In teaching mathematics to freshmen at MIT I found myself frustrated being continually confronted with the challenge of representing the mathematics to students concretely enough so they could respond to it, but abstractly enough so the general picture was clear. I could write out a specific example, or write out a general formula. The deep significance of the symbols on the page eluded the students. Chalk on the blackboard is static and cannot capture the fact that the abstract theory is no more than a family of examples. Furthermore, for howework I found myself asking for mastery of algorithm over concept.
Aided by a grant from the d’Arbeloff Fund for Excellence, I collaborated in 2002–2004 with graphic artist Hugh Hohn to produce a series of "Mathlets" designed to address these challenges. They are presented on this website. We have used these applets every year in 18.03 Differential Equations, for lecture demonstrations and as the basis of homework assignments. Some illustrations of these uses are presented here as well.
I invite you to explore these teaching and learning tools, and find your own way to integrate them into the course. I am very interested in how they are used and whether and how they aid in development of skill and comprehension.
MacVicar Faculty Fellow