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When I have TAed calculus courses and led discussions, while I did not find myself grossly inept at interacting with students, there was a bit to be desired with making discussion interactive. I am probably average or below average with interpersonal skills. My evaluations always came back with the lowest scores on engaging with the class--asking and answering questions. I have never had my students work in groups either. It takes a bit of social courage to involve the students. What are strategies for getting students actively involved in discussion?

EDIT: With respect to some of the answers and comments, things that are not an issue include mastery of the material, preparation, good diction and clarity of words, and otherwise lecturing forms of communication. One-on-one tutoring or office hours with small groups I carry out successfully, though I am not too personal and mostly I just respond to questions with explanations or do certain problems they are interested in.

I have the impression that engagement is much better than simply lecturing. I am asking for an explanation of how engagement improves the quality of learning calculus and the specific steps and tasks I can take that I can learn as a skill, not as something that comes naturally.

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I'm not sure whether this question should be solved. It might need rephrasing (personally I think not, but I may be mistaken), but while I don't have similar problems (probably thanks to some inborn/early acquired capabilities), I'd love to hear a competent response. –  mbork May 15 at 6:33
I find your question extremely interesting but it would be great if you could make it (by editing) more focused. What you ask has many aspects and it would be much better to address a more specific problem. –  András Bátkai May 15 at 6:39
I don't really understand why we would close this question for being too broad. The TA is asking for strategies on how to connect and engage with his students. We should welcome beginning questions like this! –  Chris Cunningham May 15 at 11:53
@BenjaminDickman, to me, I have an impression of there being elitism on this site where those who don't have PhDs in education are discouraged from both asking and answering questions. I get the value of specific questions and well researched answers, but many people without education degrees participate in math education with all that it entails. My experience is that many grad students never get teaching training and it is better for answers to a question like this one get answered than not. –  nayrb May 15 at 22:32
@nayrb I have the opposite impression: I think there are very few people with doctoral degrees in (mathematics) education who are using this site, and that most of the questions are posed so generally that the answerer needs to introduce many of his/her own constraints in order to make things tractable. Though you asked here specifically about Calculus, the broad nature of your question seems to have elicited only general education answers thus far (one on biology, one on improv classes; none with references to how to do this for Calculus). –  Benjamin Dickman May 16 at 0:35

4 Answers 4

I've taught about 100 biology discussions and get good interaction evaluations; you can decide if this advice applies to you and calculus.

I am making some assumptions about your teaching environment:

  • You have 10 - 30 students in the room
  • Students had lecture elsewhere, so you don't need to lecture
  • Nobody is telling you what you have to do in discussion (e.g., cover homework problems)

If these are true, then your main job is to provide an environment for students to learn calculus. This is best done by students practicing problem-solving while you are available to help them over sticky points. Here are some simple mechanisms that you can use to hugely increase your "engaging with the class" scores:

  1. Learn their names. I do this by bringing my camera on the first day, and passing out index cards, and having them write their first name on the card, and then they hold the card under their chin while I take the picture. I can sort these by discussion, and either print thumbnails or just flip through them on my phone or in Picasa. I can learn most of the names of a class of 100 in the first two weeks. Plus, students LOVE that you learn their names. They think the photo thing is kind of silly, but they LOVE that you know their name. The cool thing is they think you know the names of everyone, even if you only really know 60%.
  2. Pick 3-5 good problems (from book or homework or whatever), and have a worksheet for them to download the night before, print, and bring to class. These should be as much like exam problems as possible.
  3. Put students in groups of three, and actually make them turn chairs and face each other. Tell them to start Problem #1, and you'll come around and help. Students can just work with people near them, but I'll sometimes randomize the groups with playing cards so they don't sit with friends.
  4. Walk around the room, and be friendly. Ask questions that encourage the group to try to answer you. Ask, "What did you try first? How did that work? What part got you stuck?" If you find that a lot of students are stuck on the same principle, go up to the board and say, "hey everyone, let me help with this little part here" and talk for 5 min. Then shut up, and let them work.
  5. Don't get trapped by one group. Encourage them to ask a neighboring group, and keep moving.
  6. Stop every 15 min or so, and ask them, "what answer does your group have for #X?" This puts less pressure on the individual. You can have a random-order class list so you call on everyone equally. But give them time to work first, so they can answer.
  7. If you are talking less than 20% of the time and students are on-topic talking for more than 50%, that is a good, engaging discussion.
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I'm not a natural extrovert, but I've found that this is less about social skills than about establishing clear expectations. For example, if I put up a question on the projector that says "Discussion question: ..." and tell the class we're going to discuss it, there's no real uncertainty about what is expected. On the other hand, when I observe other teachers teaching, sometimes I see things like the teacher asking a question, pausing for about 500 milliseconds, and then answering his own question. This sends the opposite message: the expectation is that the students will not participate. If your expectations aren't clear, then students will revert to the default, which is to sit passively.

Another important point when seeking active student participation is that the most common mistake for me has always been to give them tasks that were too hard. Tasks that seem trivial to me are not trivial for them, because the subject is new to them. You can always start with an easy task and then follow up with a harder one.

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It seems to me that there are two things that I would want in a teacher who is looking to improve their interpersonal skills: (1) ability to master the subject (2) ability to lead a flowing discussion. The first is not the question that I think you're really referring to, so I'll talk about the latter.

I have had the discussion with a few teachers about the idea that teaching is a form of stage acting. There are many similarities between teaching and being on stage. An excerpt taken from a colleague:

Students are known to tout their favorite teachers as "funny.” Taking improv classes would presumably loosen me up a little at the board and make me more confident about my stage presence, thereby helping to facilitate the occasional joke or witty aside that could make for moments of shared humor between me and the class. Now, some years and many improv classes later, I have come to recognize that the art of improvising and the art of teaching share fundamental themes. In fact, I believe that they can be seen as crafts that share some fundamental rules.

To keep a class (or audience) engaged, you want to be able to present the material (plot) in a way that keeps them involved. If you're a TA at a college, many colleges have Improv acting classes or groups that perform. You may want to see what's available at your school or in town to help you become better at keeping your students engaged.

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While I do believe much of this is natural talent, there is lots you can learn, by looking at how more experienced colleagues do it, asking around ( e. g. here :-) , ...

Much of the problem might be just nervousness/anxiety. Work on that: Get very familiar with the subject matter, see if you can (also) work in situations that are less threatening to you (tutoring one-on-one, work with small groups).

Have a few problems prepared, from easy to somewhat hard, ask the class to solve them, after doing an example. Step aside! Let them do most of the work. Ask for volunteers to write down the evolving solution.

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