Students today have many excuses for not turning in work and then proclaiming that they did not realize that they had a zero when their report cards show a lower grade than will please their parents.  The no zero initiative is meant to address this issue.

The teacher creates a board in their classroom where each class is given a space and all assignments are written under each class.  The teacher can name the board creatively such as "bored with zeros", U does not equal 0, or  no zero heros.  Then after each assignment due date, the teacher writes the name of students who have not turned in the assignment on the board so that they are aware that they have a zero on that assignment.  The student then is given a time period to turn in the assignment and erase their name from the board.

Every four and a half weeks the students who have no zeros are given a treat.  At the end of a nine weeks period, the students who have no zeros are posted on a list in the hall to praise them for having no zeros.

The percentage of students having zeros has dropped at our school since using this system.

My concerns are that we are rewarding students continually for doing what they should already be doing.

My school is beginning a similar program called Z.A.P., with stands for Zeros Aren't Permitted.  What is going to happen, is that if a student doesn't turn in an assignment, they will be required to stay in the lunch room during lunch and complete their assignment, instead of being allowed to leave when their meal is done and go hang out with their friends.  So, this form of what you are talking about is a punishment, not a reward.  Hopefully, it will motivate the students to do their work.