I've been collecting homework and checking individual problems this year. I grade it on completion, though if students tell me directly that they had trouble with a question before class (and it is obvious it isn't a case of not being able to do ANY of it because they waited until the last minute to try) I don't mind if they leave some things blank. I did this in the beginning since I had heard there were students that tried to skip out on doing homework if it wasn't checked. We do occasionally go over assigned problems during class, but I tend not to unless students are really perplexed by something.
I have lots of opinions on homework and its value. Some can use the extra practice and review of ideas developed in class. Some need to use homework time to make the material their own. In some cases, it gives students a chance to develop a skill, but in those cases I insist that students have a reliable resource nearby that they know how to use (textbook, Wolfram Alpha, Geogebra) to check their work. I don't think it is necessary to assign it just to "build character" or discipline. I read Alfie Kohn's The Homework Myth, and while I did find myself disagreeing with some aspects of his arguments, it did make me think about why I assign it and what it is really good for. I do not assign busy work, nor do I assign 1 - 89 - each problem I assign is deliberately chosen.
Among the many ways I try to assess my students, I admit that homework doesn't actually tell me that much about the skill level of a student. Why do I do it then?
My reason for assessing homework is for one selfish reason, and I make no secret of it with my students:
The more work I see from students relating to a concept, the better I get at developing that concept with students.
I would love to say that I know every mistake students are going to make. I know many of them. If I can proactively create activities that catch these misconceptions before they even start (and even better, get students talking about them) then the richness of our work together increases astronomically. You might ask why I can't get this during conversation or circulation with students during the class period. I always do get some insight this way. The difference is that I can have a conversation with the student at that point about their thinking because he or she is in the room with me. I can push them in the right direction in that situation if the understanding is off. The key is that most of my students are alone when they do their work, or at least, have only online contact with their classmates. In that situation, I can really see what students do when they are faced with a written challenge. The more I see this work, the better I get.
I am not worried about students copying - if they do it, it always sticks out like a sore thumb. Maybe they just aren't good at copying. Either way, I don't have any cases of students that say 'I could do it in the homework, but can't do it when it comes to quizzes or tests.' Since I can see clearly when the students can/can't do it in the homework, I can immediately address the issue during the next class.
The other thing I have started doing is changing the type of feedback I give students on homework. I still fall into the habit of marking things that are wrong with an 'x' when I am not careful. I now try to make all feedback a question or statement, as if I am starting a conversation with a student about their work through my comments, whether positive or negative:
- Great explanation using definition here.
- Does x = 7 check in the original equation? (This rather than marking an x when a solution is clearly wrong.)
- (pointing out two correct steps and then third with an error) - mistake is in here somewhere.
- You can call "angle CPK" "angle P" here.
- Good use of quotient rule - can you use power rule and get the same answer?
The students that get papers back with ink on them don't necessarily have wrong answers - they just have more I can chat with them about on paper. The more I can get the students to understand that the homework is NOT about being right or wrong, but about the quality of their mathematical thinking, I think we are all better off.