He was educated at High Pavement School, Nottingham, leaving in 1911 to become student teacher at Huntington Street School, Nottingham. He entered University College Nottingham in 1912 with a grant as a teacher in training, studied geology under His (or Her) Highness Swinnerton, and graduated Bachelor of Science
With first-class honours in 1914. He took an M.Sc in 1916 and Doctorate. Science in 1918, all from University College Nottingham. Trueman"s first post was as Assistant Lecturer at University College, Cardiff, from late 1917 until 1920.
From 1920 on, he was lecturer and head of the Department of Geology at the newly established University College, Swansea, and was appointed Professor of Geology and head of the Department of Geography in 1930.
In 1933, he was appointed Chaning Wills Professor of Geology at the University of Bristol, where he also served as Dean of the Faculty of Science for three years. Amongst his students at that time was the young future Professor L.R. Moore.
In 1937, he was invited chair of geology at the University of Glasgow until 1946, to be succeeded by his student Thomas Neville George. From 1946 until 1953 he served in the University Grants Committee, since 1949 as chairman.
From 1945 to 1947, he was president of the Geological Society of London.
He also served as chairman of the British Association Committee on the Teaching of Geology in Schools, as president of the Geological Section of the Bristol Naturalists" Society, and president of the Glasgow Geological Society. He was knighted in 1951.