Education and learning are strange beasts. At school and university, people seldom understand even close to everything, and forget most of what they did understand soon after the final exam. But yet we trust doctors to prescribe correctly; professionals to know their jobs; or professors and teaching assistants to know what they are talking about. Where does this knowledge come from??
It’s the end of my first term of teaching assistant duty — I’ve been teaching and marking (grading) for physics 2, which is a general physics requirement for all second year undergraduates. On Saturday I taught a quiz review, which is a summary of the material and further examples offered in preparation for an upcoming test. I’ll be doing this every second Saturday, for a class of well over a hundred students. It was a surprisingly stressful experience — the review itself went well in the end, by the feedback I’ve had, but the preparation of an hour and a half of novel questions and a handout took quite a while. Then during the review there was the tension of wondering whether I had prepared enough material, and also whether I was offering a useful review when I’ve never been to a Caltech-style quiz review before. Somehow I managed to pull a muscle in my elbow (probably from pulling down blackboards), so be warned that teaching can be physically risky!
The teaching assistant experience has, however, reminded me again of how completely I understand basic physics, and how easy it seems. But I remember finding it hard at the time, and not at all obvious. So somehow, in the intervening years, material on which I had a mediocre grasp has become entrenched. I’ve forgotten the lessons, but somehow learnt the physics.
I’d be very interested to hear if there’s been research or study put into analysing how we handle knowledge which was learnt years before. It seems to me that society depends a lot on this “second stage” of learning. Despite supposedly being really bright, there are a lot of students in this course I’m teaching who are not mastering much. And amongst my friends studying various professions, the talk was always of how hard work was, or of what to focus on to get the best mark possible — not really a convincing argument that any of us were mastering our fields.
Yet somehow people become professionals, and know more than they ever seemed to while studying. And hopefully that’ll happen for me with string theory at some stage!
Paul Cook 
It’s definitely a process that happens unconsciously, while you’re worrying about the next thing you don’t understand. I think a large part of the problem in physics is notational familiarity – when I teach first years I notice that they are absolutely terrified of i hat etc, and that this obscures the issues for them somewhat. Having said that, I know I’ve forgotten large chunks of my undergrad education. I assume optimistically that it would come back faster than the first (or second) times were I to review or teach it now. As for string theory, I am afraid the time frame for internalisation might be the limiting factor in my becoming a bona fide string theorist. Anyway, thanks for the interesting entry and the group mail. You’ll notice my most recent blog entry is somewhat less intellectual than yours…
LikeLike
Well, think of it this way: we’ve seen so much string theory that we don’t completely understand, that our subconscious has lots of things to internalise in parallel! Think about the productivity! Awesome!
LikeLike
I must say that my experience as a TA (for Ph1) has been somewhat different. I ‘mastered’ introductory physics rather easily as an undergraduate, in the sense that I found it simple to identify what was the ‘correct’ approach to a problem and arrive at the ‘right’ answer. When I returned to introductory physics as a TA, however, although I still remembered how to solve the problems, they seemed more difficult as I tried to justify their solution systematically. For example, Ph1 problems often involve pulleys and wires with tension. Returning to these problems, I recalled how to solve them, but also recognized I was using many assumptions as to how forces are conveyed through a wire wrapped around a pulley, and how this effects the pulley. You can work out the forces on the pulley and wire and anything connected by dividing the wire into infinitesimal bits and using Newton’s laws, and get the results you expect, but actually going through this is not as easy as the problem initially presents itself.
So, in my case, I don’t feel I really learned Ph1 material until I returned to it as a TA, and studied the problems with the mindset that I should be convinced that my solutions are truly correct (within the limits of assumed postulates), and be able to explain their solution systematically. In some sense, I guess I returned to Ph1 problems as I approach research problems–that is, when you don’t know what the answer is, or what the correct way to obtain it is, you take extra care to think deeply about what you are doing to convince yourself. Although Ph1 problems are much simpler, I did not find them ‘obvious’ as I would have expected before I started. For me, therefore, I think I really come to learn something when I study it while seriously contemplating that it could be wrong.
Then again, I often feel stupid around my peers here for how they seem to view things as simple that I see as more complicated. My only consolation is that I’ve written papers, so I know I can do it, even if perhaps I’m less agile than others. Perhaps we all think and learn more diversely than this discussion presumes.
BTW, this is my first contribution to this blog, and I look forward to more procrastination talking about your interesting topics in the future!
LikeLike