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My mathematics department (where I am employed as faculty) is considering requiring its Ph.D. students to take a two-semester course in pedagogy and educational theory. All of them also TA lower level math classes, so the proposal has some merit. I am trying to decide whether to support or oppose this proposal (or suggest modifications to it).

Although I am skeptical, I want to be open-minded. In departments that have adopted such requirements, what have been the positive and negative outcomes? Have students enjoyed such courses, and/or felt that they were useful? And has the quality of TA education been improved?

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    My 2 cents: As a student of a large research institution I am taught by a number of different PhDs. Unfortunately, many of these professors are much better researchers than they are educators. The university hires them for their research and the money they bring in, but they still have to teach some courses. By requiring pedagogy courses of PhD students, not only will your TAs improve, but they will also be able to effectively teach higher level courses if they do end up employed by an educational institution. – Ramrod Jan 28 '15 at 21:24
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    I agree with @Ramrod, though the two-semester requirement may be a bit much. One semester on effective teaching techniques, without getting too much into theory, would have been amazing for the math department I served. A second semester might have caused a student revolt, though. – Ken Jan 28 '15 at 21:47
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    I've always found it odd that this isn't more widespread. It would certainly improve grad teaching, which is often bad, and the time investment wouldn't be that big (though maybe one semester would do it). Presumably it would also help grads be competitive for teaching-oriented jobs on the other end, which could be a big plus depending on the dept's typical placements. Anyway, I look forward to reading about potential downsides! – Mark Jan 28 '15 at 21:49
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    @Mark I think there is very little downside if said courses are well-done. However, this has generally not been my experience with pretty much all pedagogy-related courses offered in my old university. For those, "waste of time" would be putting it mildly. – xLeitix Jan 28 '15 at 22:02
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    You might also want to consider the effect that this will have on your students when they go to look for jobs- many hiring committees would consider this to be a positive aspect of an application. – Brian Borchers Jan 28 '15 at 22:12
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The main negative outcomes would probably be the opportunity cost - what else the PhD students could have been spending their time on - and the risk of developing a bias against such courses and the material contained therein if they are poorly designed or executed.

On the other hand, without critical reflection and exposure to alternatives, we tend to teach in the way we were taught, which may or may not be the most effective approach. Moreover, we may be unaware of common misconceptions and difficulties with our material, having either overcome these hurdles long ago or having sidestepped them. A good course can help with this, especially if it has a subject-specific component as opposed to being completely general.

Since you refer to a mathematics department, you might be specifically interested in Alcock & Simpson's Ideas from Mathematics Education: An Introduction for Mathematicians.

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