I think that one way to improve education to have teachers help students with homework directly at school, instead of letting them complete it at home. This would help solve problems such as plagiarism and unfinished assignments.
Instead, teachers should tell students to review notes at home so that teachers can teach faster, as the students will already have previewed the material.
However, one potential problem with this approach is that many students will not be motivated to review on their own without some kind of enforcement. The teacher will then have to slow down to explain to those who cannot keep up. I'm unsure how this problem can be fixed, and it would be useful to do some trials first.