He became head boy there, excelled at sprinting and won a mathematics scholarship to Sidney Sussex College, Cambridge.
His education was interrupted by World War I, after which he took up his place at Cambridge University and briefly read Mathematics there from 1919 to 1920.
In 1924, after taking his Teacher's Diploma, he was appointed an Assistant Inspector of Schools by the Board of Education and began his career in its Whitehall offices.
He ran courses for primary teachers, often with Robin Tanner, and promoted progressive ideals and practice.
After his formal retirement in 1963, Schiller continued to lecture and advise on education and also acted as an external examiner.
He sat on the Plowden Committee at Goldsmiths' College and in the early 1970s influenced its new Postgraduate Primary Course.