By analyzing student response patterns in more detail,
which was not possible in earlier studies such as in Ref. 7
due to limited answer choices, we also found an interesting
and persistent signal of the sign error in 15%–30% of responses
postinstruction. This number is somewhat misleading:
When given a series of four similar questions, over 40%
of the students made a sign error at least once, illuminating a
significant student difficulty that warrants attention during
instruction.