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Can anyone recommend online or printed sources on anything related to teaching university level math tutorials (that accompany a lecture course taught by someone more senior, but I'd also be happy about material for the lecturer himself)?

I am looking for general strategies/insights/reflections on anything ranging from exciting students for a subject (presenting extracurricular material can motivate but also intimidate), to effectively presenting proofs (being detailed can reassure but also bore), to pointing out patterns, to structuring homework assignments, to grading assignments, to structuring the classes (solve homework in front of students? hand out solutions/hints? after or before they hand their solutions in?), to repeating old material versus anticipating future material, etc.

Should it matter, I am going to teach mostly students of mathematics (as opposed to business, engineering, medicine,..) from freshman to graduate level and am mostly doing analysis (PDE, functional- and complex analysis, numerics). However, I am not looking for course book recommendations.

I know that I should have made up my mind about these things back when I sat through tutorials myself, and I have -- partly -- but I figure it won't do any harm to double check and profit from other people's actual teaching experience, and I found it quite difficult to find anything substantial on this.

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I am very fond of the book by Steven G. Krantz, How to Teach Mathematics, published by the American Mathematical Society (AMS), now in its 3rd edition.

The book is mostly aimed at professors and lecturers of undergraduate mathematics. However, I think that much the advice would be broadly applicable. There is a section addressed specifically to TA's, but it's only a single page in length.

A review is here on the MAA site.

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    $\begingroup$ After reading through the whole question, I think this really is the best place to start. $\endgroup$ – Jessica B Nov 17 '17 at 6:54
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    $\begingroup$ @TommiBrander: I'd say: Box of tools, starting with a reasonable amount of advance preparation. $\endgroup$ – Daniel R. Collins Nov 17 '17 at 14:37
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    $\begingroup$ @TommiBrander: I added a link to a review of the book. $\endgroup$ – Daniel R. Collins Nov 18 '17 at 15:18
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    $\begingroup$ @DanielR.Collins I've added a bounty to the question, I was wondering if you have any more recommendations? I see that a great deal of the material in Krantz's book deals with professorial things such as making a curriculum, grading, etc. I will be a math tutor over the summer so I am really looking for a book that really concentrates on just the actual teaching of mathematics. $\endgroup$ – Ovi Apr 24 at 17:00
  • $\begingroup$ @Ovi: Unfortunately, I don't. $\endgroup$ – Daniel R. Collins Apr 24 at 21:34
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Talking about the old classics: I like the writings of Paul Halmos a lot. A list of his papers can be found at the history.mcs - Site.

In particular the two papers:

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