An excellent comment was made on my last post. I started to reply in the comments section, but got a bit long-winded and realized it would be better illustrated in a full-fledged post.
My initial thoughts are below, but they are in no way "best practice" as I'm constantly tweaking this new way of reporting learning.
How do you grade late work?
This could be rolled into a citizenship grade or as you suggested into some sort of new learning target. A virtual colleague suggested to me that 5-10% of a student's grade be something along the lines of "responsibility" (just to play the 'grading game' and keep students accountable), perhaps giving students one point per day for coming to class prepared and ready to ask questions about the homework. Right now, I'm just recording who turns it in, how much they did and if they turned it in late. I should have also mentioned in my initial commentary that I post the answers to all "practice" assignments on the board, so there's no incentive to copy from a friend. Check out some of my previous posts on feedback for more insight on this philosophy. If/when it is entered into the grade book, I want to do it in a way (numerically, I admit this may be difficult) that clearly makes it stand apart from the learning targets. Since understanding and responsibility are not easy to pull out from the "old system," I don't want to fall into this trap again.
Another aspect of this system is allowing students to be re-assessed on a learning target if they're not happy with how they did. For example, I would give the student who got all 4's and one 2 the opportunity to come in for re-teaching, do extra problems/activities, and then eventually a mini-assessment on that learning target. An improved score replaces the old score in the grade book so that students are not penalized for "getting it" later than others. I explained to students that re-takes must take place outside of class, are only available to students how have put forth a solid effort on the homework, arranged ahead of time, and may only be done once it is evident that new learning has taken place. It puts the burden on the shoulders of the student, eliminates the "anyone can re-take at anytime, so why do the homework?" mentality, and helps students understand it takes more time on my end to create an alternative assessment, so I expect additional effort from them, too.
I hope this helps and am open to any critiques on this current practice of reporting learning.