Revolution in Math Education

Gene Klotz, 9/30/99

We're in the midst of a revolution. More and more of us communicate by email and via Web pages, both among ourselves and with our students. We use Web pages to

- present syllabi, homework assignments, and other information about our courses and ourselves,
- spark lively and learning-filled Web-based email discussions among our students,
- deliver homework - and even use it as a vehicle for homework and tests,
- coordinate multi-section courses and train teaching assistants,
- communicate teaching materials, and
- deliver entire courses.
(Yesterday's talk made reference to all of the above.)

Since we didn't do any of these things using the Web ten years ago, it sure looks to me as if we're in the midst of a revolution!

Whatever your mathematical or teaching interests or level, there are many rewarding ways for you to be a part of this World Wide Web revolution. The WWW expands the boundaries of the classroom for both teacher and student, and it's exciting to be involved. We'll consider examples of imaginative work that others are doing, and also look at some special opportunities to join ongoing projects. From developing sites and software tools, to involvement with students through mentoring at all levels, to collaborative interdisciplinary projects, there are many possibilities for educators.

We'll first discuss what you can do entirely on your own initiative and then look at how you can join other efforts already under way.

I. Doing your own thing

Going for Gold

Yesterday I mentioned some serious problems that affect the use of the Web for mathematics education,

and which we might be able to help change. Examples:

High-quality material is hard to find.

Things you and your students need - either software or other material - may not yet exist.

As a special example, it would be wonderful to have a databank of interesting and easily and effectively searchable problems.

Not all of us have decent access to the Web in our classrooms or for non-classroom use.

Not enough school teachers are comfortable with using the Web.

You may have your own problems to add.

If you'd like to think big and attack one of these problems seriously, the chances are that funding is available out there. That's not to say it's easy to get - I've had more proposals turned down than accepted, and writing a good proposal is a hard and lengthy job. However, it can be exciting to pull together colleagues and ideas and come up with something that really might make a difference. You won't make a fortune attacking these windmills, and the 2/9ths of your salary you might get for summer work can be hard won, but it's thrilling to be able to shape work on a serious problem.

My experience is that you have a much better chance if you collaborate with others in order to leverage the skills, connections, and knowledge needed. In addition to working with mathematicians for content and ideas, it can be helpful to establish links with established Web projects, and with specialists in software and math education. It's also really valuable to have some good evaluation folks to help you sort out what is working on a project, and what isn't.

One of the best sources of funds is the National Science Foundation's Division of Education and Human Resources. The program officers can be of great assistance in helping you put together a proposal, and in suggesting other sources if your ideas don't match what they can fund. I've found that you don't necessarily need great experience in the area of your project - many times I've successfully rushed in where angels feared to tread. The key ingredient appears to be good ideas clearly organized and presented.

Sharing your teaching ideas

I'll bet most of you have examples and approaches you've developed for your classes that are worth sharing with others. I dream of having a vast collection of such material available on the Web (indeed, as mentioned yesterday, I have a plan for implementing a small portion of this).

If your examples develop into modules containing interactive material, consider publishing them in our Journal of Interactive Mathematics - send files to Ladnor Geissinger at joma@math.unc.edu. If your material is more modest in size, I'll be happy to look at it and help find the right venue for it (I'm klotz@mathforum.org).

When your teaching ideas consist of a textual explanation, consider whether a portion might be made clearer with interactive illustrations. If my applet project pans out we may be able to provide you with appropriate applets to do the trick. If you can't find such applets anywhere and you enjoy programming, consider making your own (and, of course, submitting them to our JOMA applet library, applets@mathforum.org). We'll have directions for where to go for help, and about things to keep in mind in planning your software.

Conversing about your interests

Old-fashioned newsgroups seem to be evolving into Web-based discussions, which allows all the material to be archived, searched, and viewed in various ways, such as by thread or date or author. You can check out discussions we archive at the Math Forum.

I'd especially like to point out the college-level math education discussion list MATHEDU, started by David Epstein at the University of Warwick. Although Epstein claims the list is unmoderated in that mail does not pass through him first, he does trash the irrelevant. Moreover, he moderates marvelously in a larger sense, keeping the discussions on task by stating clearly what the goals of the list are, pointing out when folks transgress: "Saxon is off topic for this list," and generally shaping the overall tone with his comments. It is well worth looking over.

