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):
