I am teaching an introductory course on proofs in mathematics in a mid-size American public university, and trying to develop some kind of consistent grading meta-scheme for grading proofs. I am writing to see if anyone can refer me to math ed papers about grading proofs, or if anyone has such a meta-strategy that was helpful to use in the past.
Such a meta-strategy might look like: grade each proof out of 20 points, assigning 5 points to each of
Correctness - are definitions and previous results used correctly
Logic (micro) - does each step follow from the previous step
Logic (macro) - has the student understood what is to be proved, and chosen a path that is appropriate (i.e. correctly set-up a proof by contradiction, or direct proof, or etc)
Readability - has the writer used sufficient language to communicate the intended arguments
(Incidentally, this is what I came up with this morning, in an attempt to start grading the first exam, but I suspect there are educators else where who have thought longer and harder about this problem, and I am dying to hear what they have to say.)
