A major milestone in a piano students progress occurs when they learn to control each hand independently and are able to play one hand louder than the other. When this happens, regardless of the level they are at, they stop sounding like plodding beginners and start to sound like musicians. It is a trans-formative skill.
I have never figured out how to teach this and I suspect it is not possible to teach it. I have tried some strategies; thinking about or concentrating on the hand you want to be loudest, or touching the keys but not pressing them with the hand you want to be quietest. In the end I just tell my students what I want them to do and let them work out how to do it.
This is much like learning to ride a bicycle. I don’t think you can teach that either. We can offer support and pick up the would be cyclist when they fall but ultimately they have to teach themselves.
Learning to ride a bicycle and learning to control the hands independently has something else in common too. Once you have done it you are always able to do it.
Advanced pianists can not only control their hands independently, they can control their fingers independently. They are able, for example, to play one note in a chord louder the the other notes.
I am a member of the ArrangeMe community and I have an arrangement of “Streets of London” available to buy at Sheet Music Direct and Sheet Music Plus. I have found this arrangement to be very useful for students to practice hand independence.