Etymology
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schoolmarm (n.)

also school-marm, "female school teacher," 1834, American English colloquial, in the popular countrified humor writing of "Major Jack Downing" of Maine (Seba Smith); a variant of school-ma'am (1828), from school (n.1) + ma'am. See R. Used figuratively from 1887 in reference to patronizing and priggish instruction.

School-mistress "woman who teaches in a school" is attested from c. 1500 (mid-14c. as a surname, scole-maistres). School-dame (1650s) was generally "an old woman who keeps a school for small children."

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Definitions of schoolmarm

schoolmarm (n.)
a woman schoolteacher (especially one regarded as strict);
Synonyms: schoolma'am / schoolmistress / mistress
From wordnet.princeton.edu