The calculus reform movement of the last decade or more has led to major changes that include an emphasis on geometric and numerical ideas as a balance to symbolic manipulations, student projects, realistic applications via mathematical modeling, the use of technology, and a more active learning environment. These efforts were intended to transform calculus into a pump, not a filter.

But if we are to change calculus, we must also consider how we “fill the tank”; that is,

• how do we increase the numbers of students who proceed on to calculus?

• how do we improve the mathematical experience of both those students and the ones who have no intention of going on to calculus?

Each year approximately three-quarters of a million college students take some variety of precalculus course; yet only a small fraction of them ever go on to start calculus. Most of those who do take calculus display a singular lack of retention of the material they were taught and often cannot complete calculus. This is a dreadful indictment of the effectiveness of traditional precalculus courses. They neither motivate the students to go on in mathematics nor adequately prepare them when they do continue, especially in view of the changing curricula in calculus and also the client disciplines.