For significant change, society would need to ensure that problems are not repeated throughout every generation. To do so, common problems would need to be identified and systematically sought out and corrected — every citizen would need to be aware of these problems, their likely manifestation, and their remedy.
Some of the repeating ills of society include: divisiveness, discrimination, class/income-based inequality, distorted resource distribution, unregulated greed, unchecked power, unbalanced political influence, inadequate conflict resolution, substance prohibition, poor food quality, inadequate health maintenance, inadequate information dispersal, shortsightedness, fraud, limited recreation, and insufficient societal training.
Instead of frivolous information — such as sentence syntax analysis or trivial historical narratives or the application of esoteric formulae — society’s incoming members would learn of the pitfalls and dilemmas facing society and the ways in which these troubles are mitigated. Instead of a decade-long sequestration from the very society they are to inherit, these incoming members would be exposed to the inner workings of their society throughout their entire education.
For the sci-fi ending: Earth School