schoolmarm
noun
°(US slang) A woman who is a teacher, especially a teacher in a schoolhouse; may carry the connotation she is severe.
"The schoolmarm, running the old west one-room school, is a stock character in western movies."
°A person, male or female, who exhibits characteristics attributed to schoolteachers of the old times (as strict adherence to arbitrary rules, is strict on those who don't comply to those rules, etc.).