Namesake of the Henry Schroeder Memorial Award, Schroeder spent more than 40 years involved in the American Turners program. Thirty-four years after accepting the position of Turn Lehrer at the N.Y. Turn Verein, Schroeder continued to instruct at the institution, earning him the 40-Year American Turners Honorary Gold Membership Card.
His teams won four AAU National Championships between 1921 and 1927. Additionally, Schroeder judged local, state, and regional meets and was selected to judge the 1948 Olympic Games in London.
