schoolroom (n.)

Middle English roum, from Old English rum "space, extent; sufficient space, fit occasion (to do something)," from Proto-Germanic *ruman (source also of Old Norse, Old Saxon, Old High German, Gothic rum, German Raum "space," Dutch ruim "hold of a ship, nave"), nouns formed from Germanic adjective *ruma- "roomy, spacious," from PIE root *reue- (1) "to open; space" (source also of Avestan ravah- "space," Latin rus "open country," Old Irish roi, roe "plain field," Old Church Slavonic ravinu "level," Russian ravnina "a plain").

Old English also had a frequent adjective rum "roomy, wide, long, spacious," also an adverb, rumlice "bigly, corpulently" (Middle English roumli).

The meaning "chamber, cabin" is recorded by early 14c. as a nautical term; applied by mid-15c. to interior division of a building separated by walls or partitions; the Old English word for this was cofa, ancestor of cove. The sense of "persons assembled in a room" is by 1712.

Make room "open a passage, make way" is from mid-15c.  Room-service is attested from 1913; room-temperature, comfortable for the occupants of a room, is so called from 1879. Roomth "sufficient space" (1530s, with -th (2)) now is obsolete.

[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.