The Movement

The first good thing that came out of the calculus reform initiative was the movement itself. There can be no doubt that it is indeed a Movement: Witness the CRAFTY volume [9], with information on more than 70 projects that were already under way three years ago. Now, the Harvard Consortium project alone has well over 100 schools using its materials, and several other major projects report dozens of active-user sites, many with multiple sections and/or teaching all their calculus students in reformed sections. NSF has funded a study that documents the extent of reform projects and experiments already under way; a report by Jim Leitzel (University of Nebraska) elsewhere in this volume indicates that 60% of responding four-year schools and 45% of responding two-year schools have at least a modest reform effort in place. Rob Cole (The Evergreen State College), co-director of the Washington Center dissemination project, reports that, by actual head count, 27% of all college-level calculus students in the state of Washington are in reformed courses.

For several years now, we have seen crowded and overflowing sessions at national and regional meetings of MAA, NCTM, and AMATYC -- panels, featured speakers, contributed papers, minicourses, poster sessions -- on the subjects of calculus, writing, technology, and education. Sessions on these topics have been fewer in number, but just as popular, at meetings of AMS, SIAM, and AAAS. An indication of the growth in interest can be seen by comparing the programs of the annual Joint Mathematics Meetings (mostly MAA and AMS) for the years 1985 and 1993. The 1985 meeting in Anaheim was the site of the panel discussion "Calculus Instruction: Crucial but Ailing," organized by Steve Maurer (Swarthmore College) and Ron Douglas (SUNY Stony Brook), that was an important precursor of the calculus reform movement. That year, about 10 out of more than 500 events on the AMS program were related to education, plus about 28 MAA events, including 10 minicourses. (At that time, most of the invited MAA addresses were on mathematics, not on education.) This year, fully 25% of the more than 1200 numbered items on the combined AMS/MAA program were devoted to education, and the number of minicourses had grown to 17.

Participants in NSF-funded and other reform projects are receiving a steady stream of invitations to visit other campuses and help other faculties get started with reform of their own programs. Many of these projects are also running workshops, on their own campuses or at regional sites, of sufficient duration to get participants thoroughly familiar with both new materials and new methods of presentation. Growing numbers of the on-campus visitors and workshop presenters are now "second generation" reformers -- not the initial developers of the materials, but users with enough experience to be ready and willing to share with newcomers. There is still a large pool of institutions whose faculties have not instituted any reforms but who are eager to begin. And most of them are finding that their administrations are also ready to commit new resources -- even wondering when their mathematicians will get around to asking.

The American Mathematical Society's e-Math service now maintains a Calculus Reform bulletin board that has subscribers in the U. S., Canada, Puerto Rico, Australia, and Taiwan. Recent contributions have included lively debates on how and whether to treat series in a first-year course, whether reformers pay enough attention to mathematically talented students, whether proofs are important (relative, say, to heuristic arguments) or even possible (in the absence of axiomatic foundations), and whether the Mean Value Theorem belongs in the course. Only a few years ago, discussion of some of these matters would have been considered heretical, and resolution of some too obvious to be worth discussing.

The earliest reform projects were already under way when the NCTM Standards [5] appeared, and the importance of the Standards was not automatically noticed on college campuses. Nevertheless, almost all of the projects have converged toward a common set of goals -- highly consistent with the Standards -- and yet have maintained widely differing approaches and materials. We already have a constructive proof that there are many ways -- affordable, transportable ways -- to teach calculus effectively. Thus, we need never again settle into the rut of offering the same course over and over, year in and year out. An important indicator that the Movement has achieved critical mass was the feeding frenzy by publishers from roughly mid-1991 to early 1992, during which time almost all the major curriculum development projects were signed to commercial publication contracts.

While there is no doubt in anyone's mind that there really is a Movement for reform, some conference participants question whether it will be possible to sustain reform, and there is even talk of a "backlash" beginning to emerge. In my view, we do not yet have clear evidence for long-term sustenance, and the pressures created by reaction and inertia may well be intense. Our job is not over, but I have no doubt that reform can succeed; it's up to us to see that it does.

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