Teachers often just ask students to play the exact concrete notes and never help them to see the patterns. And people often cannot even play a tune in two different keys.
I hate when people say "you have the exact concrete notes so just play it!". I get upset. I learn when I get help with seeing the patterns. I hate how teachers have tried to make me a person who should avoid seeing the patterns.
I disagree with dogperson, I wouldn't study with a teacher who didn't know any theory, because they would be unable to understand many of my questions, it's something every professional musician should know and does study in college. It's not rocket science.
Try to find better teachers, they are out there. I think there are a great number of poor piano teachers, they may even be the majority. I don't completely blame them, it's hard to teach because there are so many moving parts and you need to be competent at a number of things.
Here's what I would expect from a good teacher:
- Very good technical foundations and the ability to articulate movements at the piano
- The ability to observe and think of ways to improve your technical approach at the piano, for example observing where your muscles flex and realizing that you are pushing at a certain angle causing inefficiency.
- The ability to hear how that translates into the sound
- Being able to hear basic musicality and interpretation, phrases, voicing, evenness, and how your technical approach affects those
- A good enough ear to pick out wrong notes, and to play basic melodies/chords by ear. This is important because it ties into their ability to correctly hear what you are doing and improve it. Ideally they should be able to play back pieces of what you play using your technical approach, and how it can be modified
-A decent idea of other approaches at the keyboard, so that if you come across different ideas they can discuss them in class
- And they need to be able to figure out what level of pieces you can work on comfortably and improve upon.
- Theory knowledge, either implicit or explicit, preferably both. This is involved in memory, hearing chords and harmony, etc. Implicit theory understanding is a double edged sword because it's hard to teach.
I have met a number of teachers, but it's hard to find those who really understand and know how to teach. One had perfect pitch, but I felt could hear the notes accurately but didn't really give good advice in terms of phrasing or musical interpretation, or technique. She had learned technique as a kid and just expected it to come with time. Another worked on tougher pieces which I could play but which weren't optimal for technical development. You see all sorts of combinations of skills, and different approaches.
However if the teacher is considerably lacking in one area, that will result in a corresponding inefficacy of teaching. If they don't understand good technique and technical development, they will often just assign pieces assuming it will come with time. It almost never does, even for kids, who will then need to relearn it with a good teacher. If they don't understand theory and how music is structured, they will tend to make their students learn by rote. If they don't understand musicality or phrasing, they will tend to focus on wrong notes which results in mechanical playing. If they don't have a good ear, they will often neglect developing their student's ear. If they don't have good sight reading skills, their students will not acquire it either usually.
Of course, it's a lot to ask and it may not be practical to expect teachers to have a complete understanding, but in short if you feel your teacher is considerably lacking in some area, you could try another one.