The webbe of our life is of a mingled yearne, good and ill together.
Shakespeare, All's Well IV iii 83
Other important problems and the Web
The mathematics community under fire
The University of Rochester made a decision to shrink their math department, a seismic disturbance for the mathematics community. Great support and well-articulated important ideas came out in the department's defense. Good answers are still needed to crucial questions that were raised. For example,
- Why should the public support mathematics? What do we do that is important?
- Why is a research mathematics program necessary for graduate science programs?
- Why are we well-suited to teach mathematics to scientists and engineers?
- Why should people major in mathematics?
- What is a math degree good for?
- Why should students take mathematics courses?
Sure, we all know, but can we articulate these things to the rest of the world? If we can't, we face an epidemic of Rochesters. If you send them to me, I'll post your answers on the Math Forum.
A couple of places where we've been unsuccessful of late:
- Engineering faculty and Business and Social Science departments are more and more involved in teaching calculus and statistics courses. Apparently the School of Engineering at a state university has been reassigned half of the calculus courses, although the university in question has an exemplary calculus reform project. This and other treats may appear in a COMAP report written by Sol Garfunkel and Gail Young on the loss of mathematics classes to other departments. If I can track it down I'll put a reference here.
- Hiring of part-time adjunct faculty has increased so much that the ratio of part-time to full-time faculty at some state institutions is two to one.
The mathematics community is not a community
It consists of various factions marching to the sound of their own drums: research mathematicians, college teachers, two-year college teachers, school teachers, those in math education research, school administrators, students, those educating future teachers.
What the Web can do to help
The Web can be an environment where these disparate segments can meet and interact. On the Internet nobody knows you're a college math teacher. It's possible to make use of non-intrusive discussions for civilized discourse among people from various subcommunities (and also for juvenile flame wars, but we won't tell where). The Internet affords new possibilities for fruitful encounters if we can just learn to make use of them.
On the other hand, there may well be significant situations in which it is important to know each other, to know who we are; thus we're thinking of some projects that will use the Web to make visible each other's worlds.
The NSF is planning to use the Web to get the mechanics right for preparing and submitting grant proposals, allowing proposers to track their proposals through the assessment and award stages, and for reporting on grants.
Last summer at the MAA Mathfest in Seattle I was privileged to attend an MAA Section Officers meeting (I snuck in by impersonating two folks who work for the Joint Policy Board). Here are some problems that were discussed:
- it's difficult for the section officers to get information in a timely fashion from the MAA office, things like the rules and regulations that govern reimbursement
- it's difficult for the MAA office to get timely information from the sections, such as who are new section officers.
- it takes a long time for the sections to get information, such as newsletters which must be sent n-th class mail and take forever to arrive, to members.
- MAA Central is supposed to have a file of copies of all the sections' newsletters, but they are often not sent by the sections.
- officers would like to be able to look over other sections' newsletters and see what's happening on the other side of the fence
- everyone with this sort of interest would like to be able to find out who are the current members of the various MAA committees (especially those on committees); since there are around 100 committees it might also be useful to be able to find out what the committees are.
What is the common solution to all these communication problems? To put all the stuff on the World Wide Web. (I tried to point this out in a moving and passionate speech to the assemblage, but the reaction seemed to be one of polite lack of comprehension; by this summer's Atlanta MathFest I suppose the section offices and MAA Central will be converted -- it will be old hat and of course all that stuff will be on the Web. I'll have to find out from our Kay Somers, since I don't expect to be invited back. The life of a prophet is tough.)
The needs of two-year college mathematics
The Internet ain't being used; two year colleges are just getting connected -- but they teach about half the college mathematics students. An expressed interest from a two-year college teacher: dialog between two- and four-year college mathematics teachers on what four-year colleges want by way of preparation of students from two-year colleges. This is worth pursuing. Our communities need to interact.
Some of the changes in education and its structure that the Web might offer to create opportunities for two-year colleges: inexpensive education, adaptability to local needs, quicker shifts in course design to new job environments, closer work with employers in workforce training, etc.
The needs of school mathematics
A number of Web sites are concerned with school mathematics: The Math Forum, The Math Archives, The Eisenhower National Clearinghouse for Math and Science Education, NCTM. The needs of this community are so vast that we can use all the help we can get.
Some of our activities at the Math Forum
We are very interested in developing new modes of communication to meet the needs of particular audiences and discussions -- standard mailing lists and newsgroups just can't be the final stage in Internet communications! We have some ideas and are starting some experiments. Keep in touch, especially if there's anything you'd like to try discussing.
In the following, I give references to general areas of our site and mention some of our specific programs.
The NCTM Standards
The NCTM Standards, which began to appear in 1989, are a major but (surprise!) imperfect codification of forward-looking teaching ideas and empowerment ideals for school teachers. Some efforts are being made to use the Internet as the Standards are being revised. Too bad they were developed and introduced before broad teacher (and other!) access to the Internet was possible; wider discussion could have helped involve more of the mathematics community, making the Standards sounder and more broadly based. At the Eisenhower National Clearinghouse parallel efforts are being established to connect these to college-level reforms.
The NCTM Standards can be found online at the Eisenhower National Clearinghouse.
In addition to our own page on the NCTM Standards, we host a group, "math-teach" (formerly known as "nctm-l"), whose ostensible purpose has been to discuss the NCTM Standards. It has frequently strayed far from this goal, so the new name should be more descriptive. It's a rough-and-tumble group, not always polite or well-focused, but it does have interesting discussions. We host its archives.
