Having grown up attending Christian school and church, I've memorized much scripture. The problem is I know a verse here and there but not entire passages. I also must confess that I've let much of my memory verses go, having forgotten them long ago. I know that memorization is important because Psalm 119 says hiding God's Word in our hearts will keep us from sin.
So this year God has impressed upon me the value of scripture memorization, partly due to John Piper's book When I Don't Desire God. He teaches many ways to use God's Word in our fight for joy, and memorization is one of them. He cites another book that gave him a systematic way to memorize entire passages, An Approach to the Extended Memorization of Scripture by Andrew Davis. I started using his memory method, and it has been the most beneficial system I've ever tried. I've never had much difficulty memorizing, but this has been even more effective for me, especially as it pertains to whole chapters and then some. I want to share it with you, in case you might find it helpful. I'll explain it here, but you can also go to the website and read the book. You'll find this information on page 117 of the pdf file in Chapter 8.
The basic plan is to read a verse with the reference 10 times, then recite the verse 10 times. The next day you recite that same verse. Then you read the next verse 10 times and recite it 10 times. The following day you recite both verses. Then you read the new verse 10 times and recite it 10 times. You just keep adding a verse a day and recite all the previous days' verses together.
I've personally been working on the entire chapter of Romans 8. Today I am through verse 31. It just blew my mind this morning when I realized I have memorized 31 verses. THIRTY-ONE! Mind you, I don't have all of them perfect yet, but it will come. It is okay to look at the verse when you hit a snag. Eventually, it comes.
I believe it's biblical to pray over your memory work. Ask the Lord to use His Word to work whatever He wants to accomplish in your life. It's amazing the new meat you will find as you meditate on His Word in this manner. You'll see things that you haven't seen before, and then when you are sitting under preaching and teaching, you'll find many things that relate back to that memorized passage.