The “other” purpose of education is job training. There are as many jobs as you like, and so there is no one way to train people for jobs in advance of knowing, for sure, what job they are going to do.
The “classus” of “classical” education is simply the
One of the many social fractures of modern society is the fracture between leaders and their followers. A healthy society consists of a series of interlocking trust relationships between those who lead, command, direct and those who are follow, obey, and are directed. Good leaders are servants of their servants, and good followers love and trust their leaders. Neither expects perfection of the other and so both have patience for the other.
In a school, the basic transaction is the transfer of knowledge from teacher to student (or the mutual acquisition of knowledge, from a book, by teacher and student.) Therefore, the practical fundament are a time and place for teacher and student to meet. In the earliest schools, teachers performed these simple and basic fundamental administrative tasks.
Our modern context values specialization over generalization, and “expertise” of the “manager” (often false and sophistic) over the activity of the amateur.
In a classical school, teachers should lead and leaders should teach.
The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving. Proclus, A commentary on the first book of Euclid’s Elements, xii, trans. Glenn Raymond Morrow (Princeton: Princeton University Press) 1992, pp. 29-30. ISBN 0-691-02090-6.
Put differently, the quadrivium studies number in four modes: pure number (arithmetic), stationary number (geometry), moving number (astronomy) and applied number (music) number.