As a longtime teacher of college-level physics, I read with interest Ricardo Heras’s Commentary on traditional versus creative styles in solving physics problems (Physics Today, March 2017, page 10). He has clearly been bitten by the excitement and satisfaction of studying physics, and he is already thinking deeply about how it can best be presented to students. My guess is that he will someday be a very highly regarded teacher.
I also think, though, that the traditional textbook problems Heras disparages have considerable value. Yes, we have all had (and probably were ourselves) students who can grind out an end-of-chapter or test problem without really internalizing the physics involved. But that is not the primary goal I have in mind when I have my students, particularly first-year students, do the problems.
Heras’s model of a creative problem-solver is Richard Feynman, a rightly revered figure. But most of us, and most of our students, are not Feynman. I cannot expect my first-year students to develop deep physics insight. Before insight comes command of the foundational knowledge and techniques of the discipline, and my students are in desperate need of accruing practice in setting up and working through problems. The inevitable disappointment of seeing that their answer does not match the one in the back of the book and having to diagnose what went wrong is often the most educational aspect of the work. At higher levels, having students dig out an old-fashioned table of integrals and see how to compute an expectation value by hand—as Erwin Schrödinger might have done—gives them a sense of the nitty-gritty that underpins the insights of great creative minds.
Insight and expertise accrete over years of such grinding practice. Developing intuition in physics—or in any challenging discipline—is no different from learning to play a sport, speak a new language, or play a musical instrument proficiently: practice, practice, practice. Each boring problem is an incremental step along the climb, an investment that will eventually pay off in the form of a coherent foundation of knowledge and a grasp of techniques that will last a lifetime.
I have witnessed the evolution from blackboard- and overhead-based “static” lectures to powerful in-class computer and projector systems and laboratory sensor-interface units being used to illustrate concepts, calculations, and phenomena in ways I could only have dreamt of when I began teaching. But before a problem is thrown to the computer, it always goes up on the board first to have its physics, units, mathematical nuances, and orders of magnitude examined. To be sure, many traditions are inertia incarnate, impediments at best and destructive at worst. But not all are without virtue, and the best can be adapted to the times.
