IAGO: With as little a web as this will I ensnare as great a fly as Cassio.
How is the Web being used in college teaching?
-- as a conveyor of mathematical material
Here are a few samples to go with those given previously:
- Famous curves index (history and interactive graphs).
- A Visual Dictionary of Special Plane Curves
- The Chance project.
- Geometry Center materials
I've tried various experiments in using the Web for conveying mathematical concepts, and have posted an Introduction to Vectors, Limits for functions of two variables, and elementary Tangent Planes. (To accompany the latter, one of my students made some super pages on constructing physical models of surfaces.) I'm sure that many of you have constructed interesting Web material and I'd sure like to link to it and share it with the rest of the world. Please let me know if you have or if you encounter anything!
Mathematicians are even beginning to publish texts jointly on the Web and in paper. For this, one requires a very enlightened publisher, one that understands that few people will download a whole book, and that being able to sample a good book may encourage us to purchase it. Laurie Snell and Charles Grinstead are doing this with their new probability book.
The Web makes it possible for all of us to publish -- not to make money or to get points toward tenure, but to put together our mathematical and teaching ideas in an attractive form where they can be widely read. The thought of having good mathematics broadly accessible is appealing. With many attractive math sites out there, more young people can have access to high-quality mathematics. I think it's worth working for; in fact it's a driving force for me.
-- as a conveyor of mathematical software
The Math Archives is an important website, where a specialty is reviewing and archiving mathematical software. The Math Forum has a shareware and freeware area, and a special section devoted to dynamic geometry software and its use, including downloadable demo versions of Cabri and Sketchpad. Some individuals make their software available from their home pages; for example, Richard Palais has his very fine 3D-Filmstrip so available. Some commercial software developers make material available on their websites; for example, Maple, Mathematica, and MatLab.
-- as a conveyor of math history, sociology, and undergraduate education research
- African-American Mathematicians
- Biographies of Women Mathematicians
- Birthplaces of mathematicians in Europe (with clickable map)
- Canadian Society for the History and Philosophy of Mathematics
- Euclid's Elements (with illustrations by a geometry applet)
- Forum Math History collection
- Teaching and Learning
-- as a conveyor of course information
Rumor has it that University of Pennsylvania undergraduate chair Dennis DeTurck commanded, "thou shalt not communicate with thy calculus class using ancient technology, in particular that constructed from dead trees." And there was weeping and wailing and gnashing of teeth, but check out this information about calculus at Penn and more calculus at Penn.
Various calculus sections have their own very nice pages:
- Katherine St. John
- Jerry Porter
- Robert Powers.
- Jerry Porter is also involved in linear algebra.
- Dennis DeTurck has a mighty Java-enhanced home page in the AMS Gothic style.
Other institutions also make excellent use of the Web to convey course information. Our speaker Frank Beatrous will have told us about the interesting activities at the University of Pittsburgh, in which their calculus labs play an important role.
-- as a conveyor of courses
The Web is highly touted as a future conveyor of courses, often by administrators with visions of cost-cutting and increasing enrollments. However, folks in mathematics with actual experience in this are very rare. We are doubly fortunate to have Frank with us, since he has been involved in distributed learning environments at Pittsburgh.
NetMath is a consortium of universities investigating distance learning in Mathematics. The group includes Pittsburgh, Ohio State, and the Universities of Iowa and Illinois. Their goal is to provide a real mathematics learning environment via the Internet. They are not interested in correspondence courses, but in university courses with classes sitting in various states and countries around the world. I trust that Frank will have things to tell us about this as well.
Our own indefatigable Jerry Porter has been instrumental in encouraging the MAA to use the Web for professional development workshops, the first of which will be given this summer.
-- as a focus for curricular reform projects
- Frank Wattenberg, another of our speakers, will have told us about his Connected Curriculum Project, which hopes to break down the barriers between disciplines -- to study mathematics in the context of the real problems;
- EPADEL's own MACMATC project involves Penn, Villanova, the Community College of Philadelphia, Polytechnic, some Philadelphia high schools, and the Society for Industrial and Applied Mathematics. It seeks to improve students' appreciation and understanding of mathematics by infusing math courses with real applications;
- Moravian College has a project implementing an integrated Precalculus/Calculus I Course;
- Temple University participates in the Collaborative for Excellence in Teacher Preparation;
- Reform calculus groups make a variety of uses of the Web;
- The Annenberg Institute for School Reform at Brown University seeks to promote a comprehensive, nationwide school reform movement.
