In this article we propose the notion of differentiation from an advanced standpoint as a teaching strategy, particularly valuable for working with students with low prior attainment. The notion arose from an enactivist analysis of the work of three teachers, engaged in action research in their own classrooms. All three teachers chose to teach their students (who were aged 15-16) topics that are usually only offered to those with relatively high prior attainment in mathematics. No intermediate or bridging topics were offered, instead, these teachers found ways to differentiate work for their classes, from this advanced standpoint. There is tentative evidence of students experiencing their relationship to mathematics in new ways, recognising they were doing "A-grade" work, and of gains in their attainment. There is also evidence of the teachers' own surprise at what their students could achieve.