The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the perspective of experiencing the mathematics curriculum as a coherent story, and neither seems likely to take best advantage of the accumulated body of knowledge in the education research literature about effective didactics for mathematics. In this position paper, as we embark on the collaborative, research-informed design of a complete, fully-resourced, free-toaccess mathematics curriculum for students aged 11-14, we use the conceptual framework of mathematics curriculum as a story to draw out five key curriculum design principles. A mathematics curriculum should harness and develop the skills and expertise of teachers; balance the teaching of fluency, reasoning and problem solving; give explicit attention to important errors and misconceptions; compare and contrast alternative methods; and engineer coherence through strategic use of consistent representations and contexts. We use these five principles to set out our vision for the next step in research-informed mathematics curriculum design.

My math lessons are all about learning from your mistakes": how mixed-attainment mathematics grouping affects the way students experience mathematics Mixed-attainment mathematics teaching is not a common practice in England despite evidence that ability grouping is not an effective strategy for improving educational outcomes. This study compares mathematics in School M (mixedability groupings) and School S (sets) in relation to student beliefs, and teacher beliefs and practices. Questionnaire data from 286 students and twelve teachers were triangulated with lesson observations and interviews. This article suggests grouping practices could indeed influence students' mindsets, teachers' mindsets and teachers' beliefs and practices. An above average proportion of students in both schools reported growth orientations although these beliefs were held more strongly by students in the mixed-attainment grouping. School M teachers also held stronger growth-mindsets than School S teachers. Mathematics teachers in both schools reported connectionist beliefs but the students' experiences differed. Most students in School M perceive typical mathematics lessons as involving a substantial problem or challenge worked on collaboratively in pairs or small groups, and having several entry points. Students in both schools valued learning from mistakes but School M students were more likely to both believe this would help them, and have access to this type of learning opportunity. Students taught in sets experienced mathematics as procedures delivered by teachers and reproduced by students. This has implications for further research as mixedattainment groupings may be a factor in determining the way in which students experience learning mathematics.

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