First of all, when writing an exam problem I identify the concepts used, reasoning
steps taken, and calculations made in order to solve the problem. Each conceptual
nugget is worth 5 points. For example, a (clearly fake) problem that says
“Is 17 positive or negative? Explain.”
is worth 10 points, because to answer it someone must (a) say that 17 is positive
and (b) explain that this is because 17 > 0. That's two conceptual nuggets
in my assessment scheme. (A full-credit answer to the problem: “17 is
positive, because it is greater than zero.”)
So, with each exam problem there is a list of conceptual nuggets that represent
necessary parts of a complete solution.
When grading an exam problem, I look at each nugget individually. I use the following rubric:
5: Conceptual understanding apparent; consistent notation, clear explanation.
3: Conceptual understanding only adequate; careless mathematical errors present (for example, algebra, arithmetic); explanation correct but unclear.
2: Conceptual understanding not quite adequate; procedural errors; explanation unclear but with some correct element.
0: Conceptual understanding totally lacking; significant procedural errors; incorrect reasoning; poor response to the question posed; explanation unclear. OR, nugget is absent.
The sum of the nugget scores is the score for the problem as a whole.
(The above rubric is modified from Emert and Parish's MAA Notes article, available in this PDF book.)