Respect the teachers? Yes, as people, but not for their math. I have to re-grade my children’s math because of all the grading errors the teachers make. Learning opportunities. Most of the teachers don’t understand math, are nervous about it and prefer rule based approaches.
Second, Common Core is full of mistakes and serious conceptual flaws, but don’t expect the teachers to catch them, even less the administrators.
Finally, a big source of frustration in school (and college, to some degree) was that I could and did find shortcuts to many of the problems, sadly, few of the teachers understood them. So of course my grades suffered, including in the big board exams. It was only in grad school that an alternate derivation of a homework problem (in mathematical physics) earned me the suggestion to publish it!
The way I would have (and have graded), I would have given extra points for the correct answer arrived at in a different correct way, and double extra points for a method I hadn’t thought of.