Why not the whole piano?

Often students are taught to play only 10 keys on the piano at a time. This of course is good for learning hand positions; however, I always encouraged my students to explore the whole piano in addition to the hand position exercises. It is absolutely amazing how young children can discover patterns, derrive unique rhythms, and use the instrument to tell a story. So much can be learned by exporing the instrument that can be even more valuable than what a teacher can teach. This type of learning also must develop and stimulate problem solving skills as the explorer is involved in such concentration as they seek to understand the instrument.