What Mathematics is Needed by Teachers of Young Children?

There has long been a dichotomy between the mathematics that is learned by trainee teachers ‘for their own personal development’ and the mathematics they will need to teach to young children. My viewpoint is that a student should be encouraged to study whatever it is that interests them, but when it comes to prerequisites for teaching mathematics to young children, different criteria apply. I shall provide an analysis of how mathematics grows cognitively in different ways in different individuals. This will provide a basis to formulate what is needed for teachers to participate actively in the long-term mathematical development of their children.