To a certain point, make sure you can describe with words what is going on in a piece. The deeper things in music are pretty hard to describe, but the structure of the piece and the superficial levels should all be crystal clear to you. Narrating the piece, actually putting it into words, helps unmuddle our minds and have clear exactly what is going on and what we are supposed to be doing each step of the way. Organizing your thoughts and the structure of what you are playing does not hinder spontaneity or emotion, it actually gives you freedom to be spontaneous and a more meaningful comprehension of the music. By really understanding the superficial goings on of a piece, a musician gains the freedom to start thinking of deeper things.
For example, to describe Mozart’s sonata “Semplice” in C major (the easy one everyone plays, K.545) you can start by saying:
The main theme starts with an arpeggio of the C major triad, going to the dominant and returning with a mordent on C; the second part of the main theme is in the sub-dominant resolving with a I-V7-I cadence. Meanwhile, the left hand has a Basso de Alberti realization. Our first bridge is made up of scales in the right hand going through each step in the diatonic scale while the left hand plays the chords in half notes….
There is no need to have an advanced knowledge of music theory, though. You can just as easily say to yourself:
The first four measures of the piece are the main theme, which is repeated in another key starting the third page (according to your edition). The left hand alternates between the the fifth finger and the rest, playing chords…
It is best to start from general things, and later on specify more and more:
The first half of the first page goes like this (sing the theme) which is kind of a singing theme, then there are a lot of scales that go on until we get to this other thing (sing it) which sounds kind of bouncy and then to finish it up, we have a kind of triumphant ending theme and the repeat sign. We have a middle section with the original theme sounding kind of gloomy and then….
The number of musicians who can’t really describe what is going on in their music in really simple terms is surprising. It will help you understand what is going on, and it is a very important skill for a teacher to have. The ability to describe music in words.