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A search in Google returns lots of studies and thinkings about teaching in undergraduate schools. Could anybody come up with any research/references about teaching in graduate schools (graduate courses taught by professors)? (When I search "teaching in graduate schools" in Google, what returns is mostly about teaching in undergraduate school by graduate students, which is not the topic I'm talking about.

A related book I have found so far is The Graduate School Mess: What Caused It and How We Can Fix It. But it is not directly about graduate education in mathematics.)

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    $\begingroup$ I think omitting the first paragraph altogether would make a better question. To me this starts out as a complaint that is not backed up by anything except personal opinion and ends in some question that could be interesting. $\endgroup$
    – Dirk
    Feb 29, 2016 at 19:21
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    $\begingroup$ @Dirk: Indeed. I edited the question. Thank you for your comment. $\endgroup$
    – user5897
    Feb 29, 2016 at 19:46
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    $\begingroup$ Reads much better for me. $\endgroup$
    – Dirk
    Feb 29, 2016 at 19:54

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As far as I remember Krantz's book How to Teach Mathematics is not restricted to undergraduate courses and contains a lot of great advice. His book A Mathematician Comes of Age is not focused on teaching but on "mathematical maturity" and how to develop it. Consequently, it contains many thoughts about teaching and mentoring on the graduate level.

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    $\begingroup$ I'm running a reading group for Krantz's How to Teach Mathematics right now, and it's mostly about lower-level courses like calculus. (Preface to 1st Ed.: "My examples are drawn from the teaching of courses ranging from calculus to real analysis and beyond... Graduate courses are dessert. You figure out how you want to teach your graduate courses.") Basic teaching hygiene should of course be the same, but if one was looking for advice specific to teaching graduate courses it's not in there. $\endgroup$
    – Daniel R. Collins
    Oct 3, 2016 at 23:21
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You might want to look at the book One Field, Many Paths: U. S. Doctoral Programs in Mathematics Education (Reys & Kilpatrick, eds.). (See http://www.ams.org/books/cbmath/009/). I don't have access to the book right now, but the table of contents suggests that it may contain relevant research on your question.

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  • $\begingroup$ Relatedly: See MESE 2079 for the AMS Notices' "Doctoral programs in mathematics education in the United States: 2007 status report" (Reys et al, 2007). $\endgroup$
    – Benjamin Dickman
    Feb 29, 2016 at 17:14
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Another source:

Friedberg, Solomon. "Teaching mathematics graduate students how to teach." Notices of the AMS 52.8 (2005). (PDF download.)

This article cites (and quotes from) an earlier book (which I have not examined) by the same author:

Friedberg, Solomon. Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom. Vol. 10. American Mathematical Soc., 2001.

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  • $\begingroup$ Thank you for your reference. I think that is mainly about undergraduate courses taught by graduate students. $\endgroup$
    – user5897
    Oct 4, 2016 at 23:50

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