Improvisation is the ability to navigate through an ocean of options, the myriad possibilities of sounds.
Improvisation involves training to make instant structural decision that enrich the cognitive process.
(Walter Ponce, The tyranny of tradition in piano teaching)
Through teaching and learning process based on improvisation, students would start learning music by imitation (rhythmic and/or melodic), then discover simple words (simple music patterns), and finally learn how to organize words in sentences (music structures). As historical evidence and effectiveness of this approach, allow me to reckon that the most important composers in the history of classical music (Bach, Mozart, Beethoven, Chopin, Liszt just to say few names) were excellent improvisers. Improvisation was systematically taught in classical music at least up to the beginning of romantic era and practiced up to the beginning of 20th century. Nowadays several treatises about improvisation are very well known and widely available, moreover a number of studies by eminent scholars and musicians appeared in the last circa 20 years.
If you wish to know more about classical improvisation, and how it could be integrated in the traditional piano teaching and learning, feel free to contact me.