Reflections on Teaching

I was recently asked to be part of an advice panel for newly minted teaching assistants. Oh, how time flies! After assisting with numerous classes and teaching vector calculus twice, I’d like to think I have some advice to offer. Since I took the time to put my thoughts onto paper, I may as well share them with the blog. (Consider this a “reply to public”, one of Matt Might’s tips for low cost academic blogging.)

1. Go watch Prof. Mahajan’s teaching course. Take notes. Seriously. I cannot stress enough the excellence of the advice he dispenses. I have returned to these videos many times in the past four years.

2. Be flexible. It’s easiest to manage a course or recitation when you maintain a mental model of the student’s learning. Prof. Mahajan discusses many techniques for building such a model which I have summarized in a previous post.

I almost derailed my vector calculus class in its first week. I assumed that because the students completed linear algebra, they would be comfortable reasoning about lines and planes in three dimensions. After receiving feedback from the students, I quickly realized that one of the goals of a vector calculus class is to develop spatial intuition. I corrected the mistake by devoting an extra lecture to the basic material, which brings me to my next point.

3. Less is more. If you are lecturing, you will cover one page of handwritten notes per ten minutes of class. Often less. Find your ratio and treat it as law.

4. Be clear and direct; doubly so when discussing course policies. Each character you write or figure you draw will be copied into 129 notebooks. Every quiz or exam will be read by 129 people. Your syllabus will be interpreted 129 different times. The exercises will be discussed in dozens of small study groups.A not insignificant fraction of students will attempt to bend a rule or ask for a more favorable interpretation of a grading policy. If you’re unsure how to respond, then don’t. Ask them to submit their case via email and sleep on it.

5. Work on your shtick. It sounds silly, but a gimmick can help break down the communication barriers which develop after twelve years of schooling. Some of the social norms students pick up are downright toxic to learning!

I learned about the importance of your shtick by observing a UCSB professor known for his elaborately choreographed, 850-student calculus lectures. But it didn’t really hit home until I went through my teaching evaluations with a fine tooth comb. My first time as an instructor, 88 students completed an evaluation. Eleven of them mentioned my beard or included a little picture of me, accentuating my beard. Ten of them talked about my effort to learn names. There were only a handful of comments with a greater “hit rate”.

I thought I was bad at learning names until I forced myself to try. Every time a student asks a question I either ask them their name or, if I think I know it, address them by name. The remainder of my system is based on two principles. First, I have a pretty good spatial memory. Second, students tend to sit in the same location every day. Give it a try!

6. When you begin lecturing, you will have to choose a side: slides versus chalk. I’ve written before about some of the issues with slides. For the record, out of those 88 evaluations, seven liked my use of the chalkboard and four suggested I use slides.

7. Spend a little bit of time reading research in mathematical education. At a minimum, this will give you a language to describe your existing habits in the classroom. This is the first step in improving or changing those behaviors.

8. Keep a journal. I’ve written before about my love of journaling; I view it as an integral part of the scientific method. Here’s a more literary take on keeping a diary. At a minimum, this record of your thoughts and experiments will provide great material for the teaching statement you will eventually have to write.

9. Be knowledgeable about your department. Know answers to common administrative questions and know where to direct students when you don’t know an answer. Inform students of the resources available to them. New students, especially, need to be reminded about office hours, drop-in tutoring opportunities and review sessions.

10. Use teaching to practice your public speaking. As a former software developer, I can tell you that this is an integral part of a professional career both in and outside of academia.

11. Go watch Prof. Mahajan’s videos. Seriously.

About Derek Smith

Former weather dude and scientific software developer. In the upcoming 2015-16 year I will complete my PhD at UCSB in nonlinear dispersive equations. I enjoy spending time with my two young daughters and running.
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