You asked for a productive way to fix the misconception. Here's one: Nobody really knows it! Always incorporate enough content to reflect this. Try to construct a series of problems that moves from the very basic to the extremely tricky (think Putnam Exam level).

The point is, any course is just an introduction to a topic. Just because I teach Calculus doesn't mean I know it. This is the real misconception that we need to debunk.

Regarding the "stupid mistakes", just because you can throw a ball doesn't make you Nolan Ryan.

You asked for a productive way to fix the misconception. Here's one: Nobody really knows it! Always incorporate enough content to reflect this. Try to construct a series of problems that moves from the very basic to the extremely tricky (think Putnam Exam level).

The point is, any course is just an introduction to a topic. Just because I teach Calculus doesn't mean I know it. This is the real misconception that we need to debunk.

Regarding the "stupid mistakes", just because you can throw a ball doesn't make you Nolan Ryan.