In this paper, we elaborate on the notion of Fundamental Mathematical Knowledge (FMK) which we understand as the minimum mathematical content knowledge essential to enter a degree in primary teacher education. We propose that FMK can be assessed in terms of competency in different areas of primary mathematics. The aim of this paper is to present our on-going work to specify FMK based on the common content of mathematics as a primary school subject in Catalonia, England, Finland, and Sweden.