On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

As adults, we represent and think about number, space, and time in at least two ways: our intuitive--but imprecise--perceptual representations, and the slowly learned--but precise--number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test…

The authors discuss the use of "real life" activities that are interesting to children in the teaching of measurement and number concepts. In this article, they present a series of lessons targeting volume and capacity that seamlessly incorporate genuine "real-life" experiences with practical mathematical applications. In…

First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations…

Number and operations form the backbone of the school mathematics curriculum. A high school graduate should comfortably and capably meet an expression like, "Let f(x) be a function of a real variable x," implying that the student has a robust sense of the real number continuum. This understanding is a central objective of the school…

Estimation is an essential competence with a developmental role in the learning of various mathematical topics. Yet, as previous studies highlight, this competence is either excluded or ambivalently included in intended curricula around the world. The current study investigates the estimation-related opportunities in the primary curricula of three…

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,…

The proliferation of standardized testing and administrative statistics in compulsory education is embedded in the rise to prominence of quantified accountability as a mechanism of education governance. Numbers work by stripping away the contexts of their production and the granular and ambiguous detail of the phenomena they claim to represent.…

We examine opportunities and challenges of applying a single, explicit definition of multiplication when modeling situations across an important swathe of school mathematics. In so doing, we review two interrelated conversations within multiplication research. The first has to do with identifying and classifying situations that can be modeled by…

On November 16, 2018, at the 26th meeting of the General Conference on Weights and Measures (CGPM), a resolution was adopted that introduced historical changes into the International System of Units (SI). This decision, effective from May 20, 2019, established that the SI units of measurement will be defined by means of a set of seven fixed…

This guide draws on English-related errors from around 6000 papers written by non-native authors, 500 abstracts written by PhD students, and over 2000 hours of teaching researchers how to write and present research papers. This new edition has chapters on exploiting AI tools such as ChatGPT, Google Translate, and Reverso, for generating,…

Explore young children's remarkable everyday math that can lay the groundwork for formal math education in kindergarten and beyond. Readers will learn how math is embedded in children's everyday lives, how daily routines contribute to the development of important math concepts, and what adults can do to foster the joy of early math learning.…

Unlike other data collection modes, the effect of labeling rating scales on reliability and validity, as relevant aspects of measurement quality, has seldom been addressed in online surveys. In this study, verbal and numeric rating scales were compared in split-ballot online survey experiments. In the first experiment, respondents' cognitive…

The process of quantification is a powerful development shaping many domains of life today. In the area of education, for example, performance measurement, testing and ranking have become common tools of governance. Quantification is not a neutral way of describing society, but a process of valorisation. It has three sociologically relevant…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…