Parker was Professor of Classics at the
University of Texas at
Austin for forty years, recruited there in 1967 by
William Arrowsmith. Earlier he had been a professor at
Yale (1953–55) and at the
University of California, Riverside (1955–67). He taught classes in Greek and Latin languages and literature, as well as a discipline of his own creation,
parageography—the study of imaginary worlds. His courses crossed traditional disciplinary boundaries and were popular; he was known at the University of Texas for his breadth of knowledge and teaching, and won graduate and undergraduate teaching awards. In 2011, the journal
Didaskalia dedicated its new endeavors to "Douglass Parker, who embodied the interplay between scholarship and practice, between an acute understanding of the ancient world and a keen sense of modern audience."
Didaskalia subsequently published a pair of wide-ranging interviews from 1981 and 1982. == Other interests ==