The Many Faces of a Computational Medium: Teaching the Mathematics of Motion

This chapter reviews the development and deployment of two editions of a course on the mathematics of motion. The course was based on the premise that everyone involved—students, teachers and researchers—should develop a flexible competence with a general, programmable computational medium, Boxer. We illustrate the many ways that Boxer was used in the course, from microworlds and flexible tools to tutorials, from a compact and precise notation in which to define and use fundamental concepts, to providing the basis for extended and thoroughly personalized independent projects. A computational medium has many attractive qualities that help foster a gradual but effective shift in classroom practices to new ones that support more effective and more enjoyable learning of important mathematical and scientific ideas.