My institution is now in the process of "standardizing" our calculus classes. One issue we have is the variation among instructors in grading problems. I am interested if there are ways to objectively study such variation and so my question is whether anyone knows of a standard set of questions where there is an agreed upon rubric as to how to grade the problem and also how to deduct points for cases that don't fall nicely into the rubric. I know these types of rubrics do exist for AP Calculus tests for example, so I was wondering if anyone in math ed has ever constructed a bank of such questions.
So as a brief example: consider the problem of finding the derivative of ln(sin(x) + tan(x)) that is worth, say 10 points. The rubric would have a breakdown of what points are awarded to each part (maybe +4 points for knowing to use chain rule, +2 for the derivative of each trig function, etc) but would also consider all the possible common student errors (such as ln(x+y) = ln(x) + ln(y)) and how to deduct points for them.
I'm not sure that such a set of problems whose grading had been standardized would actually answer my question, but I am thinking it might be a first step in understanding how much variation we have among the instructors and how to interpret it.