Alexander trained with Charles Neil in 1958 and subsequently at The Constructive Teaching Centre in London. He was First Flautist with the London Symphony Orchestra before accepting a professorship at Michigan State University in 1967.
He was professor in the Hague from 1974-77. He was appointed to the University of Illinois in 1977 when The Urbana Centre began training teachers. With his wife Joan Murray he continues training teachers in Urbana.