Trained as a classical pianist, Alexander studied composition with Jack Gallagher and received her Bachelor of in Composition from The College of Wooster in 1984. She received her doctorate in Composition from Cornell University in 1987, where she studied with noted composers Steven Stucky, Karel Husa, and Yehudi Wyner.
Reporter The Washington Post, Washington, 1984-1985. Instructor various schools, Philadelphia, Boston, 1985-1989. Scholar in residence Haverford (Pennsylvania) College, 1990-1991.
Assistant professor English University Chicago, 1991—1997. Poet-in-residence, director Poetry Center Smith College, 1997—1999. Professor African American studies and American studies Yale University, since 2000, chair African-American studies.
Freelance writer The Village Voice, Washington Post, New York Times, 1990.
Member Modern Language Association, American Studies Association.