There is a growing consensus in research that children's numerical competence starts to develop at a very early age. However, there are few tools for screening the development of early numerical competence and thereby making this development researchable. One obstacle in designing such tools is that verbal utterances cannot be used as the primary…

Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

A vast body of work highlights executive functions (EFs) as robust correlates of mathematics achievement over the primary and preschool years. Yet, despite such correlational evidence, there is limited evidence that EF interventions yield improvements in early years mathematics. As intervention studies are a powerful tool to move beyond…

What is the nature of the relationship between different lower-level numerical skills and their role in developing arithmetic skills? We consider the hypothesis of a reciprocal relationship between the development of symbolic (e.g., Arabic numerals) and nonsymbolic (e.g., arrays of objects) numerical magnitude processing. Evidence for…

In Singapore, where primary and secondary students routinely top standardized worldwide mathematics examinations, a paradox emerges: when reaching university, many struggle to apply their skills critically in real-world contexts. This commentary examines the challenges and strategies involved in teaching quantitative reasoning (QR) to…

The OECD Future of Education and Skills 2030 report on mathematics curriculum presents first-of-its-kind comparative data on how countries are adapting curricula to meet the demands of the 21st century. The project's unique data illustrate a 25-year evolution of mathematics curricula in various countries, looking at content coverage and the…

Since the development of the term numeracy in the mid-fifties in the United Kingdom, the concept of what numeracy is and how it is defined has undergone many changes. The Australian education community continues to explore the concept of numeracy, consider the place and definition of numeracy in the curriculum and consider its relationship with…

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and…

This issue of the Adult Skills in Focus series looks at gender differences in reading (literacy) and mathematics (numeracy) skills, and in particular how these differences evolve as people grow up. The analysis use data on three different assessments, administered to children in fourth grade (around 10 year-olds), to 15-year old adolescents, and…

The Programme for the International Assessment of Adult Competencies (PIAAC) has recently drawn additional attention to "mathematical literacy" as an important influential factor for individuals' life chances. High levels of mathematical literacy have thereby been linked to using mathematics in daily and working life frequently. In this…

Many resources have been created with the aim of helping children and adults overcome difficulties with mathematics and to develop or improve their numeracy. However, these are only used once the individual has decided to act -- to do something to improve their mathematics and numeracy. Unfortunately, someone who knows that they need to improve…

In the 2012 PIAAC Survey of Adult Skills of 23 industrialised countries, the UK (England & NI) scored below average on adult numeracy. Several recommendations focus on the need for (some) individuals in the population to undergo training. Yet, even in "high-performing countries" like the Netherlands, many adults (1.5M) score at or…

In this chapter, we review two approaches for understanding these national differences in math abilities. The first approach attempts to link cross-national differences in educational input to cross-national differences in test scores. A tacit assumption of this approach is that children's performance on tests of mathematics is a direct effect of…

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…