The protestants have us beat on this. Memorization of Scripture is seen as important, every Sunday school kid has a memory verse for the week.
They sing many songs that are Scripture and songs are such an easy way to memorize things (that is also the reason we need to be careful about the Theology in the songs we sing).
I know the books of the New Testament in order because I learned them in a song when I was a little girl. Same for so many Scripture passages.
For example, I know a childhood song that goes like this:
"Beloved, let us love one another
For love is of God
And everyone that loveth is born of God
And knoweth God
He that loveth not
Knoweth not God
For God is love
Beloved, let us love one another
First John four seven and eight."