Let The Child Lead The Piano Lesson
Piano teachers need to let the child appear to lead the piano lesson. This is better than presenting them with an unbending lecture and drill. Both have their place. So much of k-12 education is force fed these days. It is a pleasant surprise to ask a child, "What shall we do today?" even if you have a secret teacher's agenda in mind. I find that almost all kids can make music at the piano if you make it simple enough. I'm referring to improvised music which has a rhythmic basis. In this situation, a child can join and be part of the musical fabric. This is the essence of music making, even at its highest levels, and children relish it just like adults. Simple songs like Chopsticks are the proof of this, and Heart and Soul as well. These are songs you'll find that 90% of children have heard or played on the piano.
The Lowly "Chopsticks"
The essence of Chopsticks is a simple tune that is enjoyable to play, and not very hard to do either. Like a toy, children get happily lost within the song, and repeat it until they are bored with it. Most piano teachers disdain such songs as "beneath" them. But you should watch the child's enthusiastic reaction to it. My point is that a clever piano teacher will see the following skills being taught by playing Chopsticks:
Rhythm: you can't play Chopsticks unless you play evenly
Fingering: even two index fingers involve many important muscles and reactions
Musical Form: the song repeats from the beginning very neatly, like a circle that keeps rolling around
Ensemble: there are two parts to Chopsticks, and you'll have to cooperate with the others in the band
Counting: Chopsticks has three beats, and you'll be nodding your head in that fashion, 1 2 3, 1 2 3, 1 2 3
Black Keys: the first two notes of Chopsticks are on either side of the lowest of the group of three black keys. To start the song, you'll have to be able to find it.
No Agenda, Just Observation
Thus I don't necessarily have an agenda unfurled every lesson. The child's abilities and deficiencies are obvious, and one could start anywhere in an effort to expand their musical education. The one unchangeable item on the piano teaching agenda is that the child progress. And the student must progress without a loss in enthusiasm.
How enthusiasm is accomplished varies with the day, and the mood. Like a ship in the wind, you will get nowhere if you push in the wrong direction. And, like a ship in the wind, if you learn to really gauge the child's mood (the wind) you will sail as far and fast as you like. I can't tell you the number of times that a subject, properly introduced, is first rejected by the child only to be accepted later as "interesting." When a child rejects something because it seems too difficult, they are telling you that they have not been properly prepared. They don't know it, but this is what their rejection indicates. For example, many children reject fingering outright as "absurdly complicated," only to embrace it utterly after you have made their fingers into a game, both on and off the piano. The lesson is to pay more attention to the child's reaction than to your own. Your method is irrelevant, and only the child's understanding of it matters.