By Tom Wright
This entry is a list (with explanations) of the five most important things I have learned in my years as a teaching assistant (i.e. leading a recitation section for a professor). Individual results may vary…
1.) Make sure you know how to do ALL the problems when you go into class. You don’t have to have them all written up nicely, but the one at the end of the chapter where you say, “Eh, I’ll figure it out in class,” is invariably the one that someone will ask and you can’t answer.
2.) You may mess up in class. If you do, admit your mistake and make sure students understand that you messed up; otherwise, they will be trying to figure out why A implies B without understanding that A was written incorrectly. If you realize your mistake is significant enough that you can’t finish the problem, say something like, “I’ll let you do the rest as a homework, but here’s how you start,” and then do whatever you can. On a related note:
2a.) I generally allow myself one absolutely major screw-up per section per semester. That way, you’re prepared, but if you do screw up, you can write it off as your mulligan. Any more than that, though, and you’re wasting the students’ time.
3.) Students will come to you with complaints on how hard their homework/tests are graded or how unfair the curve is. Refer them to the professor. He or she will be more than happy to take responsibility for his class being “tough”. On the other hand, don’t let a venting session break out in class; it’s not productive, and it only serves to demean the professor.
4.) Actually write stuff on the board – don’t just say it. Students will zone out in a 50 minute class, often to think about what you just said; they shouldn’t be penalized for this. When you do write, start at the top left, go down the board, go to the top of the next board, go down the board, repeat until you run out of boards, then erase the first board entirely and start again. Simple, but it makes boardwork much clearer, and you’d be surprised how many professors just write in the largest open space on the board instead of erasing. Just remember: how you write it on the board is how it will appear in everyone’s notes.
5.) Most importantly, relax. You won’t be the best TA in the world in your first semester of teaching. Teaching is an acquired skill. On the other hand, you won’t irreparably harm the students for the rest of their careers, either. Just do your best.
Thank you for the post, it is very educating.
I would add 6.) to that list:
6.) Read your teaching evaluations carefully, even few times. If you think that you they don’t give you enough information, prepare your own questions. You can include some neutral questions, like “Does the teacher come to class on time”, “Did you attend office hours this semester” or “Does the syllabus contain information about teacher’s office hours, e-mail address, etc.”. Those answers will give you an idea what kind of student filled out the evaluation. You don’t have to wait until the end of the semester, sometimes midterm is a good time to check how the students find themselves in the class.
I would like to add something to #2. When you realize you make a mistake, you can often turn it into a “teachable moment” by challenging the students to find your mistake. See if they can figure out how you realized you made a mistake.
Error detection and correction is an important problem-solving skill, so take advantage of any mistake you make to help the students practice this skill and see how an “expert” (that would be you) practices it.
An interesting advice on teaching differential equations from Gian-Carlo Rota can be found here.
I learned some other useful tips too:
0) Fill in the blank with a non-mathematical skill at which you excel, and then try to answer the question: How did you learn to become an expert _______________? Keep this answer in mind when teaching.
1) Wait a LONG time after you ask a question, and don’t ask rhetorical questions very often.
If you answer you own question once, the students will assume that you will always do that eventually, and you’ll be hard-pressed to engage them.
2) Learn to ask questions that don’t boil down to “Are you sure you wanna do that?”
In other words, try to express as little emotion/tone in your voice as possible when asking a question so that it is truly open-ended. Otherwise, just don’t ask. Make a statement instead.
3) Create an environment where the students are not petrified of making a mistake. You can do this by making the class more about them and less about you. Try challenging the students right away by having them come to the board during class to present their work. Ask other students if the presenter’s work “makes sense”. This is especially good in a recitation where the whole point (I think) is for students to discuss the work, learn to collaborate with (and not just copy off of) one another, and feel free to ask questions.
4) Go watch another grad student or post-doc teach. Take notes while watching, and write up what you think “worked” and what didn’t. See if they will do the same for you. You don’t necessarily have to share your thoughts to benefit from doing this.
TW: I agree with all of these but I thought I should emphasize #1. The key, of course, with #1 is to have the patience to wait the students out; even waiting 40 seconds can feel like an eternity. In situations like this, taking a drink of water, coffee, or soda is a great idea because it removes the temptation to blurt out the answer.
May i put couple of more.
6.) Improve yourself always. Do not think your have completed all the stages. You will have many things to learn from the experienced teachers
7.) Get some feedbacks from the students like askin some tricki questions. those will give you an idea if you are teaching them well or not
I dont think there is a good or bad way to teach mathematics or any course per se… My own experience is reflected in my teaching statement which is available on my website……I think every teacher has his or her own style….. There are no “good” or “bad” teachers…
“Most importantly, relax. You won’t be the best TA in the world in your first semester of teaching. Teaching is an acquired skill. On the other hand, you won’t irreparably harm the students for the rest of their careers, either. Just do your best.”
This is the most diffucult to be after all these effort.
very useful advice on becoming ta, I myself will be a TA in health science next quarter and take this advice. Thanks
If I may offer some opinions as a lowly undergrad:
1. Please don’t apologize! The third-semester calculus students really just want you to do the hard homework problems so they can see where they messed up. They will be glad that you exist (because in certain departments, TAs disappear altogether after Calc III, and no one wants to go to the professor to ask some trivial question on the Linear Algebra homework]. If someone thinks you’ve missed a minus sign, look at the problem (don’t assume you’re wrong!): if you really did mess up, acknowledge it clearly and thank the student for his or her correction, but avoid profuse apology.
2. Erase up and down.
3. Especially if you are small-bodied, stand with good posture and perform “to the box,” particularly if you are in a large lecture hall. Talk to the kids in the back of the room, and make sure your head and chest project in that direction (your voice will follow).
Walk to the front of the room with authority so it’s clear that you’re leading the class/section–I don’t know how many TAs I’ve mistaken for students who’d suddenly decided to put their backpack on the podium. [This might be acceptable if the TA really is just a sophomore, but come on, you’re a grad student! You’re paid $18,000 to TA while the undergrads get about $800. Think of the power…]
4. Try to know the room! I was once in a lecture hall with 3 x 3 blackboards, the type that can be prodded up with a stick and pulled back down with a string so that the lecturer can write on nine boards before he has to erase. The TA, sadly, didn’t realize that there were strings to pull down the boards, and restricted herself to writing on only the bottom two rows of blackboards. She was also really nervous about pushing the boards up because she feared that she wouldn’t be able to pull the back down. And I agree strongly with #4 in the original post: boardwork is important.
5. Write big, speak loudly, don’t mess up. Use the sidewalk chalk if it’s there. And if a problem really is beautiful, don’t be afraid to say so: the students will agree/empathize with your passion but wish it weren’t so hard/be inspired/maybe disagree and talk to you after class.
Of course, most of this applies better if you’re TAing something relatively low-level. But then again, higher-level courses don’t really have TAs (beyond those who grade homeworks), do they?