Songs that actually teach you specific things, like Tom Lehrer’s “The Element Song” for instance. They don’t have to be comedic, though. For instance, I recall a song from Golden Bough’s *Winter’s Dance" album, “Logs To Burn” Bing Videos
Any others?
My entire understanding of American History up to the fourth grade was based on the songs of Johnny Horton.
The Hokey Pokey teaches you how to do the Hokey Pokey
A life lesson nobody needed…but it fits. 
Do these two count? They’re not like a lesson at school, but teach you valuable skills.
Tool - Die Eier von Satan (teaches you how to bake hash cookies)
The Clash - Know Your Rights (teaches you what you’re rights are. Joe Strummer introduces the song with “This is a public service announcement, with guitars!”)
On that note, the Time Warp should also count.
Oh, yes.
There are countless dance songs from the 1960s that purportedly teach you how to do the latest dance. If you haven’t actually seen someone do those dances and just relied on the lyrics the result would probably be hilarious. That’s my YouTube idea for the day. Feel free to steal it.
Weird Al “Word Crimes”
Nearly everything I know came from Schoolhouse Rock! songs.
Schoolhouse Rock! - Wikipedia!
I can’t believe nobody has mentioned the Schoolhouse Rock! videos. I watched them every Saturday morning from age 5 to 7 and learned a lot from English grammar to math to American history and civics.
I later got the videos on DVD for my son (and for nostalgia’s sake).
ETA: ninjaed by one minute!
After Schoolhouse Rock! came Histeria! A sample:
Let’s not forget:
When I read the thread title what first came to mind was Harry Chapin’s ‘Cat’s in the Cradle’, though it appears the thread is shaping up to be about songs that are actually teaching lessons as in a school setting, not morality-play type songs where the lesson is, in this case “don’t ignore your kids while they’re growing up, or they will abandon you in your old age”. Well, they’ll probably abandon you anyway, but you don’t have a chance in hell if you ignore them as kids.
No morality plays or “love sucks!” songs, please.
Actually, never mind.
I guess “Doe, a deer” teaches you the scale?