I taught Calculus 2 at my institution the past two semesters and several students have left comments in their course evaluations that advocate grading homework problems based on whether they were completed, not whether they were correct. For instance, when asked, "What changes to the course would you recommend?", one student wrote:
grade homework on completeness and not correctness because we are putting in the effort even if we don't necessarily understand it yet
I think they have a good point here. I view homework as required practice of the course material. Furthermore, I've realized that grading every problem carefully for correctness is prohibitively time-consuming for me!
I would like to implement a new grading scheme next year wherein homework problems will be assigned and I will give a grade based on whether they were done, and add some helpful comments about what students should work on. Ideally, everyone will get just about full credit on this component of their grade. (Perhaps someone will skip an assignment during a busy week, but if someone actually puts in effort, they will get credit.)
However, I'm not sure how to synthesize this new idea with the overall grading scheme. Previously, I made homework assignments were 15-20% of a student's final grade. It feels strange, though, to essentially make this a "gimme" portion of their grade just for doing the problems. But if I lower this to 10%, what should I do ... Have another in-class exam? That eats up class meeting time. Have regular quizzes? That also takes up some time, and should I grade those carefully on correctness, even though the students are not used to that? Should I have a once-a-month "take home exam" that amounts to being a difficult homework assignment of sorts?
Essentially, my question boils down to this: I fully intend to take these students' suggestion and assign regular homework problems to be graded solely on completion, and not correctness. I am curious about how to modify the rest of my grading scheme so that the students' final grades are still accurate and fair, and without too much extra class time taken away.
I am interested in personal suggestions/anecdotes here, as well as any education research (if there is any). I am particularly interested if you have made a similar change and can explain some observed differences in the two schemes.
(Note: There is a great answer here to the question, "Is it worth grading calculus homework?". My question is not the same; I have already decided to implement this "grade for completion and add suggestive comments" method, partly based on that answer I linked to. I am curious about adjusting other components of the course to account for this decision.)