Optional homework almost definitely won't get done. Making it count ensures that students would actually do it, which is useful to instructors (what do they need to focus on in class? Is the class understanding the lectures?).
You can still grade the homework (to give both lecturers and students feedback), but just have it not count towards the kids letter grade in the course. If no one is doing it, then you could make the grade for homework pass / fail: did you hand something gradeable in or not?
Hm, then I feel like students might do the minimum passable work. Which, to be fair, is pretty close to optimal for the real world.
Maybe that's the trick - make the requirements for passing good enough that the minimum still requires learning and engagement, and then just grade on a straight pass/fail.
That's how a bunch of courses I attended and TAed did it. You needed to beat a specific rating averaged over your homework assignments to be allowed to take the exams. Occasionally caused really good students to fluke the last 1 or 2 assignments since they were sure to have qualified, but generally kept everyone doing them and allowed for failing occasionally (which is useful because students then are less motivated to try and hide their failure, which gives the TAs better feedback about progress and problems)
2) Quiz (say 1 Q a week related to homework that was returned a week ago, give students a chance to figure out what they did wrong) - say 20% of grade
3) midterm and final, a 30/30 or 20/40 split.
one can adjust the percentages to achieve one's desired pedagogical goals.
personally, I don't find copying homework to be a problem if the student figures out what they copied. It's no worse than students frantically copying down everything the teacher puts on the board or slides which seems to be a common way students study.
> 2) Quiz (say 1 Q a week related to homework that was returned a week ago, give students a chance to figure out what they did wrong) - say 20% of grade
I never had quizzes except from professors who issued them to keep attendance up. Quizzes by nature are short and shallow. At the college level they are not particularly useful for establishing understanding.
While I believe "almost definitely" is a bit too strong, one of the most important lessons undergraduates need to learn asap is learning how to learn effectively. Homework is only a tool that can be very helpful when learning, but it's not the only tool available.
> which is useful to instructors
That's nice, but it's the instructor's job to serve serve the students.
> Is the class understanding the lectures?
In most classes, this should be easy to determine simply from interacting with the students in class, the questions they ask during office hours, etc.
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The ideal instructor should offer regular homework problems/projects that are clear examples of what the students will be expected to know, and check the work of anybody that wants to take advantage of the instructor's knowledge. However, if a student feels their time would be better spent elsewhere[1], that's their business.
The exam will reveal if they made a good decision. Like any skill, many students will make mistakes when they first attempt this kind of project/time management. Fortunately, as undergraduates, the consequences of failure are usually having to retake the class. Later in life, failure may mean losing a job or other far more damaging consequences.
(For the record, when I was an undergraduate at UC Davis, many classes had optional homework. I spent a lot of time working on it for some classes, and others I skipped because it was trivial compared to what I was doing every day at my job.)
[1] e.g. other classes, a job, their own self-study, or maintaining friendships at a social event
Really depends on the goal. Is the goal to teach everyone in the class? If so, "just let them fail" is a poor strategy. (It's also one that will get the teacher bad performance reviews.)
They might be learning more from 'optional' homework though. For instance, my dynamics professor didn't issue any graded homework, although the homework in the class was my largest time sink last semester. The homework was scored so you knew what you did wrong, but the entire course was graded on tests (which were difficult enough that afaik nobody managed >70% before the curve). After the first test, it was pretty clear that the homework wasn't 'optional'. While this did help w/ teaching self-study, overall I think it was a poor way to run the course, since then the tests became overwhelmingly stressful for nearly everyone. I think that grading is necessary, and at the college level quizzes are typically pointless, but without homework there is little left to judge comprehension on.