Because art music of the late twentieth century has received little attention in North American school music settings, this paper proposes a rationale as well as procedures for the teaching of one of its emerging styles: minimalism. A brief historical view of the development of minimalism is offered, the influence of Cage's concepts of music as an ongoing [if indeterminate] process is recognised, and the relationship of minimalism to other musical sytles and genres is noted. Listening lessons for works by composers Terry Riley, Steve Reich, and Phillip Glass are devised, along with suggestions for performance and composition experiences in the music classroom. Due to its eclectic nature, including the influence of rock and pop music, instruction in the music of the minimalist composers is viewed as a gateway to other art music styles and techniques of the late twentieth century.