Many long-established village areas in the New Territories still have their shu sut, or study halls. These were much more than early village schools.
A significant agricultural surplus was essential to support a study hall; subsistence-level hamlets in Sai Kung or Lantau were unable to devote scarce resources to education.
The Chinese imperial examination system was abolished only in 1906. It had existed, with modifications, for well over 1,000 years. Widely praised by 18th-century European Enlightenment thinkers - most notably Voltaire - who favourably contrasted the (relatively meritocratic) Chinese system with inherited (and for the most part, thoroughly undeserved) aristocratic privilege that was then the norm in Europe.
Village schoolmasters were men who had sat the examinations but failed to achieve a pass at what - to be fair - were almost impossibly high educational standards. The endless dumbing-down of contemporary academic life was not a problem that was suffered in traditional China, for all its faults. Those who had failed the examination were still respected as well-educated men. And as Chinese scholarship was seen, first and foremost, as moral training, all education was inherently worthwhile, whatever its extrinsic economic value.
In addition to their teaching duties, schoolmasters were called on to draft official letters in suitably florid prose, write auspicious couplets to paste outside doorways at Lunar New Year and other festival times, and write lucky characters (believed to be intrinsically imbued with mystical qualities) to be pasted on rice bins and other food storage items.
Most village children needed to work as soon as they were physically able. But that is not to say that the most promising rural children went without an education. For a bright village boy exposed to what - at its best - was a completely meritocratic system, advancement to the highest national bureaucratic levels was possible as long as they passed the examinations. To this end, whole clans and villages would club together to give promising candidates the best chance of success. And of course - if they did succeed - significant advantage would eventually flow back to their home towns. Study halls in wealthier agricultural areas usually had a few long-term boarders from more remote and backward places.