Recommended Reading
There are several factors that motivate students to practise away from the lesson situation. Firstly, if a teacher ensures from the offset that the student knows exactly how to practise in the most effective way, pointing out instrument specific methods, then they will have all the necessary knowledge when they come away from the lesson to practise independently. Of course this needs to be regularly re-enforced in order for them to really find a way that works for them, but with on-going communication with their teacher and appropriate rewards they will get there.
HOWEVER: What if the student doesn't really know why things are not working for them? What if they don't know how to communicate the problems they are having? Perhaps because they don't really know what the problems are?
Parental contribution is very important. Even if a parent feels that they know nothing about music, there is so much they can do for them. It's about enjoying the music with them; asking them what they have done in their lesson, and getting really involved in conversation. For example questions like "What do you mean?" "Show me" will encourage the child to go to the piano, show their parents something and teach them something. In this process they will often stay at the piano to practise the particular part that their parents have asked them about. Not to mention the fact that any questions asked by their parents - if the student does not know the answer - will encourage them to ask their teacher. ALSO - listening to as many musical styles as possible makes music a part of their every-day life.
Practising with other musicians, in my experience, is the most effective way of encouraging students to practise. I believe that this is because not only should music be enjoyed by others, but if those other musicians are children of the same or similar age, then students are very interested in their peers; where they are in comparison to others and just the fact that they are regularly playing as part of a group, inspires them to practise in order to keep up with their peers. This healthy competition can encourage a child to find their own way of getting to a finished product after many lessons of head-scratching conversations with their teacher where they can't quite recognise the problem.
To sum up: As the piano is a solo instrument, I really strongly believe that learning as part of a group is a great way of learning this solo (and sometimes isolating) instrument. As long as a teacher ensures that solo lessons are given where necessary (e.g. if a student's technique is not where it needs to be and bad habits are forming, they may need temporary one-to-one attention) then group teaching and learning really does work. If you are a student who doesn't learn in a group, talk to your parents, friends and other family members about what you are learning. Play to them, listen to music with them, and enjoy music with them; music is designed to be shared.
