This paper aims to contribute to the advancement of methodological practice for phenomenographic research by introducing the notion of a "lens of awareness," as a device that can enable researchers to zoom into the detail of the research process (the parts of the whole) and out again to the related context of a phenomenographic study…

This study identifies language specific errors made with transcoding tasks to inform possible future pedagogic decisions regarding the language used when teaching early number. We compared children aged 5-7 years from Kuwait and England. The spoken Arabic language of Kuwait gave the opportunity to compare not only languages where the tens and…

In this paper, we examine the national curricula for primary mathematics for each of the four constituent nations of the United Kingdom (England, Northern Ireland, Scotland and Wales) for the estimation-related opportunities they offer children. Framed against four conceptually and procedurally different forms of estimation (computational,…

Parents are frequently advised to use number books to help their children learn the meaning of number words and symbols. How should these resources be designed to best support learning? Previous research has shown that number books typically include multiple concrete representations of number. However, a large body of mathematics education…

Language-specific differences in number words influence number processing even in nonverbal numerical tasks. For instance, the unit-decade compatibility effect in two-digit number magnitude comparison (compatible number pairs [42_57: 4 < 5 and 2 < 7] are responded to faster than incompatible pairs [47_62: 4 < 6 but 7 > 2]) was shown to…

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide "a good foundation in mathematics", has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations…

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N?=?345) in five different secondary schools…

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

We report a randomised controlled trial evaluation of an intensive one-to-one numeracy programme--"Numbers Count"--which formed part of the previous government's numeracy policy intervention--"Every Child Counts." We rigorously designed and conducted the trial to CONSORT guidelines. We used a pragmatic waiting list design to…

This article reports on work undertaken by schools as part of Qualifications and Curriculum Authority's (QCA's) "Engaging mathematics for all learners" project. The goal was to use in the classroom, materials and approaches from a Royal Institution (Ri) Year 10 master-class, "Number Sense", which was inspired by examples from…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Background: Previous work has yielded knowledge of teachers' attributions for children's behaviour. Other studies have helped to develop understanding of teachers' efficacy beliefs. Little work has been undertaken to examine teachers' efficacy beliefs with regard to classroom behaviour. Aims: This study aimed to investigate the relationship…

In recent times considerable attention has been devoted to the performance of schools and in particular, of students in literacy and numeracy. As part of a national agenda addressing what is portrayed as a crisis in numeracy, and hence mathematics education, governments have introduced a wide range of reform initiatives to improve performance.…

A fundamental question in developmental science is how brains with and without language compute numbers. Measuring young children's verbal reactions in Spain and Finland, we show that, although there is a general arithmetic ability for small numbers that is shared by monkeys and preverbal infants, the development of such initial knowledge in…