I was a teacher too, but have never been asked if I was one, or been told that I looked like one! Perhaps they thought I was too tiny at 5ft nothing!
Mind you I did take over the singing time at the end of DGDs' playgroup once as the regular leader was absent....
And I did notice at our regular hotel in Crete that most of the British women there in the summer holidays were teachers.
People used to think that DH was a police officer. He actually worked for the Foreign Office for most of his working life, and they would say they never would have thought it! Perhaps they were expecting a very posh Civil Servant diplomat type - but he retained his Northern accent all his life. His final job before retirement though was actually the police.