It is probably difficult for any 11-year-old to believe that he or she should be any different from all other 11-year-olds. I recall wondering at that age whether I was supposed to sound like everyone else who played the piano. It was not a pleasant question and it was a highly isolating one to ponder--it could certainly not be expressed aloud.
But I have seen an 11-year-old student become fascinated with the vivid drama of sounds in a composition that I found too troubling to play myself. Her insistence on the piece despite my cautions demonstrated to me as few other instances have in the course of my teaching, that there is a deeper level of mastery than simply being able to play the notes. In fact, one of the more amazing things about her selection was that the notes were awkward, involving complex hand positions and subtle fingerings as well as challenging dissonances of both tone and time (rests with
fermatas are not comfortable--they are, indeed, not supposed to be).
I call this mastery; perhaps the better word would be self-possession. How old were you when you experienced that while playing your instrument?
This child was taught in the manner I described in my last post: to give primacy to her responses to sound, whether from a printed score or in music that she improvised.