At least you admit to the mistake.

I had a HS math teacher that was so by the book that when the book was wrong he would still keep right on going and mark anyone's papers wrong if they used the correct formulas opposed to his wrong book formulas and believe me the books we had had a lot of basic mistakes.

Very likely that the teacher lacked the math knowledge and skills to even do the work for themselves and so all they could do was accept whatever the book said as gospel. I've seen it so many times. It's very disheartening.

If I have a student that can prove that one of my solutions (or the author's solutions, though I usually work all the problems myself and catch those before the students see them) is wrong, I generally reward them with extra credit.

 

Unfortunately the school I went to was and still 22+ years later is well known for hiring the bottom of the barrel.

A few years ago they manged to get a well educated and experienced lady in as the head principal who put an active effort into cleaning up the school. They fired her for her efforts then she turned around and sue the pants off them for wrongful termination after having been warned by her ahead of time that their idiotic actions towards who they kept and who they got rid of were going to cause a huge amount of legal trouble.

Her replacement got jailed last year for human trafficking and sex offences in the school and they didn't find reason to fire him before hand when it had been brought to their attention he was a problem.

 

While I firmly believe that the overwhelming majority of schools and districts genuinely want and try to do well by their students and communities, there are certainly places where there just seems to be some entrenched ... disease, for lack of a better word, that makes it a long-term cesspool that actively resists any effort to change it. In most such cases, it's a "follow the money/power" situation.

But let's not let things wander too much further astray; Of Topic is the better place for this to continue (though it will turn too political very fast).