 Matthews was a trustee of the District of Columbia Public Schools from July 13, 1813 to 1844.For a part of his term, he served as co-director of the school system, and as one of three members of the board of trustees who collectively acted as superintendents of the Lancasterian school—one of three schools of the public school system alongside the Eastern and Western schools.In this capacity, he visited the school quarterly, and oversaw instruction of the students and performance of the teachers.