archer earned an l mus from mcgill university in 1934, and a b mus from mcgill in 1936 where she studied composition with douglas clarke. she travelled to new york city in the summer of 1942 where she studied with béla bartók, "who introduced her to hungarian folk tunes and to variation technique. she taught at the mcgill conservatory from 1944–1947. later in the 1940s she studied with paul hindemith at yale. she earned a b mus from yale in 1948, and a m mus also from yale in 1949. from 1950–1953 archer was composer-in-residence at the university of north texas. from 1953 through 1961 she taught at the university of oklahoma. returning to canada in 1961 for doctoral study at the university of toronto, she set that aside when, in 1962, she joined the faculty of music at the university of alberta. there she would become chairman of the theory and composition department. she remained at the university of alberta until her retirement. her notable students include larry austin, jan randall, allan gilliland, and allan gordon bell.