TITLE: effective teaching
QUESTION [46 upvotes]: Eric Mazur has a wonderful video describing how physics is taught at many universities and his description applies word for word to the way I learned mathematics and the way it is still being taught, i.e. professors lecture to students and sketch some proofs. Suffice it to say I'm not a fan of the current methods and I don't think it would be too far from the truth to say that I do all the actual learning outside the classroom. Has anyone tried anything different and seen any difference in student understanding and comprehension in graduate or undergraduate courses?
Some background motivation: I'm a TA and my current method of doing things is to just write some problems on the board and then go through their solutions. This is fine and it's what the students expect but sometimes I feel guilty because I'm just teaching them problem/solution patterns and reinforcing all the bad stereotypes about what mathematics is instead of showing them the underlying conceptual tapestry and helping them rethink their attitudes toward mathematics. It's kinda like the old saying “Give a man a fish; you have fed him for today.  Teach a man to fish; and you have fed him for a lifetime”. So basically I throw a bunch of fish at the students hoping it will feed them for the semester.

REPLY [3 votes]: This very stimulating presentation on teaching math effectively came out in May 2010 and addresses some of the issues presented in the other answers:
Dan Meyer: Math class needs a makeover
Although applied to high school math, at least some aspects of the technique could be incorporated, if only in a few sessions, into advanced classes. Comments to the video by educators and students provide some feedback on the technique.
Another potential method for revamping math classes for the 21'st century (maybe start viewing at time stamp 6:50):
Salman Khan: Let's use video to reinvent education
And always a good read and reminder: V.I. Arnold, On teaching mathematics