[2] As a youth, he was encouraged in his musical ambitions by Ureli Corelli Hill, a well-known conductor and violinist at the time, who was a friend of the Goetschius family.

In 1905, he went to the staff of the Institute of Musical Art (which later merged into Juilliard School) in New York City, headed by Frank Damrosch.

Goetschius retired from the Institute in 1925 and spent the remainder of his life in Manchester, New Hampshire, continuing to write into his eighties.

Goetschius's notable pupils include Pauline Alderman, Henry Cowell, Lillian Fuchs, Howard Hanson, Swan Hennessy, Julia Klumpke, Daniel Gregory Mason, Wallingford Riegger, Bernard Rogers, Alice Marion Shaw, Carrie Burpee Shaw and Arthur Shepherd.

Although Goetschius as a teacher had a fundamentally conservative outlook, he appears to have been sensitive and supportive towards his students' individuality, encouraging, for example, Henry Cowell's early experiments with tone clusters.