This article revisits methods and debates about teaching mathematics that were common in the 1980s and early 1990s, and then moves up to date with the findings from three mathematics departments that set out to make a difference for their lowest attaining students. The methods they used were distinctly focused on core mathematical ideas, and how all students could work with these. This Vygotskian approach supports students' development towards thinking in new-to-them mathematical ways, rather than accessing mathematical enquiry through particular social structures or non-mathematical modes of engagement. The author claims that any school which does not take seriously the mathematical understanding of the lowest achieving students is not truly comprehensive. (Contains 1 note and 1 table.)