In Greek, our word for play is paidia and the word for education is paideia, and it is very natural and right that these words should be entangled at the root, together with our word for children, paides, which gave you your words pedagogy and pediatrician.
Plato at the Googleplex: Why Philosophy Won't Go Away (ed. Pantheon, 2014) - ISBN: 9780307908872