Grading sends a direct message to students about what is expected in class. However, often there is a gap between the assigned grade and the goals of the instructor. In an interview study of faculty teaching calculus-based introductory physics, we verified that this gap exists and identified three themes that appear to shape grading decisions: (1) a desire to see student reasoning, (2) a reluctance to deduct points from a student solution that might be correct, and (3) a tendency to project correct thought processes onto a student solution. When all three themes were expressed by an instructor, the resulting conflict was resolved by placing the burden of proof on either the instructor or the student. The weighting of the themes with the burden of proof criterion explains our finding that although almost all instructors reported telling students to show their reasoning in problem solutions, about half graded problem solutions in a way that would likely discourage students from showing this reasoning.
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