The use of structured ability grouping is increasing in English primary schools and is regularly seen in primary mathematics classrooms. Ability is a normalised discourse with beliefs that some individuals are 'born to do maths' permeating society and infiltrating school practices. In this paper observation and interview data illustrate the persistence of fixed-ability thinking, even in situations where explicit ability-grouping practices are not used. The data analysis suggests a mismatch between mixed-ability practices and fixed-ability thinking, and the paper argues that change will be difficult.

This case-study, drawing on an unanticipated theme arising from a wider study of ability-grouping in primary mathematics, documents some of the consequences of educational triage in the final year of one primary school. The paper discusses how a process of educational triage, as a response to accountability pressures, is justified by teachers on the basis of shared theories about ability and potential. Attainment gains show that some practices associated with the triaging process work for the school, pushing selected pupils to achieve the Government target for the end of primary school. However, other practices appear to coincide with reduced mathematical gains for the lowest attaining pupils and a widening of the attainment gap. This case-study examines the mechanisms behind this, focussing on resource allocation and assumptions about learners and their potential. The paper suggests a need to create dissonance, challenging shared assumptions such as fixed-ability, which currently support triage processes.

Embedding setting (subject-based ability-grouping) into the primary-school environment creates structural conflict -physically and culturally -fundamentally changing the nature of primary schools through the imposition of secondary practices and cultures and the loss of pastoral care. This article examines the hidden implications for teachers and pupils of taking on secondary-school roles within the primary-school context. It highlights the wide-ranging, yet nuanced impacts of the use of setting, examining the shift towards subject-based thinking and the erosion of the pastoral-centred holistic ethos of primary education.

This weighty volume is part of the monograph series: "Advances in Mathematics Education" (series editors: Gabriele Kaiser and Bharath Sriraman), which brings together key previously published research within particular themes, continuing the tradition of the international journal "ZDM -The International Journal on Mathematics Education". These syntheses of research are debated in light of the future of, and new approaches towards, mathematics education.