Working as a teaching assistant for college mathematics or general mathematically inclined courses turns out to be not as trivial a task as I’ve thought it to be. This semester I’m TAing for Advanced Optimization –– an obligatory course for sophomore students. I’ve also took last year. Moreover, I took an even more advanced version of it (convex optimization) while I was visiting Stanford last summer. Still, teaching and tutoring turns out not to be something that comes out of thin air. I thought I can just do the assignments and gradings within minutes, give the recitation session without any efforts or too much investment in preparing––turns out the truth is quite the opposite.
A Handbook for Mathematics Teaching Assistants established an excellent framework to structuralize our reasoning about what is important in being a good TA.
Types of TA Assignments: Recitation, Lecture, Grading
Most teaching assignments for graduate students fall into one of three categories:
recitation instructor:
a faculty member lectures to a large class of students two or three times a week on an assigned topic from a textbook, after which a graduate student answers questions about the lecture and discusses assigned homework problems.
lecture:
It’s more demanding, almost like an upgrade of the previous task. Schools vary as to when in a graduate student’s career this is to be done; at some institutions you are handed an algebra and trigonometry text and told, “Go teach this. Don’t mess up!” Other schools wait for a year or two until you have had some less demanding assignments before they ask you to plan lessons, make up your own exams, determine grading policy, and generally deal with the problems of teaching undermotivated freshmen (or worse, undermotivated seniors!) the joys of precalculus.
grading:
Many TAs describe such assignments as “easy” or “boring.” While the assignments can be either or both, grading jobs, however, can teach you how far you have come since the days when this coursematerial was a real effort. These assignments can also show you how hard it is to teach others to write clear, concise answers and proofs.
A third benefit to a grading job is that you can use it to review the material that may be asked on a graduate comprehensive examination.
recitation
Explain those chapter exercises from the textbook seems not much of a big deal––since most of the problems even have solution manuals. However
A shocking number of TAs and instructors try to “wing it” often with unpleasant consequences for themselves, their students, and for their end of term evaluations. So I will say this again, with emphasis:
A recitation instructor will show up on time prepared to discuss past and current homework problems.
This means that you will read through all the problems the night before recitation, you will perform the required computations (Yes, the chain rule is dull, and you have used it so often before, but, just when you don’t prepare a set of problems because they’re too easy, that’s when you’ll get stuck in front of your class on the day before the exam.), and you will get “the answer in the back of the book,” because that’s the one the students prize so highly.
Why do you want to prepare meticulously when you know this stuff so well? Because:
People never learn course material as well as when they have to explain it to others. Even though you took and passed this course some years ago, that doesn’t mean you can’t learn from a refresher. After all, it was six years ago in high school that you took AP calculus, right? Textbook authors love to put little tricks into the exercises to keep students on their toes; these tricks can trip up unsuspecting instructors, too. You are getting paid to do these exercises. Even a TA who has done this course three times already needs to recall where the pitfalls are placed.
grading issues
Ever since being a TA do I finally realized scoring rule design––recall Jason Hartline’s research papers that used TA as a motivating example. TA needs to exert effort (cost) so as to grade with high accuracy (utility maximizers), but professors and students somehow always wants accuracy (value maximizers). Therefore, on one side there’s the tricky design problem that aligns the incentive of the principle (professor) and the agent (TA), one the other side, being a TA means that one should be responsible and say no to the lure of grading everyone a 100 out of nowhere.
A common, but not universal, technique for grading homework is to assign each problem a fixed number of points. Some graders use a two-point system, “0” for a wrong answer, “1” for OK but not complete, “2” for fully correct. After using this methodology once or twice, most graders find that it doesn’t have enough points to properly distinguish among the variety of possible errors that a group of students can make. Students also tend to sense the same problem. Their complaint about the grading is usually to say something like, “I only got one number wrong, and all I got was a 1”.
A zero to five scale is probably better:
“0”– didn’t even try the problem,
“1”– tried, but not even close,
“2” and “3”– various levels of somewhat valid but mistaken attempts,
“4”– correct answer but with some minor errors,
“5”– the correct answer with details spelled out.
Uniformity with fairness and speed are keys to grading exams. Doing the job though, is almost like an online learning process:
As you grade the first few papers, occasionally review your scheme to see if it still seems to fit what the students actually knew and did. This review will also help avoid grade inflation or deflation that seems so inevitable over ten hours of work (“This is the same mistake that I’ve seen a hundred times now well, this time you get a zero!”)
Uniformity and fairness are related to one another. You may be a harder grader than your officemate, but if you can defend your methodology to other TAs and students, they will “generally” accept it. (Note that last generally. Some may not; see the section on being a good colleague.)
Most TAs see the “speed” part of “grading with speed” as only being of benefit to themselves–“I want to get this pile of papers done and out of here!” But speed with accuracy also benefits students, because they get to have their problems back while they still remember what the questions were.