Pattern is fundamental to mathematical learning yet pattern has been conspicuously low key within early mathematics curriculum guidance in England despite evidence that it predicts later attainment in mathematics overall. Whilst recent curriculum changes have seen pattern afforded enhanced status, this is within a conception of pattern that marks…

Continuing to study mathematics is currently a requirement for low attaining 16- to 18-year olds in Further Education, as part of an ongoing drive to raise basic numeracy skills in England. However, these students, widely regarded as demotivated, often fail to make any progress in mathematics over the two years. This research explores how students…

Continuing to study mathematics throughout schooling is considered important in most developed countries, where mathematics is incorporated within the curriculum until school-leaving age. By comparison, in England, relatively few post-16 (upper secondary) students study mathematics once it becomes optional. Core Maths qualifications, introduced in…

This study investigates associations between mathematics pedagogy and teachers' integration of Information Communication Technologies (ICT). As an early adopter of presentation-oriented hardware and software in mathematics classrooms, England represents a critical case for investigating associations between mathematics pedagogy and teachers'…

Existing research establishes that lower attaining pupils derive mathematical learning benefit from working in mixed attainment groupings. However, gains for lower attaining pupils are seen to derive from the contributions of higher attaining peers; evidence of the contributions that lower attaining pupils make to mixed attainment activity 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…

Mathematical reasoning requires perseverance to overcome the cognitive and affective difficulties encountered whilst pursuing a reasoned line of enquiry. The aims of the study were: to understand how children's perseverance in mathematical reasoning (PiMR) manifests in reasoning activities, and to examine how PiMR can be facilitated through a…

We demonstrate the power of Variation Theory as an analytical tool used to understand the underlying conceptual structure of mathematics lessons taught by English primary school teachers. We study excerpts of three lessons that are posted on a professional website. We show how lesson analysis using variation allows us to focus on what is made…

This article examines patterns of classroom organisation and interaction associated with the use of a particular type of digital technology -- the dynamic software GeoGebra -- in the lessons of an opportunity sample of three English secondary-school mathematics teachers. The concept of activity structure is used to organise this study, further…

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

This study aims to explore the conceptualisations of function that some students express when they are responding to fictitious students' statements about functions. We also asked them what is meant by "function" and many voluntarily used examples in their responses. The task was developed in collaboration with teachers from two…

This study compared models of assessment structure for achieving differentiation across the range of examinee attainment in the General Certificate of Secondary Education (GCSE) examination taken by 16-year-olds in England. The focus was on the "adjacent levels" model, where papers are targeted at three specific non-overlapping ranges of…

The relationship between the characteristics of 33 mathematical problem-solving questions answered by 16-year-old students in England and the quality of problem-solving elicited was investigated in two studies. The first study used comparative judgement (CJ) to estimate the quality of the problem-solving elicited by each question, involving 33…

The UK Government has set a goal that the "vast majority" of students in England will be studying mathematics to the age of 18 by the end of the decade. The policy levers for achieving this goal include new Core Maths qualifications, designed for over 200,000 students who have achieved good grades at the age of 16 but then opt out of…

Paraprofessionals increasingly work alongside teachers in many countries, with research suggesting they undertake pedagogic roles for which they are not formally prepared. We investigate this from the perspective of paraprofessionals supporting individual children with special needs in primary schools in Cyprus and England and develop a typology…