Lastly, and this was advised from Josh Wright and I agree with it, feel free to sight read a piece a couple of times. It is still sight reading, and the general idea of sight reading is to improve recognition of notes, which is more easily done if you work with the same combinations multiple times.
This is a good idea. I would go a step further: take a piece you do not know and first read through it silently, not at the piano. Reading is about pattern recognition. See if you can recognise familiar rhythmic elements, melodic elements or harmonies. Then try to sing the melody (always without the piano). Also look for anything that might be tricky: a change of key, some sudden fast notes, a rhythm you aren't used to, or a passage with a lot of accidentals.
Now sit down at the piano and read through the piece. Do your best to keep a constant tempo, but don't make it too fast! Concentrate on the essentials: rhythm, melody, harmony. When you've read through it, take a moment to reflect on how it went. Were there passages where you lost the tempo? Did you catch all the important accidentals? Were there passages where you totally panicked?
Now read through it again. You might play it a bit faster, but this isn't the most important thing. The second time through, try to pay more attention to expression and dynamics. Try to get to the essential of what's important in the piece.
As to the choice of pieces to read, be adventurous! Of course it's good to read pieces that are within your technical limits, but sometimes it can both fun and instructive to try something that's probably too hard for you, even if you play it slowly with loads of mistakes. The important thing is to read good music and try to instantly make sense of it. When you get to the stage where reading through a piece gives you a pleasurable, emotional musical experience, nothing will stop you: you can spend countless hours going on wonderful voyages of discovery.
I saw that somebody had invented an app that was meant to help with sight reading. It would give you ever-changing random combinations of notes and rhythms. The idea was that you would be
really, really sight reading since it was sure that you would always be presented with a combination of notes you had never seen before. I think this is a dreadful idea: it's like trying to learn to read a language by ploughing through random combinations of letters. To learn to read, you need to read things that make sense, that tell a story. With music, it's the same.
Topic: I need to improve sight reading skills