[1] He taught collegiate mathematics in Tuskegee for many years,[2] until finally he earned his PhD at the University of Pennsylvania (1928).
[3] His doctoral thesis was entitled, On Two-Dimensional Analysis Situs with Special Reference to the Jordan Curve Theorem, and was advised by John R.
[4][6] He also published a study for the Committee of twelve for the advancement of the interests of the Negro race on Jackson, Mississippi in 1909,[7] a textbook, Practical Arithmetic (1911),[8] and an article on geometry teaching at Tuskegee in 1913.
[9] Woodard was a respected mathematician, professor and mentor to his students at Howard University in Washington DC, where he established the masters program in mathematics.
[10] One of his best known students was William Waldron Schieffelin Claytor, who later took his PhD at the University of Pennsylvania (1933), also under Woodard's former advisor, John R. Kline.