When my daughter was winning 3 Gauss math competition gold medals she had to keep correcting her Grade 7 math teacher in class. He should have stuck to teaching PE, but I guess the opportunities for that in elementary school are limited.

In higher grades she got into Peer Tutoring in Math to earn some sort of required credits. She saw a stream of students from one particular teacher unable to complete assigned work. Reviewing their notes she found them identical, but wrong. The Teacher was clearly teaching math by rote, from bogus teaching notes. All of the students were in class and attentive enough to take identical notes, but garbage in garbage out.