Edelman, the son of Ralph and Nettie Edelman of St Louis, attended University City High School in Missouri and earned bachelor's, master's and doctoral degrees at the University of Missouri. He taught there, at the College of William and Mary in Williamsburg, Virginia and at UAB before going to work for Birmingham City Schools. He taught at Lincoln Middle School, where he mentored Parker High School graduate Crystal Wadsworth. Later he served on the system's athletics committee.
In retirement Edelman remained a tireless advocate for education, social justice and transparency in government, attending countless public meetings and hounding public officials and media figures. Besides his passion for civic causes, Edelman was known for his eccentric behavior and dress, usually appearing in a bold plaid jacket and propeller-topped ballcap. He was a regular caller on talk-radio, calling himself "The Bean Counter", and was known on the Paul Finebaum Radio Network as "Robert from Shoal Creek".
Edelman forged friendships with several long-serving public and media figures, even if his presence was often an annoyance. He was a critic of Birmingham's sale of the assets of the Birmingham Water Works to its governing board, and often criticized Operation New Birmingham, calling it "Operation New White People" and complaining that it gets funding to encourage white residents to move downtown while doing nothing for the city's decaying neighborhoods. When income tax was deducted from his buy-out from the Birmingham Board of Education, he blamed Birmingham mayor Bernard Kincaid. He entered the 2003 Birmingham mayoral election to unseat him, but finished 16th in the field of 18 with only 54 of the 44,806 votes cast.