalescing into groups based on strong and useful ideas. I don't think that things will ever become monolithic; rather that reasonably stable clusters will come together with lots of satellites around them. Images from Conway's

Game of Lifedance in my head, but without the simple rules and regularity.The new communication possibilities will allow us to do many things better, to examine teaching ideas from a broader perspective, and to re-form math education with wide participation. They will also let us take more far-reaching and nastier potshots at those with whom we disagree, or whom we'd like to blame, or to whom we feel superior. Current discussions about reforming math teaching are often inflammatory and we really need to learn to make them productive - many people care passionately about math education, but too many of us care too passionately and are unreceptive to the ideas of others. How can we help good will and shared common concerns to erase prematurely drawn battle lines?

## If you take a stroll around school, college, or university teachers' Web pages you'll find quite a bit of charm and interest. The Web is being used for much delightful individual expression. Whereas in the past the public was for the most part unaccustomed to interacting with mathematicians and was inclined to see us as colorless, inarticulate, and out of touch, we now run the risk of being perceived as colorful and mildly amusing - and out of touch. One of the most important things the Web will do for us is to provide a splendid arena for self-expression; we'll come to know amazing facets of our colleagues, deepening our interactions and also humanizing us to the rest of the world.

The Profession## The Internet has made it much easier for folks to find and interact with kindred souls, which should mean that our professional organizations will modify the services they offer us. You won't need an annual meeting to get together to discuss how to teach your favorite subject. Of course non-virtual discussions are important, so they will certainly continue at professional meetings. Maybe we'll have important discussions over the Net and continue to have long strings of short talks at meetings so that faculty can give one and get their way paid to the meeting, while cutting most other sessions to go to Disneyland.

Professional OrganizationsUp-to-date organizational information should soon be kept on the Web where it can be easily found and searched through. For example, I'm on an MAA committee and it's sometimes hard to find out who the other members are. I've just received a list of all 99 MAA committees and until I lose it I'm okay, but if I wanted to know what committees

youhappened to be on, it would be a real chore to search through and find out.Our professional organizations will be able to operate in a much more open manner, and committees will post agendas and get member feedback, discussion, and support.

## Check out the Math Forum. We regard these things I've talked about as important issues, and we'll be around for at least 3 more years. We won't just preach to you - we offer you a soapbox to express your own ideas and the chance to discuss them with the rest of the world.

How to Keep Up## We all know about dynamical systems, and that butterflies can effect momentous changes, but this has always been more likely in some times and places than in others. Ours appears to be one of these times and places, when we as individuals can cause significant changes in the communications revolution swirling around us. It's possible that great good - as well as great disaster - can come out of this. I think the former is likely only if a lot of us get involved and keep trying.

Why Keep Up?

Swarthmore College

16 April 1997