Differential equations are mathematical descriptions useful for modeling dynamic phenomena. Problems such as describing fluid flow, the spread of a disease, and stock option prices are often solved by appealing to differential equations. When students of science and engineering learn the techniques of differential equations it can be difficult for them to move from technical, symbolic mathematical manipulations to a more qualitative, conceptual understanding. This project investigates how to tutor students in such conceptual understanding. It will study the techniques and pedagogical knowledge employed by expert tutors and try to teach these techniques to less experienced peer tutors. It will develop new tests to measure how well students comprehend differential equations on a conceptual level and study the efficacy of various tutorial methods. And it will investigate how to build software for computer-assisted tutoring of differential equations, where a computer follows the conversation and suggests some of the expert methods to the inexperienced tutor.
