What does “polishing” mean?

There are two main parts of learning to play a piece:(1) Basic mechanics — understanding which fingers play which notes, how long notes are held, how to follow the notes on the page, and so forth.(2) Polishing!
Polishing is when you put all of the pieces together and combine them so that the piano playing sounds musical.  This step can be difficult to grasp when you don’t know how the final musical piece (or musical exercise) should sound.  With some experience, piano students will develop a good sense of “how it is supposed to sound” just by working on the mechanics,  without hearing the finished piece played, — but in beginning students that sense is undeveloped.
When the student has figured out the basic mechanics, it can be helpful to listen to a recording of how the musical piece is supposed to sound.  There are many examples on https://youtube.com of people playing songs from the Piano Adventures book.  With knowledge of how it is supposed to sound, now the student can use the mechanics and put all of the pieces together — polishing — so that they can play the piece as it is intended to be played. 

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