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In most universities that I am aware of, graduate courses in Mathematics are taught almost exclusively by research mathematicians. My question has two parts:

What is the justification for this practice?

Has research been done showing any correlation between research ability and students' learning in graduate courses?

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    $\begingroup$ Probably it is because programs with graduate schools need researchers to advise graduate students, and it is not practical to hire one set of faculty for teaching phd students, and another set for advising them. $\endgroup$
    – Steven Gubkin
    Apr 10, 2014 at 13:01
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    $\begingroup$ I don't know of any such research. Nevertheless, there surely is a connection between research ability and (deep) understanding, moreover, teaching does require understanding (the deeper the better). My guess is that understanding and knowledge play a major role here. On the other hand, if we would correct for this factor, I would guess that the correlation between teaching and research abilities, is actually negative (if exists at all). $\endgroup$
    – dtldarek
    Apr 10, 2014 at 13:28
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    $\begingroup$ I'm not aware of any research to this end either. Out of curiosity: How are you conceiving of "research ability" and "student learning"? E.g., I could imagine measuring the former with citations (this would be closer to research output than ability, but perhaps a safe enough approximation). I'm not so sure how you'd want to measure graduate student learning in this case, though. If you just mean students who go on to academia, then maybe you could look at how many attain tenure track positions, or their own citations in a longitudinal study. Or maybe you are thinking qualitatively... $\endgroup$
    – Benjamin Dickman
    Apr 10, 2014 at 13:34
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    $\begingroup$ I am not a maths educator but I find this question interesting and relevant to university teaching generally. It's always been my assumption that professors were assigned to teach undergraduates because only people actively researching in the field were likely to have enough cross-discipline, cutting edge knowledge to teach at the required level. In other words, it's a matter of necessity and has nothing to do with skill at teaching. $\endgroup$
    – Bob Tway
    Apr 10, 2014 at 16:17

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Researchers have philosophized about and demonstrated that there is a specific kind of knowledge that teachers need that is likely different from just knowing the content itself.

So, there is data that demonstrates that knowledge of content alone is not what good teachers need. Rather, they need knowledge of things like how students make sense of the content, how to design tasks that align with knowledge of how students think and move their thinking forward, how to create representations that help students see mathematical relationships, that sort of thing. This knowledge aligns with what John Dewey called "psychologizing the curriculum," to connect the logic of the discipline with how the learner thinks and experiences the world.

I think that the common assumption is that subject matter knowledge is enough to be an effective teacher -- experts in the discipline could explain what they know and then students will learn it. A faulty aspect of this assumption is the idea that teaching is more than transmitting knowledge. Teaching involves translating knowledge in ways that make sense to the student and giving students an experience to make sense of the knowledge.

So, I don't know of research that correlates between knowledge of the discipline and ability to teach. I just knew of research that shows that it's more than knowledge of the discipline that matters, but instead an additional, more specialized knowledge for teaching that matters.

(I recognize that the research I am sharing is about teaching at the K-12 level, but I think the general principle -- that knowledge needed to teach well is more than content knowledge located in the discipline -- carries over and transfers into the university level.)

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Graduate school is about research, what the students are supposed to learn is how to do it on their own (and in uncharted areas, to booth). The only people who have shown they know about research, and know where uncharted areas are, are active researchers. Most presumably suck baby elephants through straws as teachers, but it's all you have got...

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    $\begingroup$ The question also asked about research to support this. Do you know of any research supporting your claims? That would be great. $\endgroup$
    – András Bátkai
    Apr 10, 2014 at 19:17
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    $\begingroup$ It is taken as a given that to teach <subject>, you have to have intimate, working knowledge of <subject>. In this case, the only group with this prerequisite are researchers. Finding the research you ask for is quite unlikely; and if found, most probably on very shaky statistical feet due to scarcity of comparative data due to the above. $\endgroup$
    – vonbrand
    Apr 10, 2014 at 19:32

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