In traditional Chinese culture, does "elementary school" mean private school?

"Primary school" initially referred to the primary school for the children of the nobility. "Primary school" was first seen in the "Dai Dai Li Ji - Paul Fu chapter": "and the Prince of the young long know (women have) color is in the elementary school, small scholars learn the Palace also. ...... The ancient people were eight years old and went to a foreign house to learn small arts and fulfill small rules." During the Western Zhou Dynasty, the heyday of the slave society, people were divided into classes, and only the aristocrats were able to receive education at that time. This type of school to teach literacy to schoolchildren, Xu Shen "Shuowen Jiezi Narrative" cloud: "Zhou Li" eight years old into the elementary school, Bao's teach the state son, first to six books." Duan Yucai note cloud: "the state son, the Secretary of the children of the great, the teacher's teaching, the Paul's raise, and the son of the world is also teeth. The six books, the text of the sound of righteousness is also the total collection." On the small arts, "Zhouli - Paul's" said: "Paul's in charge of admonishing the king's evil and raise the son of the state way, is to teach the six arts: one said that the five rituals, two said that the six music, three said that the five shooting, four said that the five harnesses, five said that the six books, six said that the number of nine." And "is taught the six rituals: one is said to sacrifice of the capacity, two is said to guests of the capacity, three is said to the court of the capacity, four is said to the capacity of the funeral discipline, five is said to the capacity of the military, six is said to the capacity of the car and the horse." Visible in the Zhou Dynasty education, elementary school refers to the study of the six arts (small arts) and six rituals (small sections), and then the meaning of elementary school gradually narrowed down, only refers to one of the six arts "book", that is, refers specifically to the study of language and writing.

The Eastern Han Dynasty's Cui Shi (崔寔), in his "Monthly Orders for the Four Peoples", wrote: "In the first month of the lunar calendar, before the start of agricultural work, children above the age of 18 were ordered to enter the Great Learning Center (太学), to study the Five Classics (五經), and were not allowed to see the Bingxue (冰释), and children were ordered to enter the elementary school to study the chapters. "Primary school" contains the meaning of the text began here.