I agree that partial credit should be awarded when a student starts out correctly, then a mathematical error may have occurred somewhere in the middle, hence getting the wrong answer. Partial credit in that sense says, “Good attempt, but you made a small error but I won’t dock you completely for it.”

On the flip side, if a student attempts a problem and obviously has no clue of the material, then no credit should be awarded whatsoever. Why should a student receive partial credit on a problem where it was completely lucid that the student had no idea what he or she was doing?