# How to teach

There are two kinds of teachers: lecturers (“professors”) and teaching assistants (TAs). (We ignore the cases where this is not the case.)

The difference is mainly that TAs are human. Lecturers, having cleared the hurdles of a Ph.D. and postdoc-dom, are ascended energy beings contained in shells of chalk dust and rigor. This is why they keep to themselves at the front of the class; if they came closer the cracks in their skin would show the blinding fires of power within.

Since a Ph.D. confers perfect understand and unerring teaching ability to all those who have it, the rest of this page is about being a TA.

## Teaching assistant life

(March 25, 2013)

As a TA, I sometimes TA'd for a course whose coursework had no ready solutions. Then the following happened.

Iteration 0: No solution. These problems are impossible. The lecturer is a sadist. These are his research problems.

Iteration 1: Death is the only solution.

Iteration 2: Hey, if we know “A” this problem is easily solved. Hooray!

Iteration 3: Oh, “A” follows from this problem. Dang.

Iteration 4: If we assume “B” is known, this is both easy and elegant!

Iteration 5: If we assume “B”, we're assuming something not known or proven on this course!

Iteration 6: It's one page if I hand-wave the hard part!

Iteration 7: It's three pages and no hand-waving!

Iteration 8: It's three pages, no hand-waving, and assuming 1 < 0 holds!

Iteration 9: Hang on a minute, this is not a problem about “X”. That's why no “X”-literature had a peep of it.

Iteration 10: This is about “Y”! And it's an easy “Y”-problem!

Iteration 11: Three lines, easy peasy— aw crap, that inequality's not strict.

Iteration 12: Three lines, plus eleven special cases, can this really be… (phone rings)

Iteration 13: “Misprint, Mr. Lecturer? The one in Problem 3, right? Right right. What? I meant the inequality— oh, that's a different misprint?”

Iteration 14: It's not an “Y”-problem. It's an “X”-problem, and the zero was clever misdirection for infinity.

Iteration 15: I have— a solution? A skeleton anyway; let's throw some meat on this pony!

Iteration 16: It's an elephant. I can't give this solution to the little ones. First thing, my wrist would break at the blackboard.

Iteration 17: I could use transparencies— Wait, no, I'd better try simplifying this. Get some jumping jacks, elephant solution!

Iteration 18: Right, I don't need the special case where r > 1 and r < -1; silly me.

Iteration 19, the homework meeting: “Mmh, yeah. You can prove it that way too.” (crushes paper, cries a silent tear, moves to the next problem)

Iteration 19 can be averted by having a handout. (“Yeah, I guess you could use the obvious, elegant solution Mr. Poopypants put on the blackboard. If on the other hand you want a solution with pizazz and loxodromic Möbius transformations— well, one out of two ain't too bad— here's a handout— Aw, come on people, don't you have saunas to set fire to or something?”)

## Independence is not good for some people

(March 25, 2012)

So lecturer X, for whose course “Coursename A” I am the teaching assistant, is away on a research retreat at Mt. Wolfdoom. This leaves me to spellcheck, photocopy and supervise the final exam.

I am so fighting the temptation to add one more question to the test.

Possibly this:

Essay. Inner products and me. (6 p.)

Or this:

Let P be the set of polynomials with real coefficients. What is the third element of P? (6 p.)

Or this:

Do you feel this course will prove to be useful in your professional life? (6 p.)

For the person that has not given in to the Darkness Which Is Math, the first question is ludicrous; the second nonsensical; and the third is a standard stupidity from the course evaluation form, made more exciting by the promise/threat of six points hanging in the balance.

— but probably I will resist this temptation, because after the test is over (ha!) I'll scan the produced chickenfeet into pdf, and send them to Mt. Wolfdoom. And then thunder will flash over the mountain, and a voice dead cold and inhuman will utter many bad words.

Then again, if I said this special extra question should be answered on a separate sheet of paper…

Or if I handed out a special sheet which was the answer sheet for that question in itself —

(E1) What is the biggest natural number?

- one
- two
- four
(E2) The exam supervisor is thinking of a function. Write that function here: f(x) = __________

(E3) Your answer to the previous question is…

- Correct.
- Incorrect.
- I don't know.
(E4) Your answer to the previous question is…

- Correct.
- Incorrect.
- I don't know.
(E5) Your answer to the previous question is…

- Correct.
- Incorrect.
- I don't know.

Once you think a while about the chain of those last questions, you may shudder. (“Well, I don't know the function so for E3 “I don't know” if my guess was correct. But what if it was? Then should I choose both “I don't know” and “Correct”, and do I get partial credit from choosing just one? Should I hazard a guess? And if my answer is just partially correct, what do I answer the next one?”)

It's a soluble problem, I think, but it would cause some twitching.

For those lecturers whose Ph.D. has not yet conferred upon them perfect understand and unerring teaching ability, and who have thus scrolled down this page looking for hints and sweating profusely, I give this last section.

## Tips for lecturers

First, don't accept tips. Or donations. Especially ones of food or drink. This is bad form, and also the food may be poisoned.

Practice chalk-throwing in your free time. Aim at hitting a target the size of a human head at approximately the distance from the blackboard to the back of the room.

Chalk-throwing should be used only infrequently to ensure maximum effect. (Also, to minimize the probability of lawsuits by overzealous university chalk-counters.)

Practice drawing the following figures on the blackboard until you can do them perfectly and seemingly without any effort:

- circle
- square
- rectangle
- the co-ordinate axes and any function in the lectures
- crosshairs and a “non-student”

Be sure in advance whether there *is* a blackboard in the lecture hall. Whiteboards are just like blackboards but you should ask the maintenance to make sure there's black chalk in the room.

If you accidentally use a permanent marker on the overhead projector or the blackboard, you can defuse the tension by asking the students to loan you a bottle of alcohol. (Permanent markers are alcohol-soluble. So is shame.)

You can use a laser pointer if you want to. You can also ask the students to be quiet, but this is rarely as effective.

Always check whether you have something on your USB stick you wouldn't want shown on the data projector. (Though I would suggest creating an empty directory called “all the exams and answers”, and then “forgetting” the stick in the class computer. The IT department can provide you with cameras to see who takes the bait. You should “turn” those students and make them work against their fellows through promises of extra credit.)

Your voice is the key ingredient of teaching. If something is important, talk louder and slower. If something isn't that important, talk softer and quicker. (These judgments should be made relative to the course average, not your judgment of the merits of the course compared to some larger class of subjects, as these tend to leave you shouting or muttering all the time.)

Remember, they can ask you questions, but they can't make you answer!