The ideas given above are quite helpful. A few additional comments…
Give students photocopies of passages being memorized–one to keep at school and another at home. Parents should always know (via newsletter) what passages are currently being memorized. Some review them during family devotions.
Introduce students to a variety of memory methods including motions, frequent short reviews, group oral practice, chanting/singing, picturing visuals. Some learn better in particular ways, but might not discover that unless you introduce them.
Consider giving them a sheet with only the first letter of each word. For example–for Psalm 23:1 TLIMSISNW