Demonstration is essential. Playing for the student to listen is not – however nice it may be.
At its most basic level(and there are many other levels to add later on to this most basic level) piano playing is done by the motional mind (which involves everything that has to do with movements, co-ordination and the five senses). The motional mind can only learn by imitation. Therefore the purpose of demonstration is to provide a model for the student to imitate.
Is the student going to become a copy of the teacher, then? Surely not. But at the beginning stages where s/he knows nothing, s/he must imitate the teacher. Eventually, s/he will develop his/her own peculiar and individual pattern of movements. But at first s/he must be shown[i/].
The importance of demonstration can be clearly seen in threads that deal with the palying of scales Thumb under (TU) or Thumb over (TO). You can read those threads (and there is quite a number of them), and no amount of explaining is going to help you. Yet five seconds with a teacher (who knows about it – not every teacher does) will dispel any doubts. Not only that, you will start by imitating the teacher´s movements, but soon you will realize that you can do the same movement in a slightly different way that for you
happens to be more comfortable.
The same is true of any motional art: dance, Olympic gymnastics, skipping rope, martial arts, walking, etc. Without demonstration the beginner will never have a clue. Many times, even the demonstration will not help – the teacher must correct the student: he may think he is imitating but he is not – so most of the times, even watching a video (= demonstration after all) is not going to help. You need not only the demonstration as well as the feedback.
A teacher who will not demonstrate is either well above the level of the student and the student would do better finding a teacher more to his level (you would not expect a Nobel prize in literature to be good at teaching someone how to read, even though he may excel as a teacher at the post-grad dept of the local University), or the teacher is lazy, or the teacher does no know himself what is it that he is asking the student to do. Many times, he may well be able to do it[i/] but be completely at sea about how he actually does it[i/]. This is often the case with the playing of fast, pearly scales – which can only be done with the thumb over – yet the teacher insists in demanding form the student that he uses thumb under. Yet when the teacher himself plays the scales, he clearly uses the thumb over. Other interesting examples of completely misguided verbal instructions are Cortot´s “Rational principles of piano technique” and of course Hanon´s “Virtuoso Pianist”.
Best wishes,
Bernhard.