The basic undergraduate differential equations course at MIT, 18.03, is taken by some 85% of all undergraduates in their freshman or sophomore year. This course faces several challenges common to such courses across the country.
A grant from the d'Arbeloff Fund for Excellence underwrote a project to address these challenges. A principle outcome has been the creation of a suite of Java applets, "mathlets", for use as lecture demonstrations and, most importantly, as the basis for homework assignments. These applets can be used directly or in modified form in downstream courses, enhancing transfer.
Three dilemmas face basic university mathematics courses, especially differential equations courses.
The applets are used as lecture demonstrations and, more importantly, as the basis for homework assignments. Each applet represents information in several forms, linked by placement or color. This linkage helps convey the connection between physical system, the parameters specifying the differential equation, and the graphical representation of solutions. System parameters or initial values are varied by means of sliders, and the effect on solutions is represented dynamically. Students enrich their understanding by making measurements and then verifying them by calculation.
Prof Haynes Miller speaking about Mathlets: