Somebody found my blog while searching for the etymology of that word.
I could be a typical teacher and tell my reader to go look it up in the dictionary. :)
But I guess, since I'm in a good mood right now, I'll tell you anyway.
Here is one definition I found on Dictionary.com--including etymologies, such as are available:
From the American Heritage Dictionary (AHD)
school·marm (skōōl'märm') n. --A woman teacher, especially one who is regarded as strict or old-fashioned.
Schoolmarm is a a compound of the word school and the dialectal marm (variant of ma'am).
According to the AHD, the etymology of school is as follows:
[Middle English scole, from Old English scōl, from Latin schola, scola, from Greek skholē; see segh- in Indo-European roots.]
Ma'am is itself a dialectal variant of madam, which, according to the AHD is derived from the Middle English word madame, which itself is derived from the Old French ma dame (which, if I'm not mistaken translates as "my lady")
There you go. The etymology of a schoolmarm.
For the origins of this schoolmarm, read this post.