As another semester at the University of Wisconsin – La Crosse reaches its halfway point, it’s time to start preparing for my spring class – MTH 265: Mathematical Models in Biology. This is a course that only has a first-semester calculus prerequisite, meaning that it is unlike many of the mathematical biology courses around the world (which often require differential equations and/or linear algebra as a prerequisite).
My thought process when teaching this course is that the students likely do not have the mathematical background to fully appreciate the breadth and depth that mathematical biology has to offer. Whether it’s the global and/or asymptotic stability of equilibria to difference equations, principal component analysis applied to multivariate data, or Markov Processes applied to Allele frequencies, research-level mathematical biology requires mathematical flexibility and maturity. However, most of the students in my MTH 265 class are not mathematics majors. Many will be researchers or practitioners of the life sciences, though, meaning that they will have to interact in a meaningful way with mathematicians, statisticians and computer scientists at some point during their careers. Thus, my goal for the course eventually became to give a survey of many different topics pertaining to mathematical biology during the 15-week course. This way, they will know that a solution (possibly) exists to their quantitative problems (even if they may not be able to come up with it themselves). Simply knowing such a solution exists allows one to approach the right people for collaborations, and keeps the math-biology interface a fruitful one.
Survey courses are fairly common in graduate work, but students in their second semester of mathematics are pretty new to reading mathematics. Thus, to cover the material in 15 weeks, I created a collection of videos as a part of an inverted, or “flipped” classroom. Videos appear to be a medium that reaches current students better than (or in conjunction with) traditional textbooks. Students were asked to view these videos prior to class, while during class they were assigned groups in which they worked on “case studies” that took the duration of the hour. I provided assistance with the case studies, as well as any homework questions the students had.
The term “flipped” comes from the way the course is structured relative to a traditional course, where lectures occur during the regular class period (where the professor is present but the student engagement is low) and homework/case studies occur outside of the classroom space (where demands on the student are high, but direct help from the professor is not immediately available).
This course has been a great success. Some of the things we’ve learned from flipping the course can be found in this paper, and were used in a section of Grand Valley State professor Robert Talbert’s new book on flipped learning in the college classroom. I owe a great deal of my ideas to the Mathematical Association of America, especially their Project NExT program. The progress we’ve made as educators even in the short time (six years) I’ve been a mathematics professor has me excited for what is to come for the future.