There are many platforms for improvisation. One of the most effective I have tried involves selecting a certain number of tones: four, say, or seven. Once the tones have been selected they may appear in any register of the piano. The child then tells a story using only those tones.
The game is even more interesting when two children play it. They take turns initiating the story. After the story is first told the listening child reconstructs it and the first child gets to respond to the reconstruction, whether or not it reflected the nature of the first playing.
This procedure is particularly useful for relating to non-tonal works. The tones of the first bar can become the basis for a story that the child unfolds at will. The story then can be delegated to the composer.
This works extremely well for Hindemith.
