Hi one more time Zlia,
I 've just looked once again through your posts to this thread and to another one ( beginner pianist ). Well, if you manage to play the Adagio from the Moonlight..., then you are not the very beginner... Much compliments to that!!!
I liked the advices of Rojo, and I can add to the recommended list Die Kinderszenen of R.Schumann - there are pretty much of them , you can choose the easiest one and practice to memorise it.
You mentioned that you would like to improvise too - my very first choice is Improvising Blues Piano by Tim Richards. It is the best Do-It-Yourself book I ever had, 2 cm thick, full of examples and pictures of the strange looking guys torturing their shabby looking pianos . It begins with the very basics and ends with the Honky Tonk Train Blues, which is a challenge for a pianist of any level. Much to learning scales, chords and improvising - Schott & Co London, 1997 , ISBN 0-946535-97-3.
To your memorisation problems - now I guess they can be much similar to those which had a few of my pupils who learned to play piano as the second instrument (after a flute or violin ). They would normally first think of the melodic line and not of the harmonies ,and tend to play it from the score, which can work until you have to make the first leap. So the only way to get a flow in your performance is memorising the patterns, if not the whole piece.
Now a bit more specific about what you called "my method" ( which is actually not mine ) -
as you play piano by heart ,you must normally think of the harmony and melodic line simultaneously. It's extremely difficult to memorise the piece if you have no idea of what are you actually playing. The melody is normally only the upper voice, the rest are chord tones. Surely you must keep in mind the inversions, voicings , bass figuration as well, but it is significantly easier if you see the basic line.
Some practice-
- try to analyse the harmony of the piece you are playing. The good example here is Präludium 1 C-Dur from WTK of JSBach, which consists of the arpeggiated chords , no melody above. Moonlight Sonata can suit as well , but I'm not sure C#m is the easiest key to begin with. In Bach's Präludium, try to find out which chords you are going through. Write them down as the chord symbols, play each one as a chord and as an arpeggio in both directions until you see all the chord tones on your keyboard. Then close the score and try to play by heart the first 4 bars - I guess it will be no problem by now.
- try to think of the chords in terms " Root - Dominant - Sub..." - you know. Do it as you're just beginning to exercise the piece. Every harmony has its place in the piece and its logic. You may as well try to play the said first 4 bars of Bach as a chord progression and even place a melody of your own above it. The main point is, you should know, which chord is expected to come next and where your hand must approximately go. Then you of course must think of the bass figuration, invertions etc - but the good half of your job is already done.
I really do memorise the music in this way and can state it works on Chopin not worse than on Ellington. Hope it will help you too -
best regards
Andrew