I’m a student teacher who teaches beginner piano, and most of my students are young-ish (5-6 years old). I’ve only been doing this since January, and ironically enough, most of what I do is a ‘learn as I go along’ as far as teaching is concerned. The master teacher there (my piano teacher and boss) gives me a lot of freedom as far as curriculum. This was rather disconcerting starting out, since I had never taught piano before, let alone to a five-year old, so much of what I do/know is stuff I picked up along the way. Granted, some of it you just have to learn through experience; its difficult to directly tell someone how to teach someone else how to do something, a big part of it is interpretive since everyone learns at their own rate.
Anyhoo, I don’t have any official ‘method’, but the beginner book I give to little kids generally emphasizes how to sit properly, locating ‘middle C’, differentiating between ‘high notes’ and ‘low notes’, identifying letters of notes on the piano, and learning how to identify notes on the staff, learning to count along with the piece and maintaining tempo, etc. Each private student spends 30 minutes with me, and the younger kids always have a parent present (I prefer that arrangement, as opposed to having an adult male alone with a child in a small room for 30 minutes). Much of my teaching is explaining things to them, and I try to make things interesting and break it down to be understandable to a 5-6 year old. A lot of what I talk about also relates to the parents. IMO, the parent has a big part in helping the child learn the piano, by being dilligent about getting them to practice. Many parents are clueless about music theory/piano, so I help them understand what their child is working on, and how they can help their child master the pieces assigned properly. Generally, they are given a few simple pieces explaining something new (rests, time signatures, half notes, legato, etc). Its kind of like math- what you learn is built on things you already understand. Because of this, I generally only have them progress in the book when I am confident they understand what they are doing. Since many of the children are very proud of themselves when they master something (they love to show off to me. Its the greatest feeling in the world for me, especially when I’m still learning how to be a good teacher ) If they are struggling, I’ll spend more time on what they are currently working on, and generally won’t make them do something new until they understand what they are currently doing.
4 is a bit on the youngish side. I’m not that experienced as a teacher, so I’m not sure if I could help China Bambina hypothetically (although I would sure be willing to give it a shot). I do work with 4-year olds at my tutoring job, and I know that it is about having a lot of patience with them, and not going too fast. If the teacher makes it fun, the child will learn very quickly. I had a student about a year older than your child, China Guy. When she first started she was very shy, avoided eye contact with me and barely spoke. However, after only a month of playing the piano starting from scratch she was playing a recital piece by memory and absolutely loved taking lessons.