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.

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    $\begingroup$ At my institution, we just do "cafeteria" grading for exams, write the rubrics together, and generally have one individual grading all one problem for uniformity across sections. Homework is automated, and only a small quiz percentage would introduce instructor grading bias into final grades. $\endgroup$ – Steven Gubkin Oct 12 '18 at 17:18
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    $\begingroup$ @StevenGubkin We are trying to do the same but the problem I am being to see emerge is that we aren't producing uniformity: we are just redistributing the variance. Rubrics (instructors draw up) are great but the time when the wheels fall off is when a student answers in a way that the rubric doesn't cover (hence my example). I am seeing that some teachers grade a mistake based on when it occurs in the problem, others grade based on how significantly it affects the answer, etc. This is the main problem I am trying to gte a handle on $\endgroup$ – Matt Brenneman Oct 12 '18 at 17:22
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    $\begingroup$ Now I know why some people hate Common Core: because it attempted introducing the same over-formalized concepts to elem/middle/high school. Breaking down and deducting points for this and that is one the most mind-numbing ideas one can come up with. Not only there is no joy of learning anymore, there is no joy of teaching (unless grading is offloaded to clueless TAs or Mechanical Turk drones, but I would not want to study in a uni where stuff like that is common). $\endgroup$ – Rusty Core Oct 12 '18 at 19:27
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    $\begingroup$ @MattBrenneman So you are norming your measurement tools, bringing the instructors to the level of merely lexical analyzers. Are they so bad that you cannot trust their judgment? Again, the same concept as in Common Core for grade school: no trust to individual teacher, instead over-formalization of curricula and testing. The computers are not smart enough yet to teach kids on their own, no problem, we'll pretend that humans are as two-bit as computers. Excuse my rant, could not help. $\endgroup$ – Rusty Core Oct 12 '18 at 19:52
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    $\begingroup$ @RustyCore While discussion of the common core is almost certainly off-topic here, the fact is that it is merely a set of standards and guidelines for what students should know at a particular point in their educational careers. You seem to be ranting against the assessments which are ostensibly written to be aligned with the common core, which is an entirely different issue. Perhaps you should actually download the standards themselves, and have a look at how little they constrain teachers... $\endgroup$ – Xander Henderson Oct 12 '18 at 21:50

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