The Invisible Piano Method
The invisible piano method is a way of teaching where the child does not feel they are in school. It is more like educational play. The form of the usual piano lesson, to a child, is torture. They sit in a strange room with a strange adult and have to be quiet while complex things are explained to them. This is no fun.
Lectures are usually meaningless to a child of six. You have to show, not tell. Do it, don't talk too much. Ideally, your delivery of the piano lesson should be invisible. It should not feel like a lesson but a visit from an interesting, sympathetic adult.
Imagine you were an uncle of some kid, and the child asked you to show him how to start playing. Would you immediately pull out a piano book and begin some long explanation of theory? Would your demands be implacable from the first second? No, you'd play some silly game, maybe learn Chopsticks or some other silly childish song, like Twinkle Twinkle. You'd show the kid a fun time.
An Empathetic Teacher
This same avuncular attitude can easily apply to piano lessons not taught by a hypothetical uncle. You will find you get much more done with a friendly, collegial attitude. One of the first things that will happen in such a lesson is what I call the "apparent digression." The child will say, "I want to learn that song that goes......." but you were planning on teaching fingering that day.
The child wants to digress. Do you follow the child's suggestion, with a clever plan, or order that the digression will not happen? "We are learning fingering today, not that song you like." You follow the child, not the pre-arranged curriculum. You can deliver the curriculum in any order.
Follow The Child's Interest
A child who is interested in a certain song is far more likely to be open to ideas about how to play it. If you're a clever teacher, these "ideas" will consist of curriculum: fingering, chords, positions. But the child is just having fun playing a song they like.
Try introducing the same ideas using a song to which the child is indifferent, and you will see the value of "digression." Wherever the child's mind leads is where you should go. Your job is to cobble together the curriculum using the songs in which they are interested.
The Hand Me Down Method
Many piano teachers are unable to teach this way, using what I call the "hand-me-down-method." What this means is that the teacher can only teach the way they were taught. They cannot adjust to the needs of the individual child in front of them.