If this method is impractical for you and your students, you might try having them copy out just a few measures or passage that they are having difficulty with. It helps focus the attention on what the notes are.
Another method for memorizing pieces is to analyse the piece harmonically. In other words, do a chord analysis, analygous to a grammar analysis of a sentence, like: definite article-noun-verb-preposition-indefinite article-noun. The music analysis would go something like this: The first chord is a tonic chord with the root on the bottom. Next is a scalar passage in the right hand, up 1-1/2 octaves, starting at the 5th of the scale. This method is the same idea as writing the music out, without the writing. It makes the player focus on the details of the piece.
When I was a child and a teenager, I used to memorize by playing the music over and over and over and over again. Pretty soon, I just had it under my fingers. I had what they call "good muscle memory". The drawback was that if I don't keep playing the piece regularly, I lost it. The two methods above do not suffer from this drawback.
A better way, I think, to apply muscle memory to memorization is to use the eyes as well as the fingers. In other words, watch what you're doing. Take the piece one phrase at a time, and play each phrase several times, watching the notes being played.
The bass is the life of a piano piece, I think, even though it sometimes doesn't seem that way. I have learned that if I focus on and memorize the bass part, the whole piece goes better. I have had some success memorizing the left hand and right hand separately in order to focus on the low part.
I think that the essence of good memorizing is to simply pay close attention to everything you are playing. Don't play blindly.
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