DIMA: what do you mean with "traditional" teaching?
All teachers/music schools who teach reading before the student can actually do something on the instrument. Ideally, if a person is a beginner, he/she should first learn the piece or the formulas used in the piece, and then find out how to write that down in our musical notation. This *can* be done, but it requires a lot more from the teacher. As I understand, the Suzuki method works that way. That's also how gipsies pass on their art - no notes, but still great virtuosity.
what SYSTEM do you refer to?
The teacher you are now with and his/her ideas about how to teach you.
what do you mean with DESCRIBING?
Reading just noteheads and determining their names very quickly is not a very exciting thing to do, so you want to learn that skill as soon as possible, so it can't bother or hamper you anymore.
What you really want is visualize what is BEHIND those noteheads - the structure of black and white on the piano, for example, and what hand positions you will be using. Sometimes the music looks really frightening, but all it turns out to be is a SEEMINGLY complicated variation on a simple chord (Chopin's "Winterwind" is an extreme example). In order to "see" such details immediately, you would have to know that chord already, and then find out through analysis HOW the composer created his variation on that known chord, and if there are any repeating figures, either in notes or in finger sequences.
If you don't know from your own experience (both knowledge and hand memory) what A minor, D minor and F major triads/chords look and feel like, it doesn't make much sense to learn Schumann's Horseman piece. If you do know those chords, please describe for us exactly what you see on that Schumann page, either left hand, or right hand, or both. It doesn't have to be theoretically correct. This is only about your perception of the notes. You might be missing something, which we can correct or open your eyes to.
EDIT: All this experiment is set out to do is to prove that you don't have to wait until you know the piece to be able to enjoy it. Even the process of learning can be VERY enjoyable.
