Improvisation pedagogy has presented a challenge to music educators since jazz courses began being offered in North American universities in the 1950s, a development which has raised important pedagogical questions ranging from 'Can improvisation be taught?' to "Should it be taught?" Following on the increase in academic writing on improvisation over the past decade, in this article I draw on practice-based and ethnographic research on the under-documented yet influential American jazz ensemble the Jimmy Giuffre 3 to propose alternative approaches to teaching improvisation at the post-secondary level. The remembrances of these master improvisers offer an accessible entryway into free improvisation for educators and students who have been either resistant to this part of the jazz tradition, or simply unsure of where to start exploring collectively improvised music-making. I argue that if properly presented, improvisation pedagogy can aid students in developing a disposition for creative thinking, potentially enabling them to become critical, engaged citizens and productive participants in the cultural field.