Nor, for that matter, does literacy necessarily have anything to do with schooling.
If you're old enough to remember Eric Hoffer, you know what I mean. Hoffer was one of the intellectual darlings of the New Left, back in the '60s and '70s. A longshoreman by trade, he'd never been to school, but was widely read in numerous disciplines.
Somebody once said about him, "being self-educated, he never had to read a bad book." One of the truest indictments of the American education system I've ever heard.
I had a teacher once who told me "If you can't do, teach. If you can't teach, teach teachers."
Lot's of variations on that one, KK. The original quote, from GB Shaw, was: "Those who can, do. Those who can't, teach." Somebody later on added, "Those who can't teach teach teachers how to teach."
A former neighbor of mine was Al Cullum, who literally invented the concept of creative play (his term for the idea that there's no reason learning can't be fun). It's probably long out of print, but his book detailing the concept was called Push Back The Desks.
One quick example. He discovered, in his classroom, a trapdoor leading to an unused storage space. He cleaned it out, and tacked math problems to the walls. The kids then had to earn the right to go down into "King Tut's Tomb," with a flashlight, choose a problem, and solve it. Imagine that! Elementary students competing for the right to solve math problems. Amazing what you can do when you make a game out of it.
At any rate, he'd finally decided it would be nice to get his PhD, and enrolled in an Ed School of some repute for that purpose. He stopped attending after about three months, because he was appaled over what was being taught under the guise of teaching skills.
They have taken the oath of the brother in blood, in leavened bread and salt. Rudyard Kipling