If you don’t know what the Dunning-Kruger effect is, go here. In a nutshell: it takes a bit of intelligence/competence to recognize one’s own incompetence.
THAT is why I often dread handing exams back in off-semester “faux calculus” courses (frequently called “brief calculus” or “business calculus”).
The population for the “off semester”: usually students who did poorly in our placement exams and had to start with “college” algebra, or people who have already flunked the course at least once, as well as people who simply hate math.
That many have little natural ability doesn’t bother me. That they struggle to understand that “a number” might be zero doesn’t bother me that much (context: I told them that ALWAYS fails to exist if both limits exist and and .)
What bothers me: some won’t accept the following: if THEY think that they are right and I tell them that they are wrong, there is very high probability that I am right. Too many just refuse to even entertain this idea, no matter how poor their record in mathematics is.
Of course, other disciplines have it worse….so this is just a whine about teaching the very bad students in what amounts to a remedial course.