Despite extensive research on attainment grouping, the impact of attainment grouping on pupil attainment remains poorly understood and contested. This paper presents evidence from a study conducted with 2944 12-13 year olds, from 76 schools in England, who were allocated to between-class attainment groups ('setting') in English and mathematics…

Promoting engagement is crucial for encouraging student participation, interest, and learning in mathematics. Student engagement has been conceptualized as interrelated types comprising behavioural, emotional, and cognitive characteristics. Cognitive engagement, our focus in this paper, relates to students' psychological investment in learning and…

This study investigated task contextualization as a means of assessing students' ability to apply their subject knowledge to new situations. Through analyzing 527 Functional Mathematics examination questions that claim to assess students' application skills, it developed a set of principles for embedding questions in context: deep…

We study teachers' choices about how to allocate class time across different instructional activities, for example, lecturing, open discussion, or individual practice. Our data come from secondary schools in England, specifically classes preceding GCSE exams. Students score higher in math when their teacher devotes more class time to individual…

Drawing on Bourdieu's theory of social and cultural reproduction, this article utilizes the conceptual tools of habitus and cultural capital to examine intergenerational inequalities in attitudes towards mathematics and mathematics learning in three secondary schools in England. Data from 1079 students aged 14-16 included mathematics achievement,…

One of the key problems to be solved in mathematics education in England is that the demand for mathematics teachers is far in excess of the supply. Acknowledging that there are simply too few mathematics teachers, the UK government has invested significantly in retraining programmes. These programmes 'retrain' out-of-field teachers, that is,…

An ongoing debate concerns whether novel mathematical concepts are better learned using contextualised or decontextualised representations. A barrier to resolving this debate, and therefore to progress in the discipline, has been the paucity of validated methods of measuring students' understanding of mathematical concepts. We developed an…

It is generally agreed that good subject knowledge is an important prerequisite for successful teaching. However, what constitutes good subject knowledge is debated, with multiple perspectives taken by policymakers, researchers and schools. This article reports on research into interpretations of 'understanding mathematics in depth' (UMID) of…

This study is aimed at comparing the content in mathematics textbooks from Japan and England, focusing on symmetry and transformations at the lower secondary level. We adopted the concept of praxeology, a main construct of the Anthropological Theory of the Didactic (ATD). Using the ATD framework, our approach regarded textbooks as an empirical…

Drawing upon data gathered from 9301 Year 7 students (12-13 years old) from 46 secondary schools in England, this study represents the first larger-scale attempt to compare their actual set allocations in maths with the counterfactual position where their allocation to sets is based solely on their prior attainment at the end of primary school…

Following sustained discussion regarding the relationship between advanced mathematics and science learning in England, the government has pursued a reform agenda in which mathematics is embedded in national, high stakes A-level science qualifications and their assessments for 18-year-olds. For example, A-level Chemistry must incorporate the…

This article is about Pete's story. It is a story about introducing all-attainment teaching in a secondary school mathematics department and about espousing and enacting a pedagogy and set of practices to enable learning mathematics without limits.

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 (mixed-ability groupings) and School S (sets) in relation to student beliefs, and teacher beliefs and practices. Questionnaire…

Researching students' responses to tasks at different year levels and in varied curriculum contexts can provide insights that relate their understandings to prior learning experiences and teaching approaches. In this article, we discuss evidence of students from three curriculum contexts (English, Australian, and Israeli) (n = 350) ways of…

Achieving fluency in important mathematical procedures is fundamental to students' mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasi-experimental studies carried out in a total of 11 secondary schools involving altogether 528…