Listening attentively to my young students' playing has been quite a challenge -- one of the hardest things I have ever had to learn. It has brought about a significant change in how I think about music.
What is music? The question is occupying philosophers and music theorists now that "music" is increasingly defined as recordings. The discussions, which might seem arcane in the abstract, become urgent when viewed in the light of human experience. I take a broad view of what music is. That is, I find it has less and less to do with pre-recorded versions of the printed score and more and more to do with what individuals make of specific sounds.
Perhaps that's why I feel that my students would be as at home playing and listening to avant-garde as to more traditional music.