When I began my math centers, I had to make a decision about how to handle all of the work my students would be producing. I had so many unanswered questions. Would some students never complete any centers unless their grade depended upon it? Would some students only participate in my math centers if they were rewarded with extra credit points? Would some be discouraged because they got a low score and stop doing center work, or only choose the easiest review activities to help boost their average? What about all my math games that don't actually result in the production of any "work" to grade? Will those just not count, or should I have some sort of a log where kids can record the minutes they spend playing? Isn't that record-keeping going to be a hassle that makes centers more time-consuming? How will I keep up myself? Yikes!!! While I'm not here to tell you the answers to all of these questions, I can only share my experiences with you.
I ultimately made a decision. I would try simply not grading center work at all. Not at all. You know what? It worked. Kids actually seem to do better quality work than they do at any other time, because they are assigning it to themselves and because they are enjoying it. More importantly, they are unafraid to select even the most challenging activities. What's amazing is the way kids take more risks. For instance, on my "Backwards Facts" center, I gave students a bunch of blank math facts with only the products provided, such as ___ x ___ = 36. One of my fourth graders, (don't ask me how) began putting down answers like 1/2 x 48 = 24 and 1/8 x 64 = 8. Eventually, he began putting down answers such as 2 1/2 x 8 = 20. I was stunned. Would he have been willing to try that if it was graded? I doubt it. I also learned that this particular student had a whole lot to offer. I have seen him become one of my stars, and a lot of it has happened at least in part because of math centers.
Moreover, I love the fact that the kids are doing the center work sheerly for the enjoyment of learning. I think the math centers have helped my students become more motivated in general, and my decision not to grade the work helped that to occur. I simply check any worksheets that are turned in (I keep a turn-in folder at the center) and make notes on them, and then I return them to the students. In a few cases, a center assignment has revealed a lack of understanding of a particular concept and I have met with the student to go over it one-on-one. Overall though, the work tends to be remarkably well done.
In the end, you need to find a way of implementing centers that works for you and accomplishes all of your educational goals. I can only encourage you to try not grading work from your learning centers for a little while just to see what happens. I think you might be pleasantly surprised.