-- as a former of educational communities
There now exist many groups involved in mathematics education whose Web pages are a focus for the group and a means for them to communicate with others. Here are some examples:
- ATLAST, a project to Augment the Teaching of Linear Algebra through the use of Software Tools
- C*ODE*E, the Consortium of Ordinary Differential Equations Experiments
- Humanistic Mathematics
- IDEA, Internet Differential Equations Activities
- MER, Mathematicians and Education Reform
- Project NExT, New Experiences in Teaching, a program for recent Ph.D.s who are interested in improving the teaching of undergraduate mathematics, sponsored by MAA.
- Women and Mathematics
Problems with the Web and teaching
To my mind there hasn't yet been enough done to distinguish among the normal birthing pains of any new endeavor, problems inherent in the medium, and problems that can be overcome with a bit of work. There aren't enough examples of the Web as a conveyor of mathematical ideas in hypertext. Also, we lack good examples of distributed courses, at the same time that there's a great push for them. I'm looking forward to learning from Frank Beatrous about Pittsburgh's experience.
On a grim note, some people (see end of section) are predicting the demise of residential colleges and universities. I'm not sure that overall the uses of new technology will be cheaper; I hope they'll be better. I'm also not so sure there won't be a thriving collection of EPADEL colleges in 2027, but I'll bet the colleges and college world will be a lot more different from now than we are from 1967.
I think that technology can sometimes play an important role in mathematics education, but in 30 years of observing attempts to use technology for large-scale education projects I haven't seen anything that works on the scale envisaged here except remedial arithmetic, so I find the following even grimmer (I'm trying to track down the attribution and will put the information here when I find it):At least forty college and universities throughout the nation are implementing/experimenting with interactive computer programs in developmental mathematics designed by Academic Computing Services. ACS recommends one faculty member plus student assistants per 1,500 students. Decisions to implement these programs are made by presidents and provosts, not mathematics departments. Private businesses are selling tutoring and teaching services in "remedial" mathematics to large state universities, again without the approval of the mathematics department. These services are not necessarily cheaper than that provided by the university but provide an "in" to the university to allow for expansion into reading and writing courses.
Fortunately, Andrew Odlyzko has just relesed a draft of a paper entitled "Electronics and the future of education," which offers measured and well-thought-out economic and other arguments against such diseases becoming large-scale plagues. Nonetheless, I think that vigilance here is extremely important.
There are many existing challenges in education that the Web touches -- use of computers, effective individualization, and assessing group activity. We haven't yet had enough experience to see what the new contributions that the Web can make will be like, and what obstacles it will bring. Novelty, immediate appeal, and a cultural surge may conspire to make it appear better than it actually is, especially since it's a very attractive straw to grasp for those desperate to fix the education system. Not only that, the Web is a short-attention-span environment and means must be found to encourage thoughtful reflection in order to overcome the medium's natural tendency to encourage fragmented surfing.
How will the Web change our mathematics teaching? What possibilities does the Web open?
It's becoming much easier to share mathematical environments. A new level was reached with helper apps, continued with Java, and it still may be made more seemless and easier for the user to construct a personal environment. Being able to try to do something for oneself is a key ingredient in learning, so this direction is important. (Here's some nice student work.)
The mathematical interactivity potential of Web pages is becoming spectacular. MathView, a plugin based on Maple, allows users of a page to experiment with math examples --calculations, graphs, symbolic manipulations. (The plugin is free, but you have to purchase the authoring tool.) Also try out the MathView examples on the Maple page. This is certainly the wave of the future. There's a Java version of the Geometer's Sketchpad, the dynamic geometry program popular on Macs and PCs, in the wings. (You can download an alpha version.) The Java page at the Geometry Center has a number of nice examples. All this will conspire to make Web pages the medium of choice for conveying mathematical information.
Check out this Web page by 6th grader Tim Peterson.
In terms of conveying material to students about courses, I imagine the Penn model will soon be widespread: we'll put syllabi and assignments on the Web along with interactive examples, and we'll offer help in the same place via email communications.
DRUCKER SAYS "UNIVERSITIES WON'T SURVIVE"
Renowned management consultant and author Peter Drucker says:Thirty years from now the big university campuses will be relics. Universities won't survive. It's as large a change as when we first got the printed book. Do you realize that the cost of higher education has risen as fast as the cost of health care? ... Such totally uncontrollable expenditures, without any visible improvement in either the content or the quality of education, means that the system is rapidly becoming untenable. Higher education is in deep crisis... Already we are beginning to deliver more lectures and classes off campus via satellite or two-way video at a fraction of the cost. The college won't survive as a residential institution (Forbes 10 Mar 97).
-- but see Odlyzko!
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