Confucius began private teaching without class distinction, so learning was no longer limited to nobles, and the Hundred Schools followed.

Spring and Autumn period to present
522 BCE · OriginIn the late Spring and Autumn period, Confucius began taking students at about age thirty, holding that education should be open to all and founding the practice of private teaching.350 BCE · EvolutionIn the Warring States period the masters of the various schools took many disciples and founded their own schools of thought; private learning flourished into the Hundred Schools of Thought.
Sources (2)
  1. Britannica: Confucius summary
  2. Britannica Kids: Confucius

Private learning is the passing on of knowledge by an individual who takes students, not by a school run by the government. Before it, schools were mostly run by the government.

In the late Spring and Autumn period Confucius began taking students at about the age of thirty. He held that education should be open to all, teaching anyone willing to learn, and so founded the practice of private teaching.

In the Warring States period the masters of the various schools each took many disciples and founded their own schools of thought, private learning flourished, and the Hundred Schools of Thought contended.

The name Xingtan, the apricot altar, is said to refer to the place where Confucius taught. This class is about private learning itself, and the six-arts curriculum is treated in the Six Arts Curriculum class.

Private Academies is the class in the chapter on Education on private teaching. It covers Confucius taking students from about the age of thirty in the late Spring and Autumn period and holding that education should be open to all, and the masters of the Warring States taking many disciples and founding their own schools of thought until private learning flourished into the Hundred Schools of Thought.