Mathematicians at the University of Illinois will investigate methods by which the teaching of calculus can me made more effective in conveying to students and understanding of calculus as a powerful problem solving tool. Course material planning will focus on the development of the problem sets that will lead students through the central ideas and methods of calculus and enhance their ability to read and write mathematics. The project will consult with user departments in science, engineering and other areas; develop and class test course material for Calculus I based on an approach of Artin; focus on computational and problem solving; and develop student's capacity to read and write mathematics correctly and coherently. A weekly Calculus Seminar will train teaching assistants and discuss content among faculty within and outside the mathematics department. In the Summer of 1989, a Calculus Workshop for UI faculty and high school teachers will be held. The integration of computer technology with use of Mathematica software in the calculus curriculum will be supported by outside funds.