From the FAQ:
As Sue C. Heffelfinger,M.D. put it: "My husband and I suffered through many years of dull college math, I for one didn't learn anything about calculus until I took physical chemistry." Like Dr. Heffelfinger, when most people reflect on the math courses they took in college or high school, they get a hazy look on their face. Those who have been through a conventional mathematics class are often hard-pressed to explain what the course was about. They remember math was hard but often have little memory of what they actually learned.
Often these classes presented students with collections of "skills" which they were to memorize. The problem was that many folks forgot these skill shortly after they completed the class. The skills had to be memorized because they meant little to the students' intellects.
C&M courses address this problem using modern technology to concentrate on the ideas and concepts of mathematics treating the "skills" as ancillary but sometimes important. Former C&M students can rekindle the skills when they need them because they have the conceptual background to understand what the "skills" try to do.
Jerry Uhl, one of the instructors, has this to say about "Why and (how) I teach without long lectures."
I always told my students that all the learning is done in their brains, I am just a guy to tell them something interesting exists and cannot make them learn anything. This is why I find this class description of active learning appealing.
BTW, I've been wondering about learning with tools such as Mathematica before.