1580s, "untrained," from un- (1) "not" + past participle of school (v.). A verb unschool is attested from 1820.
Entries linking to unschooled
un- 1
prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").
The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.
It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
school n.1
[place of instruction] Middle English scole, from Old English scol, "institution for instruction," from Latin schola "meeting place for teachers and students, place of instruction;" also "learned conversation, debate; lecture; disciples of a teacher, body of followers, sect," also in the older Greek sense of "intermission of work, leisure for learning."
This is from Greek skholē "spare time, leisure, rest, ease; idleness; that in which leisure is employed; learned discussion;" also "a place for lectures, school;" originally "a holding back, a keeping clear," from skhein "to get" (from PIE root *segh- "to hold") + -olē by analogy with bolē "a throw," stolē "outfit," etc.
The basic sense of the Greek word is "leisure," which passed to "otiose discussion" (in Athens or Rome, the favorite or proper use of free time), then it came to be used for the place for such discussion.
The Latin word was widely borrowed (in addition to Old French escole, French école, Spanish escuela, Italian scuola; Old High German scuola, German Schule, Swedish skola, Gaelic sgiol, Welsh ysgol, Russian shkola).
The meaning "students attending a school" in English is attested from c. 1300; the sense of "school building" is by 1590s. Sense of "people united by a general similarity of principles and methods" is from 1610s; hence school of thought (by 1848). As an adjective by mid-18c., "pertaining to or relating to a school or to education."
School of hard knocks "rough experience in life" is by 1870; to tell tales out of school "betray damaging secrets" is from 1540s. School-bus is from 1908. School days is from 1590s. School board "local committee of education" is by 1836; school district "division of a town or city for the management of schools" is by 1809.