The values and methods of mathematics education which mathematics teachers tried to impart to their students have varied historically according to the situations of each institution. The cases of the mathematics education in Cambridge University and University College, London show that the peculiar meanings or values of mathematics education were transmitted on students and the methods or focus of the teaching were uniquely determined under the influences of university examinations or conditions of students. In specific, the characteristic education of Augustus De Morgan who studied in Cambridge University and then taught in University College, London reveals better the different institutional contexts. In this paper, I suggest mathematics teachers reconsider mathematics learning motivations on their institutional contexts.