It is the course most dreaded by college students. More than 700,000 take it every term, but at least a third fail it, repeat it, and often fail it again. Years after graduation, memories of calculating the volume of an ellipsoid or the velocity of a moving object can still evoke terror.
Calculus, the foundation of college mathematics and a prerequisite for understanding physics, chemistry, engineering and other sciences, has been taught virtually the same way for decades, with little regard for changing times or student sensitivities.
Now, calculus is in a period of crisis, according to more than 600 leading mathematicians and science educators, who crowded into a standing-room-only conference yesterday to try to do something about it.
At the opening of a two-day meeting sponsored by the National Research Council's Mathematical Sciences Education Board and other mathematics organizations, the educators called for "deep structural change" in calculus courses, revisions that would tap the potential of computer technology, focus more on real-life problems and the concepts behind calculus and move away from drill and routine exercises.
"Calculus is big. Calculus is important. Calculus is in trouble," said Ronald G. Douglas, dean of physical sciences and mathematics at the State University of New York at Stony Brook. "We're not doing a very good job of teaching what we are teaching."
Educators eager to revise calculus instruction cite a number of problems: The courses are often so difficult or boring that they keep students from pursuing careers in mathematics and science; computers and hand-held calculators can perform instantaneously the operations students spend much of their class time learning; scientific advances have expanded the applications for calculus, but students are being poorly prepared to use it in other areas, including rapidly growing computer-based fields.
"It's a crank-turning course. We've reduced calculus to a course where students do almost nothing but calculate derivatives and integrals," said Anthony Ralston, professor of computer science and mathematics at the State University of New York at Buffalo. "It used to be proving, concepts. Now there's less and less of that."
If successful, this first large-scale effort to reform calculus instruction would have widespread effect. In addition to its college enrollment, calculus is taught to 300,000 high school students.
Moreover, changes in calculus would force revision of textbooks and curriculum in physics, chemistry, engineering, biology and computer science.
Created in the 17th century largely by the work of Sir Isaac Newton, calculus is a set of methods used in part to calculate continuous change, including motion, and to determine the area and volume of complicated objects. It is used broadly today -- in medicine to study electronic activity in neural cells, in space technology to track satellites and in economics to prove fundamental theories and project economic growth.
The effort to alter the traditional calculus course comes at a time when the nation is concerned about its technological prowess and competitive position internationally. But as the economic climate focuses attention on the sciences, educators worry that technological fields are not attracting sufficient numbers of students.
The proportion of entering freshmen choosing to major in mathematics, for example, dropped from 4.5 percent in 1965 to less than 1 percent 20 years later. And close to half the untenured mathematics faculty last year was foreign, according to a survey of 35 major universities by mathematics organizations.
The momentum for change in calculus is tied to two national programs.
The National Science Foundation is initiating a multimillion-dollar project to examine how calculus teaching should be reformed and the Mathematical Sciences Education Board is beginning a multiyear review of all collegiate mathematics.
Some of the problem stems from the large growth in college enrollment during the 1960s and '70s. Class sizes grew and course material, often taught by inexperienced graduate students, was simplified, moving away from the theoretical to focus instead on rote use of formulas.
Participants in the conference said they would embark on a series of meetings and projects to examine how courses can become more relevant to other "client disciplines" and how the curriculum can allow students to experience a sense of discovery and encourage them to pursue scientific fields.
"Calculus is really exciting stuff and we're not presenting it as exciting stuff," said Robert M. White, president of the National Academy of Engineering. "It must become a pump rather than a filter in the pipeline."