Schoolmarm

[Britney]

(n) One who lectures another in a condenseding manner; one who is pretentious in communicating their opinion as though it were fact, often involving exaggerated body gesturing, e.g., finger [wagging]; one who scolds or [judges] another as if they are morally, [intellectually], or otherwise superior
(v) Schoolmarmin(g) Exibiting the behavior of a schoolmarm

[Couch Potatoe]

A schoolmistress (typically used with reference to a woman regarded as prim, strict, and brisk in manner)

[Jason Yan]

a female school teacher