Toward a Lean and Lively Calculus: Report of the Conference/Workshop to Develop Curriculum and Teaching Methods for Calculus at the College Level.

Deep concerns in mathematical education have converged, like currents in the ocean, to generate both a certain amount of froth and a strong force for reform of calculus instruction. First there are the dual concerns of adapting to the needs of the burgeoning number of computer science majors and of making use of new technologies in microcomputers and hand-held calculators. Second is alarm at the decline of the presentation of calculus into an arcane study of detailed techniques of differentiation, integration, and tests for convergence of series, with artificial set-piece problems that may be checked by making sure the answer is simple. Students see little of the towering intellectual achievement of the subject, and they cannot see how to formulate physical problems of change and constancy as mathematical ones involving differentiation and integration. Moreover, even many of the best students remain unable to unite English expressions and mathematical symbolism in a single coherent sentence, much less in an acceptable student paper on a mathematical subject. Toward a Lean and Lively Calculus is a report of a conference held at Tulane University, January 2-6, 1986, organized by Ron Douglas, and supported by the Sloan Foundation. It grew out of the continuous-versus-discrete debate initiated by Tony Ralston and continued at a Sloan Conference at Williams College in 1982 [4], in Forums in this Journal [3], [5], [2], at a panel discussion organized by Ron Douglas and Steve Maurer at the 1985 AMS/MAA meetings in Anaheim, and other places. The Introduction of the report summarizes the conference and lays down a program for the development of a new calculus text along the lines of the Chem Study materials in Chemistry. The time frame proposed for this is already obsolete, and the proposed funding pattern has been altered by the probable involvement of the National Science Foundation in FY88 through the Mathematical Science Directorate. This funding was discussed at a Sloan Conference in Washington in October of 1987. There were three workshops at the Tulane Conference: Content, Methods, and Implementation. They necessarily suffered from simultaneity; the Methods and Implementation participants did not know what would be in the Content report. In fact, the Content Workshop Report gives syllabi for a new Calculus I, a new "standard" Calculus II, and alternate second semester courses involving multivariable calculus (Calculus IIM) and computer symbolic manipulation (Calculus IIC). Most of the workshop time was devoted to Calculus I, and this syllabus is presented in more detail. We comment on this one and refer the reader to the book for the others.