She taught briefly at the
Texas State College for Women in Denton, now
Texas Woman's University. Barrett served as a mathematics faculty member at the universities of Utah and Tennessee, and headed the mathematics department at the
University of Tennessee from 1973 to 1980. During her tenure there, she also worked at the
Oak Ridge National Laboratory in applied mathematics. She served as an administrator and mathematics faculty member at
Northern Illinois University, where she was Associate Provost, and at
Mississippi State University (MSU), where she was Dean of Arts and Sciences. After retirement as Dean Emerita from MSU, she was a Senior Associate to the head of the Education Directorate at the
National Science Foundation for three years and then served as a Professor of Mathematics at the
United States Military Academy at West Point for three years. She died in Knoxville, Tennessee, on January 28, 2021. ==Notable positions==