Translation:My mother has spoken to the teacher.
I would say it's a subtle difference. Saying "spoken to" suggests that the conversation was a little more one-sided than "spoken with"
Since mom has spoken to the teacher, there has been little chance for dialogue. The poor guy couldn't get a word in edgewise.
Yes, "speak to somebody" is "hablar con/a alguien".
But in that case you must add "le"... "mi madre LE ha hablado al maestro".
Shouldn't the very word "maestro" be considered acceptable, under the context of being a master of music, otherwise a conductor?
I entered "My mother's spoken to the teacher" and it was marked incorrect--reported it, but it's annoying.