In the mid to late 60s in elemetary school in south eastern Virginia, we were taught

Erie Canal
Old Dan Tucker
Get Along Home Cindy
Wabash Cannonball
I've Been Working on the Railroad
Big Rock Candy Mountain
Clementine
She'll be Coming Round the Mountain
Oh Susanna
Pollywoddle Doodle all the Day
Skip to my Lou
On Top of Old Smoky (and parody On Top of Spaghetti)
Camptown Races
Goober Peas

These were not taught (in the schools) to my kids in the mid to late 80's, early 90's.

Weird that I can only remember 2 they learned in school.

The Cat Came Back
Don Gato was a Cat

I'd say a good bet is to check out albums from the Seegers in particular Ruth and Peggy. There is a CD from Leadbelly that looks interesting. "Not for Kids Only" by David Grisman and Jerry Garcia looks good too. All on Amazon.com.

Good luck and thank you for attempting to revive interest in non-Disneyfied music.