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I am teaching a course for sophomore-level math majors this quarter, and next quarter, I'll be teaching the same thing. I haven't been in this situation before, and I'm wondering to what degree I can reuse exercises from this quarter.

On the one hand, I provide detailed solutions to all the homework I assign, and it seems likely that these solutions will find their way to at least some of next quarter's students, one way or another. And using the same (or almost the same) exercises feels lazy on my part.

On the other hand, a lot of these exercises were chosen for a good reason, and I consider them important. Sometimes I can change some numbers to get a different problem with the same flavor, but this is often not possible in a proof-based course like this. And most of the exercises were taken from the (well-known) course textbook, for which the solutions can surely be found online anyway. Even for the exercises I wrote myself, the students can ask for help on math.stackexchange or the like, or copy their friend's homework from the same class. For these reasons, I already only have homework counting 20% toward the final grade. But each exam contains one question quoted verbatim from their homework (and I warn them about this), so it's in their interest to understand the solution whether they came up with one honestly or not.

All that to say, I understand not all students will be 100% ethical with their homework, and I try to work around this fact rather than fight it. But does giving homework assignments that are say 75% the same as the assignments from the previous quarter make it too easy to be unethical?

What would be "due diligence" in this situation?

(When it comes to exams, I already know what I'll do: distribute last quarter's exam as a practice exam a week ahead of time, and distribute solutions three days ahead of time, so that no one has an unfair advantage, and to force myself to make a totally new exam.)

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For me, the answer is simply that homework is not collected, graded, or scored. I assign odd-numbered problems from standard textbooks, expect that students check the answers at the back, and I ask for discussion of any problems or surprises in the next class. This basically wipes the entire logistical/ethical difficulty off the table for me; and it highlights to students that the homework is a communal learning opportunity, as it should be. I think you want to be efficient with your time in this regard.

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I guess it depends on how you grade the homework. I don't change mine at all, unless I have thought of a way to improve it. But I don't give it much weight. I stamp it each day, and count the stamps at test time. They are supposed to check answers in the back of the book. Homework is 10% to 15% of the grade.

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I would avoid giving detailed written solutions. (I realize it's a late for that now but it's something you can do going forward.) Instead, I would suggest discussing the solutions in the next class. Students will have the solutions in their notes but it will be their interpretation of the solutions. Not only will this prevent your technically complete solutions from going into the wild but the students will understand it better if they filter it through their understanding of the material.

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