 After receiving her doctoral degree Hazlett was awarded an Alice Freeman Palmer Fellowship by Harvard, which allowed her to research invariants of nilpotent algebras at Wellesley College for the next year.In 1916 she was appointed to Bryn Mawr College, where she worked for two years before accepting an appointment as assistant professor at Mount Holyoke College.She was promoted to associate professor in 1924, the same year she gave a talk on "The Arithmetic of a General Associative Algebra" at the International Congress of Mathematicians in Toronto, but in 1925 she left Mount Holyoke because she felt she was not given enough time or resources to pursue her research in algebra.