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Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their effectiveness in discussion? I'm asking this because TAs usually play a very different role in teaching than the primary instructor, so a lot of general resources for math teachers/instructors won't apply to them.

  • TAs don't have much control over the content of the discussion section: it just depends on what the students are learning in lecture that week. Also TAs have varying control over what they do in the discussion section: some primary instructors are hands-off while others will make a worksheet or quiz or something for discussion.

  • Typically graduate students are much more interested on their research than learning to teach, so they don't want to spend much time reading about it (so recommending full books to read is not the best idea).

Despite these limitations, there must be something that would be beneficial for a graduate TAs to read and think about to improve their effectiveness as a TA.

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    $\begingroup$ I found it helpful to converse with fellow graduate students, especially older ones with more experience. Identify the ones that seem to care about teaching as much as research and ask for their advice. Most of my friends in my cohort also cared about teaching and we swapped stories, ideas, and tips. $\endgroup$ – Brendan W. Sullivan Feb 19 '18 at 18:03
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    $\begingroup$ (Comment rather than answer as it is not directly responsive.) My frank advice is to concentrate on your research. You are not being paid that much and are a student yourself. The rewards for good research are higher than those for good teaching. Plus, you aren't in charge of the course anyway. So be professional and get the TA stuff done. But just get it off the plate and keep the skull sweat for research. (I don't like the impact on the students, but this is how our system is. You concentrate on you.) $\endgroup$ – guest Feb 19 '18 at 21:04
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    $\begingroup$ @guest: Surely, this attitude will just perpetuate the system itself. Let's leave it to OP to decide how they wish to divvy their priorities and "skull sweat". And if they're like me, they'll realize that they actually enjoy "the TA stuff" a lot more and make a career of teaching. $\endgroup$ – Brendan W. Sullivan Feb 19 '18 at 22:51
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    $\begingroup$ @guest That is a pretty narrow view of what the goal of graduate school is. For many of us, the goal is to teach (at, for example, a four year college or private liberal arts institution with minimal research requirements). Research is important, but it isn't everything. Mike: do you need a problem? $\endgroup$ – Xander Henderson Feb 20 '18 at 0:52
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The MAA has quite a long guide for new TA's, it's a little too much to take in at once but as a supplement it's very good, it's got a section on everything you could hope for:

I agree with Brendan that conversations with other graduate students is the most useful, and I also generally advocate for some kind of weekly meeting for new TA's, preferably with their instructor and older graduate students (and preferably interactive, not just someone talking at them). A lot of graduate student are a bit embarrassed about having to ask for help from the faculty and so will avoid professional development that might make them look incapable in the eyes of the faculty.

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I recommend Stephen Krantz's How to Teach Mathematics. There's a fairly short section aimed at TA's, but if this will be your profession then you'll need everything in there, and the sooner the better.

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One part of teaching students is often speaking to them one-on-one and I have an acronym I use with my tutoring staff to help them focus on actions they can use with students.

Many of the strategies here are also useful for leading group discussions and for lecture-style presentations.

This is our acronym: SQWIGLES

Each letter stands for the following actions:
S: Speak your thinking when you read or write.
Q: Ask questions, especially open-ended questions.
W: Encourage the students to write.
I: Help the students to find information.
G: Guide the students’ problem-solving (as opposed to doing it for them).
L: Listen to the students’ thoughts and feelings.
E: Explain concepts a different way.
S: Help the students to sum up what they have learned.

Here is a link to a blog post I wrote about it with more comprehensive details https://blogs.adelaide.edu.au/maths-learning/2016/09/20/sqwigles/

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Check out the work of Eric Mazur and Carl Wieman, both physicists who are working to reform post-secondary science education. Much of what their work applies to math as well. Both rail against lecturing and both have had tremendous success with more interactive methods of teaching.

Many of their techniques are applicable to TA situations.

Downside: Their methods of instruction do require more prep time for teachers.

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