I have always loved to teach.
I have primarily taught geometry classes, ranging from graduate courses in differential geometry to lower-division 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 Mathematics and Physics Departments 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 received the 2011 Loyd Carter Award for Outstanding and Inspirational Undergraduate Teaching (and was a finalist on three previous occasions) and the 2004 Frederick Horne Award for Sustained Excellence in Teaching Science, both from the College of Science at OSU. I have also received two teaching awards from the University Honors College (2009 and 2012), the 2014 Elizabeth P. Ritchie Distinguished Professor Award from OSU, and the 2014 Distinguished Teaching Award from the Pacific Northwest Section of the Mathematical Association of America. In 2017, I received the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics from the Mathematical Association of America, the top national teaching award in collegiate mathematics.
I designed a course in general relativity intended for math majors; this course has been in high demand, 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. A textbook based on my course notes was published in 2014.
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 In this Paradigms in Physics project (whose new website is here), the junior year courses have been replaced by intensive, cross-disciplinary paradigms, which are followed in the senior year by more traditional, discipline-specific capstones.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); a book based on my course notes was published in 2012. I have also co-taught two of the early paradigms on electromagnetism, and am the only non-physics faculty member involved in the project.
My primary curricular focus is the 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, an Instructor's Guide, and an online textbook. We have been invited to give numerous workshops on the use of our materials, including several at major national meetings.
In addition, I have been 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, and am actively involved in efforts to continue this type of project in Oregon.
In addition to my textbook on special relativity, now in its second edition, I have also written a textbook on general relativity, as well as a monograph about the octonions. More recently, I have been developing interactive, open-access, online textbooks on a variety of topics, including an updated version of the vector calculus book.
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 make regular use of "flash cards" (similar to clicker questions) 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 of my classes have involved student work in computer labs. But my favorite teaching aid remains the one I started with: colored chalk!