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I don't think memorising level 1 pieces is going to be that much of a benefit. I have difficulty learning easy pieces. There's little or no intellectual engagement. I'm better off when there's more going on and the techniques aren't easy enough to pull off in a couple of ten minute bursts.

Give me a difficult passage with awkward fingering and blind asymmetric leaps and I'll have it memorised before I can play the blessèd thing at half speed.

Analysis is a worthwhile activity in its own right but it is also a crucial first stage in the learning process for some of us. It's the stage where you find out where the musical landmarks are by investigation instead of by hearing them through possibly flawed techniques. Where does the piece climax? Where does it build tension and where release? How should this passage be phrased and what is its context in the piece?

We need to build physical techniques for playing, we need to develop reading skills because it's the only direct means of communication we have left with the masters who wrote many of the works we now play and we need to build memorisation techniques so that what we learn is not forgotten. This doesn't mean we have to memorise our pieces and play without the score but we do better knowing the music and how to express it beyond what's on the page. Any good reader looks ahead in the score not at the notes they're currently playing - in other words they read a measure, and play it from memory as they look ahead at the next measure. They recognise chord shapes, scale runs and arpeggios from memory of the patterns not from reading the individual notes rapidly.

Anyone who improves a piece of music by repetition is memorising the music, consciously or not. So whatever we do at the piano for practise should involve improving our technical equipment, our reading ability and our memorisation ability. It doesn't mean we have to memorise all our pieces - that's a discipline reserved for those that prefer to work that way and those that want to enjoy the benefits of mental play and practise away from the piano.

For those that audiate from the score rather than just recognise the notes reading imparts so much more and effectively allows playing by ear what's being audiated from the score. My own memory is sound based not staff based and I can only write out the score by working out the notes from memory not by seeing the score in my mind's eye or memorising the staff.

I don't hold with the notion that memorising is wrong (for this thread) or that mentioning features of the music that might help the memorisation is wrong (even if all we're memorising is the expression in the music). Just knowing (or feeling or hearing) that the music moves from tonic to dominant, for example, and thereby increases the tension allows our creativity to enhance that tension in our playing, our audiating or our listening whether we get louder or quieter or faster or slower or just make subtle alterations. This is musical expression. This isn't written into the score. It is memorised. Perhaps for some it is done afresh each time but I suspect they'd be in the minority. You remember how the music goes - not the notes, any old reader can do that - but the music, the interpretation, the passion, the personalisation.
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I use the metronome differently too. I use it to restrain myself and increase my control not to chase tempo. I prefer to increment it When I feel it's holding me back - I don't increment it and try to keep up with it. I have a speed at which I can practise a piece without error periodically through the year and only take it up to tempo for a week or two now and then. Speed comes from practise, repetition, assimilation and confidence not from trying to catch a faster hare though that might increase the motivation periodically or test the ability.

My own method is to practise only as much each day as I can hold in short term memory after a few plays. I have generally memorised the sound of the piece by listening and audiating daily before I venture to the piano. I preview a passage by playing it mentally, then actually play it, then review my performance. I repeat that between three and seven times. I use fewer repetitions as my confidence grows in the passage. When I can play the notes correctly from memory each day I move on to the next passage but keep the previous material, still in short phrases, until I can also play them with the correct phrasing, dynamics, pedalling and articulation every time too. For a while that's done daily but as I progresss through a piece early material gets repeated only every few days or weeks etc.

I may still need to get out the score for another week or two each time I go over a passage but this gradually reduces. When I can play all the passages without getting out the score I'll start putting them together in larger units if I haven't started doing so already.

An easy piece that's playable, slowly or otherwise, from the score may never get memorised unless I specifically want to add it to my repertoire. Bach preludes, Clementi sonatinas, Chopin mazurkas and Grieg lyric pieces are among such pieces for me. They consitute my reading matter at weekends. I could manage many of them most of the way through from memory, I'm sure, but I don't feel the need to try.

For the more advanced musicians on this thread, what do you think about a "Concerto Analysis" thread? It would be in the Pianist Corner board, and would be basically the same as this one except 1) we would analyze concertos rather than solo pieces and 2) we would go more in-depth with the analysis. I could initiate the thread and try to keep it on topic.

May I ask what your "difficult" repertoire is, Richard?

I don't think Polyphonist was trying to catch you out, Richard. I think he was commenting that what you listed as easy sight-reading material for you would be quite challenging for many players.

For me, just working on a passage multiple times from the score does not lead to memorization.

So when you're practicing a piece, you pick a short section, you commit it to at least short-term memory enough that you can play/practice it through slowly and correctly several times?

Yes, I think you're getting it. I only practise what I can hold in short term memory. I never practise with the score - that's reading.

I might answer that better if I understood the thrust of the question. I'm not sure what you mean, especially by the wink!

Since this thread is for everyone, and a lot of people are learning, I'd like to clarify this. You are using the word "practise" and you are saying that if one uses the score, it is not "practising".

I only practise what I can hold in short term memory. I never practise with the score - that's reading.

...can you hear that in the second group of sixteenth notes it goes up to Eb...And then can you hear that the note on the third beat, coming down from the final C in the second group of sixteenth notes, is Bb?

The wink on this site is not really a wink...

Listen again to my Grieg Notturno, Chopin Nocturne or Liszt Consolation. There are no patches where every note is piano or forte. I didn't get lucky on the day with the dynamics. Each note of each phrase is worked out and worked on. It's like this from day 1, albeit slower. I don't write dynamics into the score to show how a phrase is rising, falling and inflecting. I memorise it and practise it that way from the start.

Yes, I can.