Many commentators have argued that the recent grading controversy indicates just how important public examinations are. Up to a point, Lord Copper.
Romans did jobs, not ‘education’. Most who went to school (there was no state provision) probably learnt not much more than the basic three Rs (peasant families — the majority of the population — needed their children to work the land). A freed slave in Petronius’s Satyricon boasts that he knows ‘no geometry or fancy criticism or any such meaningless drivel, but I do know the alphabet and I can work out percentages and measures and currency’; Horace mocked pupils for being asked what is left from 1/12th subtracted from 5/12ths.
One option for children was to be sent away as apprentices. That required no fees: they paid their way by the work they did around the shop, though parents were asked for help with food and clothing. Young boys and girls were trained to be e.g. sculptors, builders, wool-carders, flute-players, stonemasons, weavers, bakers, gymnasts, cobblers, dancers, shorthand-writers, and so on. Epitaphs survive for girls aged nine, one a hairdresser, one a gold-worker.
As for the elite, from the age of seven for about ten years (depending on the rate of progress) they were drilled mainly in the art of rhetoric to prepare them for success at the top, i.e. in the legal profession and government — to be fluent orators and devious politicians, with excellent memories, skilled in debate, and masters of Rome’s legal, literary and political history from which to draw their arguments and analogies.And all without a single exam, since actually doing the job showed whether you were up to it or not (Virgil pleaded one case in court and gave up).