The Children That Piano Teachers Neglect
The children that piano teachers neglect are those that do not pick up the knack of reading music. Piano teachers are notoriously impatient. These piano teachers have no tool other than reading music. They have no idea how to handle such a child. Only a very small percentage of children measure up to the piano disciplinarian's lofty standards. These elite few are nurtured in the best way the teacher can find. I should know: I was one. A talented student is pure pleasure to a piano teacher.
Kids Who Are Not Prodigies
An average piano teacher can recognize natural piano talent. What about the rest of the children? For every prodigy child there are thousands of kids who are eager to take a shot at the piano but have drawbacks such as poor music reading, and poor cognitive and physical skills. In addition, they may have personalities that may not lend themselves to most piano teacher's methods. But these children are eager to make music at the piano. You must bend your method enough to allow them space in which to roam.
Children At Play
The success of this approach is based on watching children at play: Children at play teach each other how to do things so they can do them together. Kids at play are entirely themselves, unless they adopt a theatrical pose. They are exerting all their natural intelligence in a happy, unpressured way. Kids at play will expend all their energy to solve a "problem" that they see needs fixing. Children at play are concentrating as hard as they can with no stress. Imagine yourself a child playing with another, and your companion wants to learn a song on the piano. Since you like your friend, you're going to be friendly, patient and understanding. You'll work for a bit on the song, and then you'll tire of it and move on to something else.
Teacher As Adult Child
An adult teaching a child using this ruse has a huge additional advantage. The child accepts you as leader, and will, within reason, allow you to set the pace. But as soon as you exceed a working pace that would be normal between two friends, you draw upon the good will you have "put in the bank" by being patient. If you're a friendly person, the child will allow you to lead them towards more serious work, disguised of course as play. I've found the unlikeliest of children prosper and learn to enjoy the piano with this approach. These are the kids for whom the piano is not immediately interesting without a lot of guidance and support.
Piano Teachers Reject Late Bloomers
Most piano teachers refuse to take these children in the first place, or their methods make the children into quick failures, easy to replace. To these piano teachers, there are always more six year-olds with a check from Mommy. If your goal is to make every child a piano player in their own right, in their own way, then you are on the right track. Why shouldn't every child understand the rudiments of piano? The only people preventing this are the piano teachers.