I thought this was an interesting idea. One of my colleagues does not collect homework. Instead, the students turn in a sheet that lists which homework problems they worked on and how much time they spent on homework. By doing this, the students get a small homework grade – independent of how much time they claim they spent. I am pretty sure it is not a large percentage of the total grade.
Along with this “report”, the students are supposed to keep notes on the homework they claim they did – just for reference. Theoretically, the instructor could verify that the student did the problems reported.
So, is this is good idea? Well, it is certainly not a bad idea. The best thing about this method is that reinforces the idea that homework is for the student. It helps students become more aware of how much time they are spending on the material outside of class.
I am sure there are students that over report the number of hours they are working on homework – but they are clearly just fooling themselves.
What is not so great about this method? I think the biggest downside is that students don’t get feedback on their homework. Well, they get feedback if they ask the instructor – which they should.