First, an excellent analysis of the power of zeros:
Why do students get zeros on homework? Because we allow students not to complete work. Zeros are an easy way out—simply label students lazy for not completing homework (without trying to figure out why), and the teacher is absolved of all responsibility. Zeros punish the vice of laziness, but is laziness the reason most students don't complete assignments, especially homework? I don't think so.
I'd add two things; good teaching is not predicated on punishment, but rather of learning. So, we shouldn't be in the business of "punishing for the vice of laziness". Regardless, a zero really isn't punishment. You want to punish a student who is lazy? Make them turn in the assignment!
Which, Vatterott is already ahead of me:
I think the better solution is a "Zeros Aren't Permitted" (ZAP) program, an increasingly popular idea where zeros are used merely as placeholders until work is made up or excused.
My own grading practices as a teacher eventually evolved into that practice, and it was one of the best classroom management practices I could have. Students, knowing that they couldn't pass the class unless all assignments were handed in and done well were more likely to do them well the first time. And even if they did procrastinate and turn them in late, at least I had something to assess their knowledge for the different course outcomes.
Vatterott puts this in perspective:
ZAP makes more work for the teacher and administrators, but it puts the emphasis back on learning. As we continue to move toward more standards-based grading and the argument rages about how to "hold students accountable," are we all asking the same question? Is it "How many assignments have the students completed?" instead of "How much have the students learned?" Grades should reflect what a student knows or can do, not what work he or she has completed.