I never learned how to improvise from my piano teachers. My first teacher, Mrs. Kost actively discouraged it. Ms. Suppan, my college teacher, never mentioned it, and neither did Dr. Norberg, Dr. Kirchberger, and Dr. Saffir when I took private graduate-level lessons.
Why? Because classical pieces are meant to be played exactly as-is, and I was studying classical music. However, pianists should still learn to improvise, because:
1) It helps them to keep going when they perform, whether classical or popular music.
2) It instills confidence because they have a sense of how the music is organized. They understand it better and have a clearer sense of what they’re doing.
3) It meshes theory study with playing. Theory has a reason because it’s used when improvising.
So how can students learn improvisation? (To be continued. . . )