Our children learn one stanza per week of a psalm from the Book of Psalms for Worship.
I don't know who benefits more from this memorization - the children or me.
Here are five reasons why I teach these psalms to my kids:
1) God commands parents to teach "these words" to our children as we sit together, walk together (Deuteronomy 6). The Psalmist also "hid God's Word in his heart" (Psalm 119).
2) Memorizing songs is especially easy since the words often rhyme and since they can be sung and not just recited.
3) Knowing God's Word by heart will cause His Word to come to us in times of need even when we have no Bible handy. I have met old people who remember nothing anymore and don't even recognize their loved ones but when psalms they learned as children are sung to them, they begin singing too!
4) Our children are able to sing along in church and also pay better attention when we read the Psalms they know after dinner. I am thankful for this version of the psalms since it is so close to Scripture that the children can recognize when that particular psalm is read to them.
5) Many times my two-year-old has sung these Psalms as she plays near me. Unknown to her, I am being blessed by the words she sings. The other children also break into song many times and many times they just "happen" to sing the very verse of a Psalm I need to hear right then.