**5:** All parts of the problem are present. The solution is complete
or near-complete and logically formulated. Explanations are clear, notation
is correct and consistent, and conceptual understanding is apparent. The solution
is not necessarily perfect; minor write-up problems, grammar errors, or arithmetic
errors may be present.

**4:** Almost all parts of the problem are present. The solution
is complete or near-complete and logically formulated. Explanations are mainly
clear, notation is mostly correct and consistent, and conceptual understanding
is apparent. Careless mathematical errors may be present (for example, algebra,
arithmetic). An intelligent, thoughtful, but somewhat incorrect approach may
receive this score. The difference between a 4 and a 5 is that a 4-solution
has one significant flaw. The difference between a 4 and a 3 is that a 4-solution
exhibits better conceptual understanding.

**3:** The solution is logically formulated with clear explanations,
although one part of the problem may be missing. OR, The solution is complete
and explanations are clear but there are serious logical flaws. OR, The solution
may be complete and logically formulated but the explanations are unclear or
lacking.

Conceptual understanding of essential ideas is adequate. Many careless mathematical
errors may be present (for example, algebra, arithmetic). Details are confused
or missing.

**2:** Explanation is lacking. OR, The solution shows serious
misconceptions and some correct reasoning. OR, Many parts of the problem are
not present.

Conceptual understanding is inadequate. Procedural errors are present, OR logical/relational
steps are missing. The difference between a 2 and a 3 is that a 2-solution does
not exhibit adequate conceptual understanding of the essential details. The
difference between a 2 and a 1 is that a 2-solution has some explanation, or
has some correct reasoning.

**1:** Explanation is completely missing. OR, Many parts of the
problem are not present. OR, The solution contains serious logical flaws, and
lacks some explanation.

Conceptual understanding is inadequate. Procedural errors are present, OR logical/relational
steps are missing. Poor response to the questions posed.

**0:** Solution is missing. OR, Solution is minimal and makes
no sense.

This is an adaptation of the famous document How Doug Marks Papers (which appears
in print in *The Michigan Calculus Program Instructor Training Matierials*
by Beverly Black, Pat Shure, Doug Shaw). Doug
Shaw wrote an explanation of his grading practices for fellow instructors,
as a favor to them. I've been using that document as a guideline, modified very
slightly, for many years. However, it's not a document that would make a lot
of sense to students. Thus, this is sort of a translation of his intent (or
at least my attempt at a translation) for use by students. In using How Doug
Marks Papers, one first comments/corrects the problem and then assigns a numerical
grade. This document is intended to help students to understand what the numbers
on their homework mean as an assessment by an instructor of the overall quality
of the work. It is also informed by Emert and Parish's MAA Notes article, available in this PDF book.