Ideally, I'd like my students' grades to be based on more than just exams, because I think that certain tasks, such as writing proofs, aren't best performed in a test environment. Using homework for assessment seems like an obvious way to accomplish this. But my idealized view of homework, formed when I was a student, seems to have little to do with modern reality. Educators on this site suggest that instructors solve homework problems during office hours, and my students seem to expect that I will do this, but the ability of students to transcribe solutions that I provide them with does not demonstrate understanding. Working on homework in groups seems to be nearly universally recommended and very widely practiced, but how do I differentiate the signal of Student A's understanding from the noise of his/her study partners' understanding?
Are there any studies that compare students' perception of how homework problems are to be solved (e.g, by the student him/herself or by others) today vs., say, 30 years ago?
Are there "best practices" for making valid assessments of student understanding outside the environment of an exam?