Sight-reading at the piano must be one of the most complicated activities known to humankind. Ask yourself which is faster, your visual response or your ear response. Most people would say visual, simply because the ear response is so much harder to locate, to identify, to become aware of.
In fact, however, it has been measured: the auditory response time is 200 times faster than any other sensory input in our brains.
But, since most of our training in all of education is based on cultivating rapid eye/hand or eye/brain responses, we have grown accustomed to mistaking that habitual speed for real speed. It is, in fact, quite slow in comparison to sound and to sound response.
Today I had an experience of this with one of my prize students, with whom I have worked for a very long time trying to find what she calls "the music part." I had her pick a brand new page (she picked the last page of In Winterszeit II in Schumann's Album for the Young), then find a measure whose sound she could anticipate with some certainty. It turned out to be the last chord, and, in fact, not so simple in that it comprised a tied sound and a pedaled bass.
When she played the chord it did not match her anticipation. This was fascinating. As we backed up to approach the sound the complexity of Schumann's ear became increasingly evident and overwhelmingly stimulating, While an experienced musician might see an extended C major passage with some deviations, there were detailed fluctuations of sympathetic vibration so rich that the sound she ended up with had a life of its own, dependent of any visual predictability.
This is what I call real reading at the piano. There is nothing elementary about it except that children hear that way until they are discouraged, alas too soon and too often, from paying that kind of attention.