When grading a 10-point assignment, I always struggle to decide whether the work is worth a 4, 5, 6, or 7. If I like the kid, I give her a 9. If I’m hungry, the kid gets a 4. If the kid’s mother gave me a $25 Starbucks gift card, then it's an 8 with a smiley face.
So what I end up doing is this: I give every less-than-complete paper a 1—yes, one—and so far this marking strategy seems to be working.
I want kids to revise their work until it’s flushed with coherent mathematics. A lone 1 at the top of their paper—plus my comments—either motivates them or pisses them off enough to revise. If they need help, they know where to find me. If the revision still doesn’t cut it, then it stays a 1, and they try again. And again. Or whenever the grading period ends.
I haven’t kept track of any hard data, but I’d bet that the revision rate has at least doubled.
Grading papers sucks. But grading with a 1 or a 10 has taken a lot of stress off my plate. Like I found a cure for my crazies.