One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

Differing research worldviews have typically resulted in interpretations at odds with one another. Yet, leveraging distinct perspectives can lead to novel interpretations and theoretical construction. Via an empirically grounded research commentary, we describe the value of such activity through the lens of previously reported findings. This…

Background/Context: Over the past five decades, policymakers have introduced Public-Private Partnership (PPP) programs in education as a reform in the presence of "government failure," aiming to increase the freedom of school choice, educational productive efficiency, and social equity. While the evidence regarding charters in US is…

Manipulative artefacts are considered useful scaffolds of arithmetic during early years education, but their use is considered less important as children get older. Yet adult arithmetic performance often recruits artefacts to improve accuracy and efficiency, and so the same benefits should accrue to children beyond early years. We propose that…

The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…

Young children naturally engage in mathematics as they play and explore. Although many early childhood educators are aware that children are frequently interacting with mathematical ideas, a certain level of knowledge and awareness is required to identify and highlight the mathematics that children are engaging in and to create opportunities for…

A consistent part of the literature shows the significant role of digital experience in digital natives' cognitive processes. The main goal of the current study was to investigate the impact of digital learning on the improvement of mathematical skills and on some change in cognitive processes in 166 primary school children from schools located in…

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, &…

We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, &…

This handbook presents a wide range of research on adults who have low literacy skills. It looks at the cognitive, affective, and motivational factors underlying adult literacy; adult literacy in different countries; and the educational approaches being taken to help improve adults' literacy skills. It includes not only adults enrolled in adult…

This paper discusses the critical situations I have been asked to "improve" by providing professional development for teams of adult numeracy and functional mathematics teachers in the post-16 sector in London. These situations have not been identified through any research process, but arise from internal management reviews of course…

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…

The present study examines the cognitive activity that is evoked in young children when they are read a picture book that is written for the purpose of teaching mathematics. The focus of this study is to explore the effects of pictures on children's spontaneous mathematical cognitive engagement. The study is based on the assumption that the…