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?
xykademiqz 
Feynman supposedly said that you don’t understand a result unless you can derive it several different ways. That’s one of the best parts of teaching. I learn something from deriving it several different ways, most of the students hopefully get at least one of the explanations, the better students hopefully understand several of the explanations, and they also see how an expert approaches something. My biggest beef against education reformers is that they want to remove some of this flavor from teaching.
Also, giving several presentations per week on a wide range of topics makes it really easy for me to give a seminar. Eventually it becomes intuitive. I periodically go to a seminar series with people from industry, and while some of them are good, there’s definitely a difference between a person who gives multiple lectures per week and a person who doesn’t.
The other nice thing about teaching is that it helps me sharpen certain skills that I otherwise might not use as frequently. It is no coincidence that I wrote three papers on variational techniques while teaching Lagrangian mechanics, and two of those papers applied variational techniques to a field where they are mostly considered a niche subject.
Teaching is definitely one of the best ways to learn. There have been times when I’ve had to explain things in the lab, and I not only learn the topic better, but the questions have led to new projects and ideas.
Regarding the Euro-style of teaching, you’re so right! In grad school, several people avoided Euro-style prof’s classes because they were jam-packed with so much theory and math, those brought up with the typical American education had trouble applying the principles. It was like Greek letter vomit, just spewed all over the chalk board. It’s very good you’re combining tactics.
So funny you should raise this! I just sat in a lunch with our new University President who knows nothing about academia. She asked, “So, how much do you all teach?” All of the faculty sitting around the table grimaced at the loaded question, as basically, there is not a clear distinction between the two. While we all focused on explaining how all of our research is essentially teaching (as I have 12 undergrads and 2 grad students that essentially are my apprentices and work with me on just about every research project I do), you raise a really interesting point in the other direction. I appreciate your point as, in fact, I deliberately signed up to teach a class on a topic I am extremely interested in but not all that familiar with, as a way to explore the topic in depth to come up with new research ideas.
I’m on sort of the other side of this because my job is mostly teaching, and my colleagues and I have to keep making the case that research helps our teaching. A cynical point of view is that research hurts my teaching because it represents time I could be spend teaching a fourth or fifth class (or serving on a couple more committees, ha ha). When done well, science forces one to very clearly and precisely describe one’s result and how one got there. That skill can translate very well to teaching science classes, and it was a good point made about explaining things in a variety of ways to get one’s point across in classes.
I can’t really say that teaching helps my research because most of what I teach is too fundamental. It has nothing to do with my scientific writing and I rarely give scientific talks. However, it does help when I’m working with a research student because of the “mini-lecture” aspect when I’m introducing a topic to a student. (I guess it also helps a lot when I have the opportunity to do public outreach, because it has made me pretty good at coherently explaining complicated things to a non-expert audience.)
I do generally agree with the idea that teaching is the best way to learn, but I can’t afford to teach a fourth (or fifth) class to do that. Luckily, I will have an opportunity to teach a class that does connect a bit with my research next year, so that could be interesting.
I agree that teaching, and frequent practice in communication, is beneficial to helping me communicate my research better. Similar to the first commenter, I’ve been noticing lately that those who communicate/teach less frequently, e.g., some (though certainly not all) government scientists, tend to give worse research talks than academics.