Paideia is a Greek word for formative education.
Plato said that a student, "is rightly trained in respect of pleasures and pains so as to hate what ought to be hated, right from the beginning to the very end, and to love what ought to be loved."
It was the objective of the ancient Greeks to train their children to be fully Greek – to think like Greeks, to act like Greeks, to love what Greeks love, and to disdain what Greeks disdain – so that they could take their places in the Greek city-state and thereby perpetuate their culture. This process of enculturation was called Paideia and the Greeks at the time of Christ were steeped in this concept.
Capitalizing on this word that the Greek Ephesians associated with ideal enculturation, God, through Paul, commanded Ephesian fathers to bring their children up in the Paideia of the Lord. (Ephesians 6:4 uses this word, "Paideia") The intent was not to train them to be Greek, but to train them in the Lord – to think like Christ, to act like Christ, to love what Christ loves, to disdain what Christ disdains.
The same command extends to us, and Paideia involves more than reading the Bible and participating in Church on Sunday. It is a process that prepares our children to understand and interpret how God is revealed in all things and to live in a way that recognizes His kingship and authority over everything.
Paideia is an appropriate name to remind us that we are following Christ's command to enculturate our children in the Lord, and thereby to prepare them to engage this world and affect it for Christ's glory.