I find it is very hard for me to sight read some pieces like beethoven appassionata or pathatique or even some of Chopin nocturnes. it is hard to sight read them for me both hands together. I have to sight with a slow speed then I can do with the normal speed after I memorize those pieces. Any tips to improve...Will be really appreciated? I feel I reached a level with sight reading and I can not exceed it.
Sight reading is a skill involving hand-eye coordination (like hitting a baseball thrown your way at 90mph). It takes practice. Much (if not all) classical music is composed to sound good; how easy it is to play is of less (but not zero) importance. Music practice is to some extent a matter of knowing how certain patterns in music (written on the page) map to muscle actions (fingers on the keys). Knowing more patterns makes playing things easier. Thus practicing scales, scales in octaves, scales in sixths, scales in thirds, etc. Knowing a bit of theory helps as one can use theory to fairly well guess what will come next. A knowledge of the style of a particular composer (or group of composers) all helps.
One learns to sight read by sight reading.
I'm late to the party, but here are a few modest tips from my years as a piano teacher:
When practicing, vary the difficulty of the music you are playing. Find the level of music at which you can sight-read nearly perfectly (ideally from a leveled book or a set of exercises), and use that music as one of the ways that you push yourself. As the exercises progress, so should you.
Much of the challenge of sight-reading, particularly when you are beginning, comes from being unable to see patterns quickly. When you are learning music, and have come to understand a pattern, (such as a left hand 1-5-3 pattern in this simplified Habanera) try playing around with it. Use different chords, play it in different keys, and generally spend some time experimenting with it. The idea is that, the next time you encounter a similar pattern, you will not have to spend nearly as much mental energy reading it; you will be able to glance at the measure ahead of you for some basic information, and otherwise keep your attention on other challenges.
Slowing down is quite important in order to dissect, discover, and understand what the composer has done. Once you have understood some portion of music, I am of the school of thought that it is better to play small chunks of the music at full speed than to continue to play through slowly. This accomplishes a few things for you: first, by not permitting yourself to go overly slowly, you are forcing yourself to work at reading speeds. Additionally, the actual motions that your hand makes for slow work are truly different than the motions that it makes for fast, nimble work. Thus, when you practice slowly, you are often not even practicing the correct hand-work.
Important caveat to #3: don't get into the habit of just playing through badly. If you are making a lot of mistakes, go back to carefully inspecting the music. You should be seeking the kinds of musical patterns and voice motions that will allow you to better remember the music. You will know you are doing a good job if you can come back and play the piece with very few mistakes. Also, this is not a play-through; this sort of labor is truly mental work, and can often be done away from the piano itself. As luck would have it, the kinds of things you will notice while examining the music extremely closely are exactly the sorts of patterns that will help you later when sight-reading, so this will become a virtuous cycle.