 McConnell-Mills was born Frances Mary McConnell in 1900 in Monument, Colorado. Her father was a physician and a pharmacist, and often took Frances with him when he made house calls to patients. She was sent to live with her aunt and grandfather so that she could attend Colorado Springs High School; she graduated at the age of 15 and was awarded a full scholarship to the University of Denver. She received a bachelor's degree from the university in 1918, aged 17, and graduated again with a master's degree in chemistry when she was 19, making her the university's youngest graduate with a master's degree at the time. In 1919, she began work as a teacher of chemistry, biology, geometry and trigonometry at Englewood High School.
