The purpose of this article is to present the idea that the music education profession's current drive to include improvisation in school music is limited in its approach, and that "teaching" improvisation, in the traditional sense, is not possible. These beliefs are based on an examination of current methodologies and texts in light of the historical evolution of both improvisation and the teaching of improvisation. The article provides an examination of Jeff Pressing's historical conceptions of improvisation as a continuum model and then briefly looks at the short history of improvisation in American music education in the 20th century. Current methods are examined in light of free improvisation techniques. This leads to a final argument for more free improvisation in school music balanced with the current skills approach used in the USA. The conclusion of this article examines the issues and realities for current practices in music education in light of the beliefs set forth. (Contains 5 figures, 1 table and 2 notes.)