There are things that make a piano teacher's job easier, and others that make them harder. It makes a lot of sense for a student who is new to piano lessons to ask what those are. Reading any teacher forum will show there are frustrations with students "if only they would / wouldn't". What I've picked up over the years:
- Listen to what your teacher is saying, watch what he is doing, and do what he says to do when he says it. This isn't as straightforward as it sound. You can be thinking of your next question while he's teaching or wondering what he really means instead, not really paying attention to a demonstration. When you are to "do" whatever, you may be thinking of a different way of doing it, or thinking "I can't" (or saying it). If you are an adult you may be expecting it to be more complicated than it is. Accepting that it's really that simple is hard.
- Practise at least 5 days a week (4 is borderline).
- Practise what and how you've been told. If it's piece X, measures a - b, make sure you have done at least that. If you have been told to focus on counts, or producing an even sound, or remembering that F# in your G major piece, then focus on those things specifically, every time you practise. If you have been shown a way to approach it, then do it that way. Students will come back trying to impress their teacher with how musically they can play it, what extra things they have done, or what other piece they learned on their own during the week. What has been assigned comes first.
There are a couple of reasons for this. For one, your teacher is shaping your skills by giving you those things to do. If you don't do them, how can they work? Your teacher is also seeing whether what he has given you to do works, and anticipating the progress that will happen. If you don't do it, then you've thrown a spanner into it.
- Know that an experienced teacher will see that you have been practising those things, and often, how you practised, even if you mess up in the lesson because you're nervous in front of the teacher. It can be in how you almost reach for a note that you missed that shows the habit that started to form through consistent practise, some gesture, some hesitation or fluency.
- Most (good) teachers are looking to developing your skills and giving you the knowledge you need. They don't expect you to have those things already, because if you did, then you would not need lessons. You will be getting coordination for the piano, learn how to manipulate the keys and pedals, and your hearing will expand. That is, you'll start hearing when notes are uneven (loud, soft, mushy), when timing is off, and other things. You may have the potential to hear such things, but until you learn what to listen for, you can't develop it. These things will result in music that sounds rather good. In the meantime, your teacher is listening for those things
that they have been teaching you. Not for an impressive virtuoso performance.
- Students worry about the "talent" thing, become anxious about proving that they have it, and worry their teachers will drop them or will hate to have them if they don't have "it". This worry about talent will get students to try like mad to impress their teachers with "virtuoso" performances, which teachers will then see as someone who is "full of himself" rather than seeing it for the anxiety that it is. Anyway, it's rather useless advice to cite a preference for talent, since this isn't something for you to "do".
- Arrive on time, leave on time, pay on time. Take lessons for long enough (let's see a year at minimum - but think years), and make your commitment consistent week after week, even when the novelty wears off.
- You may worry about what your teacher thinks about you, but teachers are also performing a service for you. When you listen to them when they teach, and try what they ask you to do, then you are expressing appreciation for their work and knowledge. When you appreciate your own progress
rather than castigating yourself, this is actually an appreciation of your teacher's work. Most teachers hope that you enjoy the journey, but also understand full well that there are frustrations and days of doubt.
A lot of the rest is a matter of balance. A student who is indifferent to everything is like a wet blanket or dead wood. Curiosity gives the teacher an impetus to teach more. But jumping all over the place like an excited puppy that wants to smell all the flowers at once is not fun. Where do you find the right line for following instructions on one hand, and initiative on the other. The student who goes off on his own tangent can create a mess that the teacher has to clear up, but the student who never does anything on his own is dead wood. Doing a piece by Mozart? Look up Mozart. Is it a Gavotte? Look that up. Trying to study advanced theory? Make sure you can find middle C on the piano and play those chords you've been assigned first.
COMMUNICATE! If you are having difficulties somewhere, a good teacher will often be able to see and hear it as you play what you have practised. He may anticipate it, because most of his students stumble there. But there are times that you should tell him about a problem you are having. Nor will your teacher know that you are, say, interested in theory. Teachers often hesitate to go too deeply into things because of the many students who don't want to.
If you do ask about something and your teacher responds, then follow up on it. If he tells you to do some research, or explore chords, or write something out - do that. Don't keep throwing out one question after another without also working with the answer. (The excited puppy syndrome).
ENJOY every small bit of progress you make, and don't worry that it's too small.