Sorry for the late reply. I don't have much time to post here.
I believe I'm thinking too ideally.. if that's even possible. But still, it's a little sad that I have to often stare at my hands. The 'glaring down' has become.. more relieved, just a bit. At a slow pace I can read the music but I have to perpetually place my eyes on the music, then on the keys, and repeat.
Maybe it's because this is my first time playing a piece carrying such a LARGE range, really low As and stuff. I also have to mention that my sight reading is not too good, I can read notes relatively close to the staff, but once we put in more then two ledger lines, it can take me like 10 seconds to identify a note. My treble reading is very good, but my bass clef reading is something to laugh at. I still have trouble identifying notes on the bass staff... I should practice reading notes. I've been playing for a year and 2 months or so now.
Part of the reason why I memorized the piece was because in the book Fundamentals of Piano Practice by Chang, Chang suggests memorizing a piece before playing it. I played the piece hands separate slowly, then very slowly hands together, then memorized the piece and here I am. But that does not excuse my TERRIBLE action of looking at the keys.
Either way, no matter if it is my first long-range piece, all the more better to attend to working on what I have trouble on it. Namely, note reading and training my fingers to more accurately find the keys.
Rather then staring at the keys, I think I should start glancing every so often. I need to tend to shortening the glare time.
And yes, I did make a little error - by staring at my hands I mean the keys..! Excuse my adolescence. Adults use such precise English!
And, per the OP, this is a very big deal. As one of my coaches Dr. Thomas Mark quotes Edna Golandsky as saying: You can't miss (a note) what you are right over.
Further, as Dr. Mark suggests, the overall (paraphrasing) hand/body choreography of placing your hands, lower arm, upper arm, shoulder, and upper chest structure in line with a particular piece is crucially important.
What I am saying is that your eyes are a significant part of that OVERALL process. And, yes it is a comprehensive, in my opinion, process.
Can you explain Golandsky's quote? I'm a little confused.
How can my body be 'in line' with a particular piece? Is it intuition? Feeling?
Thanks for the help guys!