In a comment thread on someone else’s blog, I can’t remember whose, a commenter said that they never understood how or why teaching and research were related.
The following is a truth universally acknowledged, but I am going to say it anyway:
You have no idea how much you don’t know about something
until it’s time to explain it to someone else.
It never ceases to amaze me how much I learn every time I teach an undergraduate course. The process to trying to convey something to the uninitiated is quite fascinating as well as useful. One comment that I get fairly often in official teaching evaluations is that the students appreciate that I can explain things several different ways. I take great pride in those comments, which mean that I am succeeding in doing what I think is extremely important. If you really, I mean really know something inside and out, you can come from several different directions and still reason your way to the central idea. You can approach it at many angles until you find one that clicks with your student.
My undergrad degree was in theoretical physics and everyone’s teaching style was heavily mathematical; I loved it and I honestly thought that was the only way. When in doubt, write down the appropriate partial differential equations, take a deep breath and roll up your sleeves, then attack as formally as possible (often expanding in terms of various special functions/orthogonal polynomials) and see what happens. I had a professor in college who said he saw everything through equations, that diagrams and other visual aids were completely useless to him. I now know that am very visual, as are many people, but at that time I didn’t even know there was such a thing as a learning style, and not that anybody would care about what I preferred. Anyway, I got used to viewing everything through the lens of the formalism. Some would say this is a very European style of doing theoretical physics.
Then I came to the US and realized that you could and should go “intuition first.” You can see/smell/taste/hear/touch the solution, or at least some of its salient features, before actually deriving it rigorously. I started seeing the concepts familiar from my undergrad studies in a new, playful, relaxed fashion. The concepts were no less true, but just became very very fun, and it was quite liberating. Some would say this is a very American style of doing physics.
I teach courses with a very heavy physics focus to young people who are not physics majors, but who really need to understand this stuff very well in order to be able to apply it to something practical. Much of the material can be understood qualitatively, but unless you can compute numbers, you can’t actually use any of it. Many students also don’t like math as much as they ideally should, and this unfortunate distaste is part of what prevents them from making connections between disparate subfields based on the common mathematics. So it is important to first teach them to feel the problems, and then, once they are empowered through their qualitative understanding, hit them with the math and show them how math translates into numbers what their gut is telling them to be true.
This experience in teaching students who have the background, interests, and ultimate career goals so different from mine has critically changed how I approach my job now with respect to my junior years. Teaching is of great importance for giving talks, writing proposals and papers. It helps you perfect the art of presenting cogently and (hopefully) engagingly; how else would you make yourself practice several times a week just for the sake of practice? Ok, maybe the über-organized ones among us would anyway, but I know I just wouldn’t.
One of my grad students said “You advisor is there to give you intuition”; I will take it as a compliment. When you are not the person who did the experiments or wrote the code, realizing when things do or don’t make sense in ways that are not trivially obvious is an absolutely critical skill for doing science .
Today I had a group meeting and a student presented his research data in the context of the work of another group. A premise that the other group had used was fairly inconsistent with some basic features of the systems considered. Another student had some doubts and we ended up having a full-blown discussion on the board on some of the key elements of quantum statistical physics as applied to the systems we study. I was able to basically give a succinct and clear (so says me) 10-min lecture to the group on the spot; while these are not the concepts I usually teach myself, I teach enough related material at very different levels that the whole skeleton of my knowledge has thereby been strengthened and these pieces have fallen into place without me even realizing it. Teaching is therefore not unlike milk — enjoyable and good for your intellectual “bones.” It helps your mind carry heavier loads and run faster, which makes it better at research.
How do you view the relationship between teaching and research?