Yes, it’s very disheartening to see math teachers not understand how to check your work.

There are algorithms (and heuristics) that have been known for centuries to verify (or estimate) check most results from arithmetic to calculus.

It’s as if programmers were not taught how to do logging or assertions.

In math there are two types of errors, not understanding the problem and mistakes. Redoing the work won’t help at all for misunderstanding or lack of understanding and has only a marginal chance of catching the mistake.