Assign a grade which is factored into their course grade. The door is now open for students to do extra. Those who do self-correct their work will receive an additional grade. Also, it should provide enough latitude to challenge the gifted and the remediation students. We have so many feeder schools that we have found it necessary for our teachers of freshmen courses of review exactly what homework is.
Some students think only written work is homework.
For the basic classes, we have discovered starting homework at the end of class to be helpful.