Yesterday I read a neat little report by one of our final year engineering students. As part of her final year project, she'd been looking at misconceptions in first-year students' thinking about electromagnetism. Learning about electric and magnetic fields isn't easy. For one thing, you can't actually see them. Therefore it's not at all obvious how something influences them. It's not like learning mechanics – where you can swing pendulums of different lengths and see for yourself the effect it has on the period of oscillation – these fields are invisible and therefore some indirect way of probing them is required. That adds its own problems.
Most of the problems identified by the student weren't terribly surprising. The theory of electromagnetism is full of horrible cross-products, which are a mathematical oddity in themselves* (try to read the Wikipedia article on them – I bet you won't get very far). It's hard relating experiment to theory when the theory is a struggle to grasp. Many misconceptions relate to whether fields and currents lie parallel or perpendicular to each other, and which generates a force and which doesn't.
But one problem that was identified by the research (based on formative tests) was the slap-dash approach to terminology. Many students used terms such as 'magnetic field', 'B-field', 'flux', 'force', 'current', extremely loosely. They have very specific, and different meanings, and they are not interchangable. I heard a case of this in the lab today – a student talked to me about the force of the wire, when he meant the current in the wire. I think there are two questions here: 1. Using terminology loosely may simply be a consequence of not understanding what the terminology is trying to describe, and therefore is a symptom of deeper problems with grasping the concepts. Alternatively, 2. The slopiness in using terminology may actually be the root cause of some of the students problems. How can you explain something if you're not using words correctly? – you end up confusing yourself. I'm writing a journal article at the moment – and it's obvious that the process of putting down my thinking on paper, in a precise manner that someone else can follow, does wonders for cementing my own understanding of it (or, sometimes, exposing my own lack of understanding of it when I thought I had grasped it.)
It wouldn't surprise me if both cases formed a feedback loop (vicious circle) where lack of understanding leads to poor use of terminology, which in turn prevents students acquiring the right understanding. I feel like a little research project is brewing here for next year…
*Cross-products would cease to be an oddity if we put them where they belong – in the dustbin. They are a consequence of a desparate attempt to represent areas as vectors. If we recognized areas for what they actually were – areas (or bivectors) – and worked with geometric algebra, physics theory would become so much easier. But, alas, we are stuck with historical conventions that are probably too far ingrained to break.