Is it permissible for a female teacher to go out to work without a mahram?

There is no evidence that obligates the presence of a mahram (definition) with a woman when she leaves her home for purposes other than travel. However, a mahram is required for her during travel. There is no harm for a female teacher in going to work alone if the path is safe and her departure is not considered travel. The default is for a woman to remain in her home, but it is permissible for her to leave for a need.