by Derek Smith
I participated in a departmental training session for first-time teaching assistants during my first week at UCSB. It showed me that I need improvement in some areas, despite many hours of tutoring and giving presentations. In particular, I’m not very good at writing on the chalkboard, so I took some notes. I’d also like to make a few generic observations and share interesting links I found.
I tutored extensively as an undergraduate, however, mostly in one-on-one sessions. I spent some time writing on the blackboard but this was during review sessions with classmates. Because we took many classes together, we had roughly the same mathematics vocabulary. I joined the military out of college and worked as an Air Force weather officer. Although meteorology has a lot of interesting examples of technical communication, weather briefings were highly scripted. Later as a software developer I gained a lot of experience giving presentations, but again the situation was different from running a recitation section. I spent weeks thinking hard about or solving a handful technical problems. If I could convey the ideas clearly to my supervisor, then there was a good chance the customer would understand as well.
Unfortunately, none of these experiences capture all elements of the TA position. First, you will most likely begin your TA career in a large recitation section. The students will have varied backgrounds and levels of motivation. Most of them will have a relatively small mathematical vocabulary and low confidence employing it. Questions will be all over the map. Next, the TA position comes with some level of authority; you may have to grade tests or give quizzes. Finally, a lot of time is spent in front of a blackboard.
Each of the above points could fill a whole post. What I had trouble finding elsewhere (and hadn’t given much thought prior to this past week) are tips for writing on the blackboard. You can find basic thing like: making sure the board is clean and visible, circling answers, etc. But I also wrote down two simple rules, which if you break will very quickly decrease legibility.
1. Face the board while writing, face the audience while talking. If you attempt to write when your shoulders aren’t parallel to the board, or when your head is turned, then you are inviting problems. Don’t be afraid to talk to the board every once in a while.
2. While writing, keep the chalk close to the shoulder of the arm with which you write. For instance, don’t stand still when writing a long sentence… your hand will trace out an arc. Instead, move your body as you write. Also, don’t attempt to write below your waistline. Your elbow and wrist simply do not have enough degrees of freedom to maintain neatness. If you must write lower, practice some comfortable crouching position. Bending at the knees seems to work for me. Moving blackboards are an ideal setup!
If you have any other similar rules (or disagree with these) please share in the comments! Now I’d like to move into the “link section” of the post. I found additional helpful hints for teaching assistants in the following two AMS blog posts:
- Five Pieces of Advice for the Beginning Teaching Assistant
- What Do These Students Want?!: Some Teaching Tips from the Other Side
Here are some tips I found from other resources:
- Improving Presentation Style
- Chalkboard Skills: How Effective Are You?
- A Handbook for Mathematics Teaching Assistants
In TA training we have to observe experienced TAs in person. But you can get a similar effect in the comfort of your own home! Many universities these days are posting video taped lectures on the internet. I wandered over to the MIT OCW with the intention of watching a lecture for a basic calculus class. Even better, I found this excellent course by Dr. Sanjoy Mahajan:
If you only have twenty or so minutes, I suggest watching lecture #8 “Teaching With Blackboards and Slides”. Around 12:30 he begins blackboard discussion. At 42:30 he moves to discussion of slides. At 1:06:00 is a really neat graphical exposition of Stirling’s approximation of ln n! which I have never seen before.
In lecture #6, Dr. Mahajan discusses three techniques for making discussions more like tutorial. The first is very simple: pause after asking a question. It’s awkward at first, but you get used to it. Another technique is polling the audience. At UCSB professors can use iclickers for this, but it can be easily duplicated on the blackboard. The most time consuming technique is the open-ended question or demonstration. It takes preparation on your part as well as motivation on the receiving end.
I’ll relay one more idea I gleaned from watching Dr. Mahajan’s lectures. Don’t save evaluations for the end of the term. Have students fill out anonymous 3×5 cards with three questions. 1) What was the most confusing or useless part of the discussion? 2) What was the most useful example or demonstration. 3) Any other comments. Tell the students that they may hand them in at the end of any lecture or discussion. You’ll note that Dr. Mahajan opens each of his lectures by answering common questions he received the previous session. This technique seems very effective, and I hope to try it out soon.