On Friday, right on schedule, Math Teachers at Play #10 was posted at Homeschool Math Blog. There’s good information on Wolfram Alpha and homework and optical illusions and a host of other interesting things.
As the students entered class the next day, they would list the page number and problem number of the problems they could not solve, on the front board in a designated area. If the problem was already listed, they placed a check (√) next to it. Once the class started, they were not allowed to record problem numbers at the board. Other students, who were successful in solving these problems, immediately went to the board when they entered the class, indicated that they would solve one of the listed problems, and worked it out in detail. When they finished they signed their name to the problem.
I tried this out in calculus, a course where I assign homework every day, and it worked fabulously. It didn’t eliminate grading, but it did cut way down on how much time I spent going over homework in class. The only change I’ve made is that I now insist that people write down what they had trouble with, so instead of writing just #23 they’d write “#23: couldn’t get started” or “#23: what do you do after [this step]?” or “#23: I got x2 but the book says x3.” And I count answering the questions correctly as extra credit. (In perspective, homework is 10% of a person’s grade in calculus; usually each assignment gets 5 points, and there are probably 35 assignments over the semester. I’ve ended up giving 1 extra credit point for each time a person added correctly, with a cap of earning 100% total for homework.)
I haven’t done this in all courses, but I do use it in every calculus-type course (where the problems tend to be shorter) and it’s gone really well. So that’s my two cents.