The Lord of the Rings discussion: Chapters 3 and 4

[Tuor of Gondolin]

Valandil's quote above (Frodo/Pippin) is actually quite revealing about Frodo's character (and, parenthetically, how PJ's movie got it wrong).
Frodo has some knowledge (presumably from Bilbo) about elvish history, character, and language. He is a responsible agent, able, to some extent, to read others motives and intentions, and even react with bemusement and objectivity to frustrating and/or unexpected situations. In a way, he's had to grow up when Gandalf isn't there rather like Bilbo in The Hobbit.
I don't recall any mention by JRRT anywhere of Bilbo's education of Frodo, but his "home schooling" must have been remarkably
deep, not just for a hobbit but for anyone of the late Third Age.

Speaking of which, were there any hobbit schools, or libraries?
Written literature was always relatively rare in pre-industrial societies, although given elvish longevity and scholarship, they would presumably have overcome this hurdle at least for themselves. Minas Tirith as the Library of Alexandria? And what of a similar library in Arnor?