Actually, it's both. Here's an example. There's not enough light falling on the surface of the earth to have ANY possibility of running this country off of sunbeams. Those who mastered the multiplication tables in the third-grade can easily determine this to be true; those who did not master these fundamentals now run the government.
After my first year of law school, I was ranked 18th of 180 freshmen. I went to my advisor and asked how this could be - I skipped a third of the classes, didn't open a book until the week before finals, and so on, while my classmates lived in the library and dreamed in Latin.
"What's your undergraduate background," he asked.
"Uh, I have a Master's in math," I replied.
"Oh, then, you won't have any trouble in law school. You see, the purpose of law school is not to teach law - that changes every day! The purpose of law school is to train you to think like a lawyer! Since you already know how to think logically, deductively, objectively, you won't have any trouble."
"In general, we find that the students who come to us from math, the hard sciences, and engineering make the best law students. Those who majored in the soft sciences and business become the average law students. Those who studied the fine arts, education, and the liberal arts like English or History, well, they never really make it."
Bottom line: It's the memorization of the multiplication tables that led to mastering math which in turn guaranteed success in higher endeavors. You can't build a worthwhile structure on a feel-good foundation.
Which argues well for the one-room schoolhouse. The older kids teach the younger ones and the lesson is further imprinted.