I really enjoyed this video (12 minutes), in which Piper shows a method for meditating on the scripture and unlocking understanding from the text. He also throws in, almost as an afterthought, (although I doubt that it is) the idea of teaching children by this method.

The method can be described as prayerfully considering the terms of a scriptural text both individually and in connection with the others. Properly done, this is distinct from private interpretation, even though it is begun by asking “what do I think this means?” It is conscious, deliberate interpretation rather than… accidental interpretation.

Meditating and deliberately considering scripture shows great respect for God’s revelation of himself in the text. It gives us a chance to consider our impression of the text and bring to mind connections with other scripture as well as life experience. We should undertake this prayerfully, expecting the holy spirit to teach and remind us of God’s word.

But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
John 14:26

When Piper mentions teaching children by expounding scripture in this fashion it suggests to my mind that this might be a glimpse into the practical application (or one of them) of this instruction:

And thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thine house, and when thou walkest by the way, and when thou liest down, and when thou risest up.
Deuteronomy 6:7