Do you have special interests in mathematics or math education for which you'd like to start a discussion group? Perhaps you'd like to discuss some recurring issues at your particular teaching level, perhaps problems in dealing with a particular course, perhaps ...

If you can't find an appropriate venue, check with me (address above) and we may be able to host your discussion group at the Forum.

If you decide it may be too much trouble to handle the moderating all by yourself, get a friend or two to help out. The Math Forum has software that makes it convenient for several people to moderate. If you want your discussion group to collect more highly polished contributions than are the norm, our software will allow you to edit submissions and to return submissions to contributors with comments, while keeping the submission from appearing to the public until it meets your standards.

Some areas that seem ripe for discussions:

- anything on a focused slice of math education (moderators will have to do a lot of focusing).
- anything on math applications - at any level.
- anything useful to elementary schoolteachers.
Start your own Web page

The WWW has many examples of mathematicians who maintain wonderfully interesting Web pages. A few favorite examples:

- Alexander Bogomolny, Interactive Mathematics Miscellany and Puzzles (Cut-the-Knot )
- Ron Knott, The Fibonacci Numbers and the Golden Section
- David Eppstein, Theory Group, ICS, UC Irvine, The Geometry Junkyard
- Kevin Brown, MathPages
If your favorite topic isn't out there on the Web, consider honoring it with a page. But do realize the ante has been upped in the last few years. Users seem much less interested in lists of links even with comments, than they used to be, and they are much more likely to read pages that have actual content - information about something, with discussion and other interactions available when warranted. One mark of quality on today's sites is the ability to offer feedback and otherwise contribute.

II. Working with others

All of the examples in Part I can be good for sharing. Here are some further ideas.

Web Projects

Some Web projects are the province of various math departments or groups, such as UC Davis'

The Calculus PageSome are even labors of love of individuals, such as David Joyce'sEuclid's Elements.But some actively advertise for help with their work.If a colleague is preparing a proposal or project for Web work, chances are there will be possibilities for others to join in. Recently funded programs are often desperate for help. We get wonderful notes from folks who wish to help with the Math Forum, and we make good use of them. For example, many of our projects have a mentor component, and this often turns out to be very rewarding for the mentor as well as the mentee - and a learning experience as well!

Ask Dr.Math is the Math Forum's best-known project. My co-director Steve Weimar describes the mentor aspect as "those who love math writing to those who might." Our Problems of the Week come in six flavors (Elementary, Middle School, Geometry, Algebra, Trig/Calculus, and Discrete Math), with no end in sight, and there are extensive possibilities for mentoring. The Math Forum has reached the end of its NSF funding (they fund startup, not ongoing projects), so we are going out into the world seeking to become self-sustaining. It's a bit scary, but there are some exciting possibilities. Whatever options we pursue, we're going to have to expand and we'll need all the help we can get - write to me!

In addition to module submission, the JOMA project mentioned above will need reviewers and other assistance. Please write Ladnor Geissinger at joma@math.unc.edu if you'd like to keep abreast.

In my talk yesterday I mentioned a Digital Library project which, if funded, will find, test, and review applets that cover the undergraduate (and soon precollege) curriculum. If funded, we will be able to use teams of faculty and students to search for applets, along with many reviewers. Write me at applets@mathforum.org if you are interested.

Here are a few other Web projects that advertise for help:

The Topology Atlas is looking for (1) People who can manage various aspects of the project and/or take part in negotiations on behalf of the Topology Atlas, (2) People with knowledge of and/or willingness to learn various kinds of computer software.

The MegaMath Project at Los Alamos National Laboratory is always looking for people who would like to help in major and minor ways.

The Electric Emissary Project based at the University of Texas at Austin helps teachers locate Internet-account holders with subject matter expertise relevant to their curricula who are willing to volunteer some of their time to share their knowledge via e-mail.

The U.S. Department of Education maintains E-MATH programs designed to help students master challenging mathematics, science & technology" describes email-based volunteer programs.

Neil Sloane's Encyclopedia is always interested in new integer sequences.

