From Dr. Jani Parsons:
For improvisation at the piano, one of the important things is to LIMIT the possibilities, otherwise the range and possibilities can be overwhelming at the piano, and it’s easy for students to say “this doesn’t sound good…” and stop exploring. I might encourage you to give (in one week) a series of guidelines for improvising as follows:
Anything: limitation is only black keys (pentatonic land!)
Anything: limitation is range (2 octaves somewhere on the keyboard…)
Anything: limitation is articulation (maybe everything staccato..)
Anything: limitation is not playing on the keyboard at all… using the piano as a percussive instrument, or playing inside the strings
Anything: limitation is all one dynamic range
You get the picture. I think the idea here is that by limiting one thing, articulation for example, the student should be encouraged to go WILD with things that are not limited. For example, try not to limit oneself to a key area or register or dynamic, explore wildly, and just keep one element in check.