I have an ancient Latin dicker - Cassell's of unknown date. It gives educare as the root for educate, educere for educe. Up the other end, things are less clear.

educatio - bringing up, training, education, from educo, found in Cicero - educatio liberorum

educator - one who trains or brings up, a foster-father or tutor (Cic. again.)

educatrix - foster-mother or nurse (Cic.)

educo (1) to bring up, rear, educate (Cic. and Livy) educo (2) (educere quoted) to draw out, lead out. eg of gladius from (sheathe?), lots, to march troops out, to lead before a court of law, to take a ship from harbour, to bring water by an aqueduct, to raise up, to praise sky high, to bring up, to rear a child. (Cic, Liv, Caes. Verg. et al)

It looks as if the two meanings were about in Rome, and overlapping.

Penny