Facilitating discussions

At the Math Forum, except under special circumstances we have generally lacked the resources to moderate discussion groups but facilitators are always needed to further discussions. Groups can go through periods when a few members are being vindictive or are monopolizing the conversation, and there's a need for cool thinkers and calming influences to step in. It is simpler but nonetheless very useful to summarize a conversation, discreetly help to shape the conversation at hand, draw lurkers into the conversation, share experiences and activities, discuss concrete situations, and develop the mathematics.

Elementary schoolteachers need discussions that are helpful for their level, and mentored discussions may be especially important here. We need situations that can help them learn the fundamentals of math. We need to introduce them to interesting questions and activities for young students. Suggestions and help are welcome!

Math problems needed

As mentioned above, there are many uses for good problems on the Web. Our various problem projects are always on the lookout - and we'll even let you help mentor the students who submit solutions, if you'd like!

Michelle Manes and Al Cuoco at EDC's Center for Mathematics Education have just received funding for an interesting project that aims to give school students research-like experiences in mathematics. They are interested in problems that can be approached at different levels of sophistication and that give students an opportunity to experience the ingredients of mathematics research in age-appropriate contexts. They are also looking for volunteers to help groups of students and teachers work on these projects over the Internet, advising them on the work and pointing them to existing resources. For more information, contact hlebowitz@edc.org.

Doing for the Web what you do all the time

As I suspect you realize, one of the big problems on the Web is that it's hard to get sources of high-quality material and high-quality sites. Some folks are trying to redress this:

Math Forum Internet Math Library

UTK Math Archives

Eisenhower National Clearinghouse

NCTM Illuminations will be reviewing Web material which contributes to using and understanding Standards 2000.

There are often problems getting enough high-quality volunteers who are willing to make high-quality judgements. But you make judgements about Web material every time you look at it. If we could figure out a way to get everyone to submit his or her own judgement at the moment when trying to find material that is of interest, we would have the problem solved. Maybe if we could make it as easy as using the Amazon review option? Wishful thinking, I fear.

There are similar difficulties in getting folks to review texts for MAA publications, for example, but I always thought that this was because you had to put your name on the review, and being wrong (or even critical) in public is hard. What can we do on the Web?

Being a good Web citizen

In addition to helping out with discussions, it's awfully useful if you help sites by telling the webmaster when links don't work, writing in about important other information they should link to, and suggesting ways they might improve their site. Simple actions like filling out a comment or suggestion form for a site you like can really help make the site better.

Special ideas for K-12

We have a section on Mathematicians in Mathematics Education run by Susan Addington and Judy Roitman. They list a number of good opportunities for work in this area, along with selected reading. They include stories from several mathematicians who have had interesting experiences, such as serving on a school board, working with groups of students, and the like. Please send your own histories to Susan and Judy.

Community work

One of the most exciting developments involving the Web has been the communities that sometimes spring up. The Topology Atlas is a good case in point, as is Project NExT (New Experiences in Teaching) a program for new or recent Ph.D.s in the mathematical sciences who are interested in improving the teaching and learning of undergraduate mathematics. It's now possibly for those with similar interests to share these interests with others, even though they may be geographically or otherwise isolated. Communities, however, are fragile, and Web communities are particularly so, since the members usually lack the physical cues and temporal experience that help other communities develop and hold together. Look for opportunities to foster the growth of communities that you like.

Conclusion

To me the most amazing thing about the World Wide Web is the possibility it gives us to communicate, not just in words, but in hypertext, vivid colors, and interactive programs. We can really create a new world of mathematics education - but it won't happen in a way we'd like unless many of us participate in building it. This process itself could be both exciting and important, and it would cause us to form a mathematics education community on an entirely different level.

There are many useful and rewarding opportunities for everyone to join the World Wide Web revolution in math education - and to make a difference in people's lives and in our profession. This paper is incomplete, but can get you started. I'd like others to add opportunities to participate in the Web education revolution, and I'd like you to contribute your suggestions and comments, so I'm starting a discussion group at

http://mathforum.org/epigone/WWW.mathed.revolution/.

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We can continue this conversation and work together in ways never before possible.

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