I am going in for an on campus interview next week. I was told I need to do a 30 minute presentation on a "calculus topic" (the job is for a math tutoring center director at a small liberal arts college). I was told I can use white board space or any other technology. Originally, I thought this meant candidates are supposed to select a section from the standard curriculum and perform a teaching demonstration.

However, when I was given details about the "Talk" I was told to submit a title and abstract. This was slightly confusing to me, as title and abstract usually are more "general audience talks" on a topic people may have not seen, not a teaching demonstration. I sent an email to the search committee asking for clarification on whether this was supposed to be a "general audience talk" or a teaching demonstration (as I would do it in class). I was told the following:

"One of the purposes of the talk is to get an idea of how well the Math Center Director would explain math when working with students, so we would like to see each candidate present a calculus topic. To be consistent with what we have requested of the other candidates for the position, please select one topic from calculus that you would like to present."

I think this means that it is a teaching demonstration for a particular section in the calculus curriculum, but how would you give an abstract in this case (presumably, they would already know about the material).

If anybody could decipher what kind of "talk" this is supposed to be, that would be very helpful. I have sent a couple of lines of communication, but I am still not completely sure what the "talk" is supposed to be.

  • 1
    Why don't you first ask them, rather than us?
    – user151413
    Feb 4, 2022 at 19:33
  • I asked whether this is a "teaching demonstration" of something I would do in class explaining a, or something that "is more general" (similar to what Buffy said, something that develops insight. The quote I gave above was the response I was given. It is still unclear to me which is why I asked here)
    – user132498
    Feb 4, 2022 at 19:44

3 Answers 3


Actually, it seems pretty straightforward. Pick a section (short section = 30 minutes) and develop a lecture. For the abstract mention the section and how you want to approach it. Stress motivation and insight rather than detail in the abstract.

My advice would be to take something that will generate insights into the inner workings of things and focus on that in both the abstract and the talk. One of my own favorite topics is how to use derivative information (first and second, say) to get insight into how rational functions behave.

I'd guess that the idea of having you write up an abstract is twofold. One is simply so that the audience can be prepared if they like, but also to get an idea of your writing competence.

  • 1
    Thanks for the information: Should I do specific examples like I would in an actual class (ex. using the first derivative test to find intervals of increasing/decreasing)?
    – user132498
    Feb 4, 2022 at 15:23
  • Maybe something like that. Note that simple applications like this are easier to do in a short period than theoretical ones (like the definition of the derivative and its meaning). Pick examples that don't lead to a lot of complications.
    – Buffy
    Feb 4, 2022 at 15:26
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    Thanks, in addition should I like to do some "active learning" activities during class (like identifying errors in student work). Do you think that this would be appropriate for this kind of talk?
    – user132498
    Feb 4, 2022 at 15:29
  • It might be hard given the time constraints, but you could mention it in the abstract. It is an opportunity to express more about teaching philosophy than can be demonstrated in a short segment.
    – Buffy
    Feb 4, 2022 at 15:33
  • 1
    Absolutely do examples like in a normal class. I've seen active learning done really well in this kind of talk, but it is a bit more difficult to pull off than a lecture. But in general I think you're overthinking this, it's not supposed to be substantially different from a normal class that you'd teach. Feb 4, 2022 at 23:30

I think you’ve understood correctly what kind of talk they’re expecting: a sample 30 minute class excerpt from a calculus class. I agree that it’s slightly weird to give a title/abstract for that, but the point is they need to advertise your talk and put it on their calendar and that requires some kind of title and abstract. You might try looking at their seminars webpage to see whether you can find how this was dealt with in the past. But I would just title pick a title that describes which section you’re covering (e.g. “maxima, minima, and critical points”) and write a short abstract (e.g. “This is a sample calculus lecture on maxima, minima, and critical points. We will discuss local and global minima and maxima and Fermat’s theorem explaining how they’re related to critical points.”).


The point of an abstract is to convey concisely what you will talk about, and not to tell the reader something new. So write your abstract accordingly.

  • My question is not necessarily about the abstract, it is more of the type of talk. Is it supposed to be a "teaching demonstration" of how I would explain a topic in calculus to a student or is it more of a "general audience" talk about something that is calculus related. When I think of "abstract" and "title" I usually think of the latter, but it seems like they would like to see more of a teaching demonstration (which I find it weird they would want a title/abstract).
    – user132498
    Feb 4, 2022 at 19:56
  • I don't think it's all to weird to give an abstract for a teaching demonstration. I mean - why not? You'd also give an abstract when you give tutorials.
    – user151413
    Feb 4, 2022 at 20:05

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