Not so, everybody makes mistakes. If you're provinding answers to problems then they need to be checkable and getting into the routine of providing evidence as to how a result has been arrived at is not only good practice it is essential.

As was explained to my daughter (who also does math in her head), "You can have a cure for cancer, but if you can't show how you came up with it it doesn't exist".

I would be pissed about a teacher using the words "lazy girl" to my daughter. There are countless reasons why a child may not be working to their full potential at any given time. Many of which are none of the teacher's concern. If a teacher has a problem with how my child is performing then they should be discussing it with me and not telling a child that they're lazy.

Someone else said it up thread - if you wouldn't say it to a colleague, then don't say it to a child. Ask yourself how you'd like to hear a student call you a lazy girl?

I left school at 16 average across the board .maths slighty below ave....but my second job at 17 it was self employed with a logging crew and me being the loader/forwarder driver and the pay was calculated by lineal ft loaded...no scrap paper out in the wet..all had to be done in your head!and that was part of my job. so very quickly my addition /math became spot on and put in my pocket book every hr. even 40yrs later I can add /subtract very quickly/accurately. so sometimes providing evidence is not essential.

I agree that sometimes where environmental issues or speed are involved it's not possible or convenient to write down calculations, but these calculations tend to be simple. More complex calculations, even where they include simple components should always be recorded for others to inspect. I take your point though, in my youth I regularly operated as a darts marker and quick accurate metal arithmetic was a must although even here the result was recorded for scrutiny.

Maybe she was a girl and maybe she was lazy

When out with small children they often say 'that man has a very big nose' etc but they generally learn eventually that most people don't do this.

It's a lesson in honesty. The teacher tells the girl she's lazy, which gives the girl the opportunity to tell the teacher what she thinks of her, be it stupid, lazy, unprofessional, sloppy, whatever. The youth are our future.