Earlier this week I had the experience of being in a lecture again, in a junior-level Electricity & Magnetism class (I will be studying this class as part of my new job). The contrast between the structure of a university class and the Exploratorium workshops was dramatic. In the university class, the material was presented in the abstract, with formulas and references to the “E-field” and an example problem. In the Exploratorium workshops, the focus is on the phenomenon, with almost no math, and the explanations are given like a story (eg., “electrons are stripped off of one material, and that charge pushes on the balloon…”).
The goal of the different workshops is different, of course — the university class is training students to solve problems and pass a test. The Exploratorium workshops are training for conceptual understanding. But can’t the two intertwine a little bit more?
In speaking with the professor for the university course, he made the distinction between theoretical/mathematical understanding and conceptual understanding. He is teaching students for theoretical understanding, not concepts. I respect this, as I do the conceptual emphasis at the Exploratorium. But, what I would like is to see more of a marriage between the two.
Many scientists argue that “popularization” of science is not useful because you can’t really get across the essence of the science, only the big ideas. The true essence of the science requires an understanding of complicated, indirect relationships, and a mathematical description of the world. That mathematical description of the world is what these young physicists are getting in their classes, and what I got in mine. Some of my deepest insights into the world were gained through understanding of these equations and what they said about the laws of nature.
However, my other deepest insights into the world were gained through a simple explanation of a phenomenon, which drew on my physics knowledge and told me what the equations were really saying.
So, the two methods of teaching certainly have their place, but I would like to see more overlap between the two. I don’t think you can truly understand the world without a good grasp of both the mathematics and the concepts, though the emphasis must change depending on the learner’s goals.