Abstraction is the enemy of learning – it is the end, not the beginning, of understanding. Mathematicians cannot comprehend this, and I suppose it is conceivable that their brains are wired differently. But most physics students learn by proceeding from the concrete to the abstract, not the other way around. It is the universal blunder of lecturers just starting out in their careers to go straight for the most sophisticated formulation – the one they recently learned in graduate school, and to which they are still in thrall. They want to start every problem with a Lagrangian, even if Newton’s laws would do it much more simply. This is like trying to potty-train a two year old on a full-sized toilet: exciting to the parent, perhaps, but frightening to the child, and potentially dangerous. Our business is to empower students, not to impress them; to instil confidence (“I could have done that!”), not awe (“How did they do that?”). The simplest tool is almost always the best one.
Abstraction is the enemy of learning