A Vision for Calculus

David Bressoud, DeWitt Wallace Professor of Mathematics at Macalester College, USA

Far too many students emerge from Calculus with little sense of why it is considered foundational to modern science. The problem is that students experience it as a collection of arcane procedures to be mastered and a repertoire of toy problems to which appropriate procedures are applied. They are assessed on how quickly they can identify the problem type and accurately execute the procedures. An alternate approach is to build an understanding of functions as establishing a relationship between variables that vary in tandem, of integration as embodying accumulation when the rate of accumulation varies as a function of time or distance, and differentiation as the ratio of rates of change of linked variables. In other words, the goal is to approach Calculus as a means of modeling dynamic situations. This talk will present concrete examples that are being implemented at a variety of colleges and universities.