I love teaching magnetism. One of the things that is particularly amusing to me is that we teach a set of right-hand rules to determine the direction of magnetic forces or magnetic fields, it happens whenever you teach vector cross products, but most frequently in magnetism. There are a number of forms that these hand signs can take. I prefer to use the index finger as the first vector, the middle finger as the second finger and the thumb as the product. Invariably, as the students work through it with me they laugh, and I get to make jokes about needing to do yoga. I suspect that many students see this as superfluous to their learning of physics.
My love of teaching right-hand rules in magnetism was tested during the shift to online teaching this spring. Right-hand rules are inherently three dimensional - a challenge in classroom settings. Teaching online flattened the presentation to two dimensions and was further complicated as I hadn’t thought about whether my screen was mirroring or not.
In the sciences, physics in particular, there is a strong expectation that understanding gets encoded into equations and quantitative models (Fredlund et al., 2014). Often this means that faculty limit the focus of their instruction on equations and quantitative understanding. I view this as a mistake, the understanding of equations and quantitative models is paramount, but understanding of equations and quantitative models develops by first understanding a variety of representations. One of the challenges in teaching is to keep in mind that the learner doesn’t have the same background knowledge as you. This means as a teacher you need to allow students to follow a developmental path and time to develop the multifaceted knowledge structures the experts maintain.
Learning in the quantitative sciences means students need time to develop a coordinated understanding of different representations (Larkin and Simon, 1987). Students in physics can see phenomena in many different ways. They might sketch the problem - which helps to identify relevant objects and interactions; they might make graphs of the motion over time - which describes the dynamic state of the system; they might make force diagrams or momentum vectors or energy diagrams - which allow students to make predictions on the future behavior of the system. All of these representations can be connected to quantitative understanding. Graphs have slopes and areas that are meaningful. Vector diagrams can be added, subtracted, and manipulated so students can determine future behaviors. And right-hand rules identify three-dimensional vector relationships.
Representations of the phenomena should not be skipped over. When I teach magnetism, the right-hand rule hand signs are, to me, not superfluous. I include questions about them on quizzes and exams because I see these as a critical component of students developing their understanding of the relationships encoded in the right-hand rule. It helps to develop a kinesthetic sense about the propagation of magnetic fields - which are particularly difficult in that they are invisible and work in ways that are orthogonal to other fields. Right hand rules are representations that reflect the phenomena and allow students to better predict and explain the behavior of physical systems. Plus, in a room full of students taking an exam with right-hand rule questions, you get to watch as they contort themselves trying to determine which way the magnetic field points.
Fredlund, T., Linder, C., Airey, J., & Linder, A. (2014). Unpacking physics representations: Towards an appreciation of disciplinary affordance. Physical Review Special Topics-Physics Education Research, 10(2), 020129.
Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive science, 11(1), 65-100.