Lately, she has been saying that she would rather learn how to play the guitar, but her father does not want her to switch intruments.
However, she is always agitated during her lessons, and does not take my comments very readily.
She says that she would like me to let her play as she likes...
I'm curious, if she is always agitated in lessons, is she ever still for long enough for you to see that talent?
It's a tricky one. A half hour lesson can feel like a lifetime with a challenging pupil, can't it! I think you should say something directly to her, that it's your job to teach her and it's very difficult when she doesn't listen/misbehaves etc. Or speak to her parents, and ask them to have a chat with her to see what she really wants to get out of it maybe.
Sounds to me like she needs a big dose of instructions. Do you have a policy? Read to her the expectation during lessons. I have a sheet I used to use for learning disabled students with pictures. Something like, "Eyes On", "Listen", "Hands Quiet." She needs to know who the teacher is, who the authority is, and how she is expected to behave in lessons. This seems to be lacking quite often now a days. Perhaps also review what the rewards will be for following lesson rules - perhaps assign a personal choice piece once per month or so. Or the last five minutes of the lesson she gets to improvise with large hand gestures. Does this make sense to you?
I've had very young students say to me that they don't want to learn the piano. I ignore it the first time they say it. If they bring it up again sometime down the track I will take notice and mention it to the parents. There is literally no point in teaching a child who says they don't want to learn something. If they vocalize it you need to take action. I've had some that say nothing and do it because their parents want them to, I will not refuse to teach them because it is never too late to learn that sometimes in life we have to do things we don't exactly want to do!Some children do not know what they want to do and say things which doesn't have real meaning behind it except to escape work. They might just want to get out of the work required from them sitting in a lesson, whether it be piano or any other subject for that matter. Some kids don't like to think that they are doing something wrong. Challenge them to do it another way rather than correcting them. If you could provide some scenarios you are experiencing then we might have better advice here.This makes me think that she is afraid to think that how she does something might not be the best way. Especially bright young students can be this way, they play sports and know they are doing it right because they win, they get high marks in class because it says so on the test papers, but with music there is a broad degree of what constitutes good. You would not want a total beginner to play like a professional concert pianist immediately because there are many other stages of good that they must achieve before they get that.I find some young students are not mentally capable rather than physically. They may have the ability to improve but their very mental capacity to deal with change and reassessing the way they do things is not at that same level. I have currently one very talented 5 year old Chinese boy who can read words like a grade 7 student and studies advanced maths for his age etc etc. He plays the piano well but of course there is areas to improve, but how much I can improve is limited to his capacity to deal with making that change. If I push for too much change he can get depressed and agitated and try to distract me from pushing the issue too hard. So I have to push but not too hard, give him space to breath and give him my trust that he will try to work it out and at least pay attention that there is need for improvement.
I didn't go right out and say it, but if she is playing the role of a superstar pianist as she imagines it, doing exaggerated flourishes and such - is she talented, or is her family telling her she is talented so that she does this acting? If she is not letting herself be taught, and if does this kind of acting at home, how can she be developing any music? Talented people are usually engrossed in the instrument and in the music, not in themselves looking like talented people. So I'm wondering whether the OP actually does see ability in how she plays. The attitude itself would be the problem, no?
Many thanks for this great, well-detailed reply, lostinidlewonder! There is so much 'food for thought' in your comments! Your experience with the 5-year-old Chinese pupil is quite similar to mine with my little girl. She is physically ready to learn certain "techniques", but the mental maturity is not quite there yet. Like you, I have to feed her some information, but only bit by bit -- otherwise, piano will disgust her forever. With her, I feel like I am walking on eggs!