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.

It is utterly fascinating that adolescents, just arriving at self-awareness, are patient with details when allowed to be. A four-hand work by Mozart is exquisitely crafted of one detail after another, combining likely sounds with unlikely rhythms or the other way around, in maddeningly unpredictable fasion. This makes rattling the piece off completely impossible, as those pesky sounds have a way of increasingly disturbing our equilibrium as we become familiar with "the music"--whatever that is!

I contrast their fascination with the memory of my own impatience at their age, feeling always the pressure of not measuring up and, in turn, being quick to look down my nose at anyone less accomplished than myself.

In a climate of mutual awareness one learns self-awareness. The two together are critical to a grasp of the artistry of Mozart.

I can't imagine anything more satisfying than seeing the face of a fifteen-year-old light up at the realization that she can make some ordinary chord progression sound like the best idea in the world by noticing how the overtones mix and letting her fingers respond on the piano.

It is the light of artistry. It is mastery. It is, to be sure, fleeting because the girl does not spend hours at the piano. But it is an experience that never comes to many young people who do spend those hours at the piano because their hearing has become jaded with too much external product and not enough inner awareness.

Memorizing the alphabet, counting reliably to ten, getting the notes of the scale in order--any of these details, if imposed too soon, can block the flow of magic that creates music and poetry or stimulates fascination with numbers. People who were always good at these rote-learned systems are probably as shocked as I was when I first heard people talk about how restrictive the alphabet actually is, or how many words the Inuit people have for snow.

This morning I was reading an essay by Alison Gopnik in the August 16 New York Times on the subject of how young children characteristically explore, as opposed to adults who exploit. Taking tone as the object of exploration young children should be encouraged to move freely within a range of sounds that correspond to the ringing of bells or the piano played with the pedal down. This is quite the opposite of the fashionable regimen of Mozart CDs.

Young children, once aroused by this vast mysterious richness, don't lose interest in sound. On the contrary, they hear and respond confidently to aspects of tone that the force-fed, young and old alike, miss.

The difficult words in my letter to the Times are: "in an environment of mutual awareness." That environment in music study is created by open-minded listening. This is not the kind of judgmental listening we know from years of being listened to critically, that is, of being constantly compared to someone else.

I mean the listening one brings to a concert of new music by unknown composers. Isn't every student of music potentially a source of the new, whether new music or fresh synthesis of old material?

Having heard too many cliche performances of Beethoven sonatas I do not how to find in them the breathtaking sounds that my student finds. He has been improvising on the piano since the age of seven. He knows the piano in ways I do not.

Our hackneyed ears are making us immune from contact with atypical players and also from the potentially mysterious elements of familiar music.

"Continuing" my letter to the Times: The learning that all children need is gross motor coordination, and trust in their perceptions. After receiving premature praise for fine motor skills it can be difficult for gifted children to deal with the reorganization that accompanies gross motor learning -- that is, having to learn at age nine or ten skills that are best learned effortlessly at age five or six. In the rush to get alphabets and numbers down many pre-school programs short change the essential gross motor bases of rhythm and balance.

Part of the "mutual awareness" aspect of my teaching is ensemble improvisation. I play something moody, mercurial, wildly lyrical, while they dance around playing various percussion instruments. Sometimes we do more organized gross motor percussion games. These activities are not met with resistance.

But the perception part is harder. Learning to rely on immediate perception rather than on memory is just plain hard. The smarter the child, the quicker the memory, and the easier it is to mask the need for that instant of confident response that is the sign of real autonomous thinking.