Sam Arbesman examines the educational ramifications of Hogwarts failure, notably that students only go to school for seven years (11-17) and aren’t actually taught any basic learning.
As near as I can tell, if you grow up in the magical world (as opposed to be Muggle-born, for example), you do not go to school at all until the age of eleven. In fact, it’s entirely unclear to me how the children of the wizarding world learn to read and write. There is a reason Hermione seems much more intelligent than Ron Weasley. It’s because Ron is very likely completely uneducated.
And even at Hogwarts, while they learn about spells and potions, they completely neglect the fundamentals. They are made to write essays on the history of magic, but are never taught to write. They take Arithmancy, but never learn mathematics.
Over thinking it? Sure. But certainly, something to consider when watching HP7. [via Kottke]