Playing with freedom
Learning to play piano and learning to read music are not the same thing! Children are often capable of playing the piano from quite a young age. Indeed, many of them do spend a lot of time exploring the piano and trying to pick out tunes they know or inventing interesting patterns before they start lessons.
The challenge for the teacher is not so much how can young children play the piano without learning to read music, but how they can continue to play while learning to read music. If every note they play has to be read first, then we are seriously limiting their experience of piano playing. After the freedom children experience of creating sound over the whole piano before having lessons, the constraint of playing only on a few notes around middle C can be disappointing.
It is often assumed that around 7 years is the best age for children to start lessons but this may have more to do with their actual reading ability than their musical and piano-playing potential. Children can learn to play the piano before they are able to read, and if a child shows eagerness to play, then it is often very productive to start younger as long as an adult is able to spend time daily at the piano with the child.
Of course learning to read music is part of learning a musical instrument and we begin to teach music reading right from usually from the first lesson (except with very young children) but we also ensure they have plenty to play which is not dependent on music reading. Short pieces with easily memorised patterns and tunes (the words of the song can be a help too) can be taught by demonstration in the lesson. Our recordings (or YouTube videos) allow children to absorb the sound of the piece at home and the parent at the lesson will also have learned something of how the piece is played. So right from the outset, young children can engage in the activity of playing the piano in an interesting and exciting way. Something of that early freedom of making exciting sounds all over the piano remains, though now with an added layer of direction.
So, from the very start, our pupils experience the freedom of playing from memory which is perhaps a skill more necessary for the pianist to develop than for other instrumentalists. Most instruments do not perform solo. The piano is the major exception. Although the piano can play with almost any instrument, or group of instruments, it is complete and satisfying to listen to on its own. No instrument in the history of music has had so much music written for it, and the majority of that music is for solo piano. When they are performing solo, both jazz and classical pianists usually perform without scores or sheet music.
In general, we admire the speaker who communicates directly with the audience much more than the speaker who is obviously reading his speech. There is a freedom of expression when the content is absorbed mentally which is absent when one is tied to the printed page.
Performing from memory seems to enable more direct communication between the pianist and the audience. Perhaps this is why the convention, now more than 150 years old, still thrives despite its demands.
Children play from memory simply because they can. By the time children have learned a piece, and can play it without difficulty, they will be able to play it from memory. Memorising will never be easier or more natural than for children, and the experience and confidence gained when young is a good basis for developing this ability.