I'm going to be a teaching assistant and I'm currently looking for books/reviewed articles/journals written by mathematicians or people who taught mathematics (at a university level) about pedagogy and/or their experience of teaching mathematics. I know that these readings can't replace the experience of teaching but I think sharing experiences can't be bad for my future students. To be more precise about what I'm looking for, I consider the following questions very interesting :
- What mathematical concepts are difficult for most students and why ?
- What are the basic errors of a new teacher ?
- What is a good course in mathematics ? What is a good exercise session ?
I know that there are plenty of different answers of this question and I'm looking for different opinions to build mine.
Thank you
PS : References in French or English only.
Check out http://tll.mit.edu/help/torch-or-firehose-guide-section-teaching-2nd-edition. Granted, this was written as a guide to teaching MIT students some number of decades ago. But Arthur Mattuck is one of the great gifted teachers.
I'm also rather fond of http://www.barnesandnoble.com/w/teaching-mathematics-in-colleges-and-universities-solomon-friedberg/1100898735?ean=9780821828236, put out by the AMS about ten years ago.
Steve Krantz's book http://www.amazon.com/How-Teach-Mathematics-Steven-Krantz/dp/0821813986 also offers some good advice here and there.