She studied organ with her uncle Henry Gideon and piano with Felix Fox.
She also studied with Martin Bernstein, Marion Bauer, Charles Haubiel, and Jacques Pillois.
She then taught at the Jewish Theological Seminary of America at the invitation of Hugo Weisgall in 1955, and at the Manhattan School of Music from 1967 to 1991.
[2] Gideon composed a lot of vocal music, setting texts by Francis Thompson, Christian Morgenstern, Anne Bradstreet, Norman Rosten, Serafin, Joaquín Quintero and others.
[3] The International Alliance for Women in Music (IAWM) offers the Miriam Gideon Prize annually, sponsored by composer Patsy Rogers,[4] for female undergraduate and graduate students who are members of IAWM.