eventhough i really did practice the piece.
If you really want a good learning curve, you should have a good look at your own playing, and try finding out what your technical weaknesses are.Then find a good etude who handles that problem and work your ass of on that one If you think you handled most weaknesses enough, go work on a serious piece and handle every difficulty you encounter on the stated above. Thats mainly it i gues gyzzzmo
Also, frankly, at 1/2 hour a day your progress is going to be slow, even with extra time on the weekends. Is there any way you can increase it to an hour? I would call that the absolute minimum daily requirement. 2 hours a day is even better, then I can almost guarantee you will see good results if you use your time well.
Half an hour can be a lot if used wisely! Spend 5 minutes to warm up, then work on the hardest part of the piece for the rest of the time - or two hard parts. Next day repeat the hardest part a few times at a convenient (slow) tempo where you don't do mistakes, then concentrate on the next part. This process will speed up gradually because everyday you get an easier part, meaning that you can do up to four, maybe even five parts after a few days. Every single day there will be an improvement. There is virtually no reason to play through the whole piece every day because doing so usually means that you are practising mistakes instead of the right thing.
I'm not convinced. Students need to spend a lot of time just to develop their muscles and their hand/arm/eye/brain coordination. Maybe a professional can maintain their performance level with half an hour a day, but I kind of doubt that too (at least if they're doing it on a regular basis).And if practicing the whole piece means practicing mistakes, something is wrong somewhere...
after i practiced i always feel i did a good job and already worked on my mistakes but during my lesson it didn't turn out so well. I also get scared when i have my piano lesson. I don't know why. I feel different or confident when i'm alone practicing than get nervous when someone is listening. So sometimes i made a lot of mistakes.
Oh yes, I like guendola's idea on pretending your teaching is listening, it helps with performance anxiety during your lesson, or why not try the composer himself?
well yeah, when i'm unable to manage a simple piece like the first movement of the italian concerto after practising for like 4 months.