I have always loved to teach.

I have primarily taught geometry classes, ranging from graduate courses in differential geometry to service courses in vector calculus. I have also taught precalculus, and most of the calculus sequence. But I most enjoy, and am best at, teaching undergraduates at the upper-division level. I have developed a variety of advanced undergraduate courses, some of which are described in more detail below.

I have been a member of the Graduate Faculty in both the Department of Mathematics and the Department of Physics since 1988, a member of the University Honors College Faculty since 2000, and have been listed as Courtesy Faculty in the Department of Physics since 1993. My student evaluations are consistently among the best in my department; I was a finalist for the Carter Award for Undergraduate Teaching in the College of Science here at OSU in both 1990 and 2006. In 1999 I was honored as a "Top Prof" by the Mortar Board Senior Honor Society, and in 2004 I received the Frederick Horne Award for Sustained Excellence in Teaching Science of the College of Science.

I designed a course in general relativity intended for math majors; this course has been in high demand (when it is offered), and is taken by both undergraduate and graduate students in math, physics, and occasionally other disciplines. This course has twice been audited by senior faculty in unrelated departments. I also developed a course in non-Euclidean geometry, taken by prospective secondary school teachers as well as traditional math majors. This course involves not only heavy use of Mathematica but also a term paper; this is unquestionably the most challenging, as well as the most rewarding, course I have ever taught.

In addition, I have been closely involved in the NSF-funded effort to redesign the physics major here at OSU. In this Paradigms in Physics project, the junior year courses were replaced by intensive, cross-disciplinary paradigms, which are followed in the senior year by more traditional, discipline-specific capstones. At the invitation of the physics department, I designed and taught the last paradigm, on reference frames (special relativity and Coriolis forces); I am the only non-physics faculty member to teach a paradigm. I am actively working on developing the course notes from this course into a form suitable for publication.

My current curricular focus is an NSF-funded project entitled Bridging the Vector Calculus Gap, whose goal is to better incorporate the way vector calculus is actually used by physicists and engineers into the teaching of this material by mathematicians. We have developed supplemental small group activities which emphasize geometric visualization, as well as a student Study Guide and an Instructor's Guide. We have been invited to give numerous workshops on the use of our materials, including several at major national meetings. In addition, I have recently become involved with two projects aimed at increasing the mathematics content knowledge of K–12 teachers in rural Oregon, namely the High Desert Mathematics Partnership, and the Oregon Mathematics Leadership Institute.

Along the way, I have tried a variety of innovations in the classroom. The vector calculus recitations have been turned into extended labs involving small group activities, somewhat along the lines of the MathExcel project. In the same class, I am experimenting with "flash cards" along the lines of the ConcepTests originally developed for other disciplines, and which are intended to break up the tedium of a large lecture. I have used computer demonstrations in classes large and small, and several classes have involved student work in computer labs. But my favorite teaching aid remains the one I started with: colored chalk!