correctional (adj.)

mid-14c., correccioun, "authority to correct;" late 14c., "action of correcting or chastising, rectification of faults (in character, conduct, etc.) by restraints or punishments," also "a bringing into conformity to a standard, model, or original," from Old French correccion (13c.) "correction, amendment; punishment, rebuke," from Latin correctionem (nominative correctio) "an amendment, improvement," noun of action from past-participle stem of corrigere "to put straight; to reform" (see correct (v.)).

Meaning "an instance of correction, that which is proposed or substituted for what is wrong" is from 1520s. House of correction "place of confinement, intended to be reformatory, for those convicted of minor offenses and not considered as belonging to the professional criminal class" was in an English royal statute from 1575.

suffix forming adjectives from nouns or other adjectives, "of, like, related to, pertaining to," Middle English -al, -el, from French or directly from Latin -alis (see -al (2)).