> 1. (US, slang) A woman who is a teacher, especially a teacher in a schoolhouse; may carry the connotation she is severe and/or a spinster.

> 2. (by extension) A person, of any gender, who exhibits characteristics attributed to schoolteachers of the old times, such as strict enforcement of arbitrary rules.

https://en.wiktionary.org/wiki/schoolmarm#English ('marm' being apparently a (US only?) variant of 'ma'am')

[NB, delightfully, and presumably unrelatedly (though not listed as a separate etymology):

> 3. (forestry) A tree with two or more trunks; a forked tree.

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