We do well, it seems to me, to distinguish Greek education from Roman. The Roman’s were masters at making things last (like, for example, their empire). They weren’t necessarily very good at making things good. The Greeks were not so good at making things last, though this problem can be exagerrated since the pragmatic Roman republic put an end to their independence after about 500 years, depending on how you look at it.
But the Greeks wanted to know what made things good. They were after essences. They either refused or failed to impose external structures on the learning process. As a result, they reached staggering heights of creativity in every field. The Romans did a good job imitating them. I would suggest for your consideration that the Romans made a fatal mistake: they systematized education.
Since then, everybody has imitated them – or so it seems to me. So we’ve never surpassed the pedagogical, artistic glory of the Greeks.