Next year, I will be teaching a very challenging second year "multivariable calculus and calculus on manifolds" course, and will assign a large number of difficult problem sets. I am thinking of assigning students to go back to problems where they had good but not perfect solutions and rewrite an elegant, well presented solution. There are two goals here:
Pedagogically, to force students to really think through and present their ideas well, and to avoid the feeling that each problem set is passed through and ignored.
Logistically, to save myself the time of writing lengthy solutions.
Have some of you tried this? How did you make the task fair, when some problems are much harder to write than others? What were the logistical practicalities: How long did students have to produce solutions, and how were they evaluated?
To be clear about the sort of student population we are talking about, this is the top 20 or so kids at Michigan, who have already done a similarly challenging single variable course and should be anticipating a high workload. For those who know Michigan, this is 395-396; I believe the Chicago and Harvard equivalents are 20700-20800-20900 and 55b (but in a year, not the term that 55b tries to squeeze into.)