This is kind of a common question here, but one point I haven't seen addressed in detail:
While sight-reading, it is recommended to practice jumps (over an octave) without looking, which is difficult, but evidently possible after a lot of practice and effort. So far I have only seen one method for practicing this, but it is not very pleasant and a bit frustrating, as it does not give a sense of step-wise progression: The method I am referring to, is to just "try" to blindly find the right keys, where the "trying" is either guessing, or touching around the keyboard to find landmarks based on the black keys.
The guessing part is important for building the spatial awareness, but clearly there is no easy start, and the result is qualitative: "you either get it or not". So there is no real practice here, just absolute result.
The finding landmarks method is what I have most conflict with. Touching around the keyboard blindly is a way to find the position, but this is not something that will happen during real playing, so its not something you should get good at (is it?). It feels like a waste of time to practice this, and instead it seems way more important to practice looking quickly at the keyboard without missing the part of the score you are reading. But this is hardly ever addressed (and even frowned upon).
As an example for this in a real practice session, my hand jumps to the position of the new chord, but I am not sure if I am over the right keys. Shortly looking down will quickly tell me that I am just shifted by one tone, so its a quick adjustment. If I want to get this reassurance without looking, I have to remove the hand of the position altogether and start touching around for black keys, therefore the "jump" is lost, and suddendly I am training to find the position from a totally different one than the original set by the music.
Is there a reason for this? Do professional piano players really practice "touching around the keys" and do this in real time?