So far, these are the labels I've come up with:
* Wrong approach - ie. the student was completely not on the right track.
* Conceptual mistake - the student had an inkling of what to do, but they made some severe error in the initial setup of the problem.
* Procedural mistake - the student understands at a high level what the question is asking and what procedures are required, but made some fundamental mechanical error in the procedure.
* Arithmetic mistake - mistakes involving combining decimals, fractions, or integers.
* Careless mistake - mistakes involving miscarried signs or wrongly recorded results, when the student exhibits overall competence in the process.
* Incomplete operation mistake - the student failed to completely answer the question or completely simplify their answers. Or, they were off to a good start and then bailed halfway...
* Mistake in interpreting the instructions - the student did not carefully follow the written directions and therefore did irrelevant calculations.
My hopes are that in this way, I can help kids to focus first on the bigger conceptual issues, and next on the other types of issues. I'd say that if a high level kid sees that they're consistently making the same types of careless or incomplete-operation mistake, it is valuable feedback for them to keep in mind for the future. Versus if a lower-performing kid sees that they're at least not missing the major concepts, then that is a good feedback for them as well, so that they know they would just have to focus on the procedural issues.
Thoughts? I'm grading semester exams as we speak. (sigh.) It's the last road block between me and a real vacation...