You shouldn't upset school staff.
Jim notices that his teacher is teaching the class something which isn't accurate.
Jim wants to let his teacher know that what they are teaching isn't correct.
Jim gives a note to the teacher discretely after class that explains the teacher's mistake.
Jim points out his teacher's mistake in front of the whole class.
Jim's teacher is able correct their mistake without losing face.
Jim's teacher feels angry and embarrassed about having been corrected publicly.