How to maintain enthusiasm and joy in teaching when the material grows stale

I recently finished my third semester of teaching calculus to freshman college students. This means I was drawing the same pictures, solving the same example problems, and discussing the same techniques as I had in two previous semesters. With multiple sections per semester, review sessions, and office hours, it is possible that in one semester alone, I'll teach the same idea/say the same sentence/do the same problem 5-10 different times.

Due to all of this repetition, this last semester I felt myself growing tired of calculus. I know that for my students, the material is new and (hopefully) interesting and exciting, but it was none of these for me, and I could feel it affect my teaching. I would battle to maintain enthusiasm and joy for the material as I taught my students, but I often lost this battle, as is demonstrated by the following comment I received for instructor evaluations:

"Jared was a great TA who could possibly improve on enthusiasm"

I completely agree with this student, and since I hope to be able to teach mathematics for many more years than just 3 semesters, this is a problem I should begin to address now.

For teachers of mathematics, how do you maintain enthusiasm and joy in teaching the same material year after year?

Solution 1:

In operational human terms, I think it is best to avoid teaching/TA-ing exactly the same thing every semester. At the very least, go through the whole year's cycle, for example, of Calc I and Calc II. Then, with the summer to further "forget", starting again with Calc I in the autumn may not seem so bad. One's mind has time to forget a little, to romanticize, especially to fool you (constructively) into thinking that "this time I'll do it right!" (and everyone will understand perfectly...).

Even better is to go through a longer cycle-time of two years, perhaps Calc I,II,III, IV, and then repeat. Such non-repetition does entail a bit more effort to "prepare", but this is the cost of avoiding staleness.

The same sort of issue exists, perhaps even more poignantly, for the basic grad courses, which most likely you'll find yourself teaching at some point. It is very important to not become jaded, to not lose a grip on how "obvious" things are, simply because one has thought it through so many times. Knowing how long it takes for one's own head to "forget" the short-term details is important, since it seems best to out-run the short-term memories to have "freshness" and enthusiasm.

Solution 2:

I also teach Calc and Linear Algebra courses several times a year. I have been doing it for several years in a row.

This may sound shocking, but one thing that works for me is preparing my mind before every class as if I were a "Math jazz musician", i.e. I try not to "act" or "intepret" but, to some extent, improvise or "rebuild" the material, adapting the exposition to the audience mood. In my view, you cannot teach anything if you do not make a connection with your audience. See every class as a "Math jazz-session". And listen to more jazz...

This may help too.

Solution 3:

This is purely from my experience. If the material grows old, then hopefully you are more familiar with it, and so you can actually concentrate on teaching. What I do is ask a lot of questions to the students, and try to make them come up with some answers. Also, if you are TAing, that means that students often ask you heir "doubts". You should first ask them what approaches did they try. For example, suppose the question is: when is $sin(x)$ incresing? You can tell them- the first thing to try may be to look at $sin(x)-sin(y)$; can we use some trig identities? What about standard method of differentiating? What about drawing an actual graph, etc etc. Also, talk about related problems.

If you are teaching, try to motivate the students with Historical examples, and again, ask them a lot of questions. Even if the material is old- the students are all new, and so teaching classes in different semesters could very well be very different experience. The better you get at asking "leading questions", the better will be your teaching, and the joy that you get out of it.

Solution 4:

Francis Su's article on teaching is a good read: http://mathyawp.blogspot.co.uk/2013/01/the-lesson-of-grace-in-teaching.html. As people have noted, it's good to loosen up control in the classroom, leave loose threads for students to follow, and go on tangents based on student reactions during class. As Su writes:

I have often started off calculus lectures with 5-minute “math fun facts” that have nothing to do with calculus, just to get students excited about mathematics.

Additionally, think about how you might give open ended questions, to motivate students to create something that you did not expect, so that they are creating value for you, not just the other way around. Su writes:

I have often given fun exam questions: students can earn some easy points just by sharing the most interesting thing learned in the class, or a question they’d like to pursue further. Or “write a poem about a concept in this course.” Or “Imagine you are writing a column for the newspaper ‘great ideas in math’. What would you put in it?”

Of course, you can adapt these kinds of questions to be more rigorous, if you prefer. Su also encourages developing personal relationships with students.

If you find yourself repeating (for example, answering the same problem 10 times), that's a good time to put it in a format so that you wouldn't have to repeat it again--for example, putting it in the lecture notes, or if you're up to it, recording videos and "flipping the classroom."

Teaching is an art and a good way to reinforce this for me is to look up how other people have taught similar material, the explanations and media they use, and think about how I might "remix" them in my own teaching--for instance, I know the stuff on http://betterexplained.com/ but I like looking at it from time to time, because the way he explains things is something I can learn from.

Solution 5:

I don't work in mathematics directly, but in engineering, whenever I'm reviewing something that has a strong theoretical component, I emphasize multiple interpretations of the theory. There's always more than one way to state a core theorem, and more than one way to prove it. Nothing stands on its own--a theorem or property justifies or implies many other things, leads to numerous corollaries. If the immediate topic is getting boring, try leaving a loose thread that leads somewhere more interesting, so that students don't feel like their imaginations are limited (and so that you remember that yours is not either).

Maybe it's not so helpful in calculus alone, but theorems and abstract formulations typically have a plethora of applications. Inner product spaces, for example, are the perfect framework for thousands of concepts in signal processing. I can go on for hours without repeating myself on this topic, and still come back to something that re-illustrates the basics.