The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.