This article considers participation in post-compulsory mathematics education (Advanced or A-level) which is currently exercising education policy-makers in England and elsewhere. I argue that the central problem is neither that of devising an economically motivated strategy for increasing student numbers nor simply raising the level of mathematical capability attained. Rather, the central problem is about "what" mathematics to teach, "how" and "why"? I will present emerging findings from two current studies of 14-19 mathematics education, highlighting socially differentiated patterns of participation. Then I will consider the values/philosophical influences on current policy and practice. This leads me to argue that the curriculum needs reframing so that all students are enabled to use their mathematics to read, understand, critique and act in the mathematically "formatted" worlds in which they live. (Contains 3 notes.)