Just as in sight-reading, analyzing measure by measure helps students memorize fast and gives them tangible clues to remember when their fingers fail them. 

• This measure is a G major arpeggio staring on B.
• These three measures are a sequence, each one starting a third above the last.
• This is a d harmonic minor scale with an added A flat.

• Try the "first chance method" at the beginning of each practice session and lesson. Sure you can play it when you've been practicing for half an hour, but how does it sound the first time though?
• Use a different copy of the piece for each lesson and mark only that week's mistakes. Or use a different color pen for each week so you know what needs fixing now.
• Get lost in the middle? Copy the piece and cut it up into sections. Pull a section out of a hat and start there.
• Get similar sections confused? Copy the piece and cut up similar sections. Line them up in the order they appear in the piece and note how they are different. (#1 has a D major arpeggio then goes up to E, #2 does the same but goes down a third to B.)
• Test yourself on that tricky section by writing it out.
• If you're not a pianist, play the tricky parts on the piano 
• Play looking at the music two times for every time you play without the music to make sure you are not memorizing your own version.