"the science of teaching or education," 1838, from Latinized form of Greek paideutikos "of or pertaining to teaching," from combining form of pais "boy, child," especially a son, from PIE root *pau- (1) "few, little." Also see -ics.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit potah "a young animal," putrah "son;" Avestan puthra- "son, child;" Greek pauros "few, little," pais (genitive paidos) "child," pōlos "foal;" Latin paucus "few, little," paullus "little," parvus "little, small," pauper "poor," puer "child, boy," pullus "young animal;" Oscan puklu "child;" Old English feawe "not many, a small number," fola "young horse;" Old Norse fylja "young female horse;" Old Church Slavonic puta "bird;" Lithuanian putytis "young animal, young bird;" Albanian pele "mare."
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.), a 16c. revival of the classical custom of using the neuter plural of adjectives with Greek -ikos "pertaining to" (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their English names before c. 1500, however, tend to be singular in form (arithmetic, logic, magic, music, rhetoric). The grammatical number of words in -ics (mathematics is/mathematics are) is a confused question.
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Harper, D. (n.d.). Etymology of paedeutics. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/paedeutics