Curriculum reform needs
The NSF has funded at least 13 major elementary, middle school, and high school curriculum development projects. Too bad this happened before Internet access made it possible to involve teachers (and students and others) more closely in the development and revision process. Too bad many of the projects (and their publishers) still don't realize what the Internet could do for them in helping to reach teachers and parents and to encourage their constructive involvement.
We offer a page on Mathematics Education Reform, and plan to work with a few of the curriculum projects to set up Web pages where they can have productive discussions with teachers and parents.
Schoolteachers are now offered potentially empowering standards -- which are nonetheless another of life's hurdles in their very pressured worlds. Many also must learn to teach with very different new curricula and very different pedagogical ideas, and they face parents who don't understand the pedagogy or the mathematics. Sometimes they now face mathematicians who are frustrated that educational ideas are not as precise or as firmly grounded as mathematical ideas, and that our students can't score on tests at the level of those in Japan). Oh yes, they also face a massive bureaucratic educational system that tends to subvert change, and a student body which seems to be subjected to more than its share of other difficulties.
Our Teachers' Place is a gateway to materials at all levels. For the past three summers we have run workshops for teachers. These have given us insight into teacher needs and have brought us into contact with some special teachers who have contributed wonderful lesson plans and Web pages. As usual, the Forum learns from its users.
We hope soon to implement an "Ask a Master Teacher" project to give teachers a new opportunity to ask mathematical and pedagogical questions. We will use this to build an online community with personal contact.
Students are often prisoners of a vast bureaucracy that neither understands nor appreciates mathematics. After that, I think it becomes much more complicated. For example, popular wisdom would have it that trouble begins early on, since elementary schoolteachers self-select because that level doesn't require any knowledge of math (but elementary teachers teach everything -- including math!). While this may be true in general, we've encountered some pretty wonderful elementary teachers out there. Here are some of their Web pages:
To answer Student needs, we have instituted a project called Ask Dr. Math in which K12 students email math questions to be answered by college students, retired professors, and other volunteers. Students can pursue their own questions at all levels, and an environment is provided where they are able to hold conversations about mathematics. We archive the questions and answers so that teachers and prospective teachers can look closely at student thinking and examine the topics that crop up again and again. As is evident from their comments, it's a valuable experience for all concerned. Let us know if you or your students would like to be involved and we'll contact you when we need new volunteers.
We also have a Geometry Problem of the Week project for students which we are learning to expand to accommodate more students and into other areas of mathematics.
Parents need help in comprehending new approaches to teaching mathematics and new curricula. They need help in understanding new mathematical ideas if they are to effectively help their children learn.
We've organized a Web page for parents and concerned citizens. We're also hoping to begin an "Ask a Master Teacher" project for parents to help them understand new pedagogy and new mathematical concepts.
We've begun thinking about how the Internet might be used to help parents work with their children on mathematics, have received warm responses from the Family Math Project, and have begun a real collaboration with BBN's National School Network project.
Many mathematicians are seriously concerned about school mathematics teaching and would like very much to help. Mathematicians need to understand what's going on in school mathematics education, and to find ways they can effectively do something. In order to be effective, some need to learn to communicate in ways that non-mathematicians will not find threatening or arrogant.
We provide a Web page of Opportunities for Research Mathematicians. Susan Addington and Judy Roitman are two mathematicians who are respected by the education community. They will help us collect resources for a Web page with information for mathematicians about contemporary mathematics education, case histories about mathematicians who have fruitfully worked together with teachers and students, and a discussion forum on this topic.
We also hope to search out and nurture good contributions to school pedagogy from the college and university communities.
Communication is the name of the game -- non-intrusive communication, at that. Discussions can be held in a great variety of formats: free-for-all, moderated, open to all, open only to select groups. The emphasis can be on immediacy or on carefully worked out ideas, structured around preannounced themes or flowing with the discussion, within a specified or unlimited time limit, carefully archived by topic (and possibly culled) or evaporating into the ether.
Understanding is certainly important as well. One of the great benefits of the Web is being able to link doing to conversation, especially at a distance, which can somewhat compensate for the lack of face-to-face communication.
We college teachers don't have a particularly good record when it comes to communicating with the rest of the mathematics community. I'll give a few examples, but on another page.
Communication could do a lot to meet the needs expressed above. The problem is that we don't know enough about what is appropriate for what circumstances. (At the Forum, we're trying hard to learn.)
If you'd like to be involved in any of our school mathematics activities, please let me know. We need all the help we can get! In his letter to the editor in the February Notices of the AMS, Sherman Stein concludes that if mathematics departments do nothing to improve school mathematics, they should stop complaining that incoming freshman lack mathematical skills.
Some special school mathematics activities
Results of the Third International Mathematics and Science Study (TIMSS) are being released. Data from this monumental study will inform mathematics education for some time. The executive summary, Splintered Vision, makes interesting reading.
Some schools are already making useful contributions. Alvirne High's Calculus Problem of the Week is the work of Forum Teacher associate Sandy Ray, and we're investigating an ongoing integration with our projects.
We are setting up a Teacher Exchange section for school teachers that should make it easy for them to share Web and classroom materials, review and discuss software and curriculum, and communicate in various ways. (We'd be delighted to do something aimed at college teachers if an interest is expressed.) Teachers we have worked with have contributed high quality model Web units to our collection. We have a Dynamic Geometry Center with considerable material for school and college teachers of geometry. We have begun an effort to discuss some of the important topics on research in mathematics education, and are continuing with a fresh approach to collaborative learning.
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