How do teachers learn to grade? I teach math with about two years of experience now. In general I have found that all the cliches about graduate school teaching you "how to research but not how to teach" are true. But I have also found many great resources (at my institution, online, in print, etc.) that are helping me, over time, work through my teaching deficits.

...in all things but grading.

I struggle with many grading decisions: from small things, like grading individual homework problems, all the way up to life-changing things like evaluating master's degree defenses.  What I lack is a coherent philosophy of grading that might motivate my various grading policies/strategies/choices.

Interestingly, I have not found good resources for this.  Yes, my institution provides a tiny bit of guidance, but it is very broad.  This forum contains a hundred or so questions tagged with "grading", which is a good start, but I wonder if there are resources that provide a more cohesive treatment of the subject.

I want to hear about theories of grading.  I want principles which flow naturally from the theories.  I want applications and strategies which build on the principles.  I want to hear different viewpoints on the issues so I can evaluate their relative strengths and weaknesses as I come to understand my own thoughts better.  In short, I want it all.

Do any such resources exist?  Can anyone point me in the right direction?  If these don't exist, why not?
One principle is that the instructor should aspire to grade in a way that results in the grade being most closely correlated with those aspects of the knowledge and skills being assessed that the instructor considers important.

As an example, it is a common belief among instructors of university level mathematics courses that exam questions should test conceptual knowledge rather than facility with arithmetic and other low-level calculations. For this reason, most instructors would take off only a very small number of points, or not take off any points, for a small error of arithmetic in an otherwise conceptually correct answer. However, some instructors might consider accuracy to be an important skill to test in and of itself, and may impose a heavy penalty of points for even small arithmetic errors. So you see, the grading function chosen by the instructor reflects that instructor's view of what's important. Decide in advance what's important to you, and grade accordingly.