Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover how numbers relate to one another in a structured number system. Do children who understand that the cardinality of a set is…

The current longitudinal study measured 279 kindergartners' (M[subscript age] = 5.76 years; SD = 0.55; 135 females) place value understanding using both approximate and syntactic measures based on previous evidence that early variation in performance on approximate measures was associated with subsequent syntactic place value understanding. In the…

The purpose of this quantitative, quasi-experimental nonequivalent control group study was to determine if there is a difference in mathematical fact fluency among third-, fourth-, and fifth-grade students with varying practice methods and spacing intervals while controlling for pre-test scores. The study filled the literature gap by examining the…

This study investigates how the approximate number system (ANS) and young children's symbolic skills jointly develop and interact. Specifically, the study aims at disentangling the directionality of the association between ANS acuity and a wide range of symbolic skills that reflect 4- to 5-year-olds' symbolic quantitative knowledge (enumeration…

Children vary widely in their number knowledge by the time they enter kindergarten, and this variation is related to their future academic success. Although talk about number predicts children's early understanding of foundational number concepts, we know little about whether interventions can increase this talk nor about the types of number talk…

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate…

Throughout the history of public education in the United States of America, the teaching of mathematics and its focus have been topics of reform and calls for change. Students need a balanced and intentional approach to learning mathematics, which supports each student in understanding and applying mathematical concepts. The purpose of this study…

Background/purpose: This article aims to analyze the use of serious games from the Hypatiamat Platform to promote mental arithmetic in a first-grade primary school class in an Exploratory Teaching environment. Materials/methods: This study is mixed, interpretative, and action-research in design. It quantitatively analyses the students' Level of…

Research has shown that computational thinking and kindergarten mathematics instruction can be integrated; however, evidence of how specific mathematical knowledge relates to computational thinking remains scarce. Additionally, we do not know if and how children's mathematical knowledge co-occurs with computational thinking and how these…

Texts presenting novel numerical data can shift learners' attitudes and conceptions about controversial science topics. However, little is known about the mechanisms underlying this conceptual change. The purpose of this study was to investigate two potential mechanisms that underlie learning from novel data: numerical estimation skills and…

This paper aims to present how quantitative literacy was made a focus in a preschool classroom of threeand four-year-old children. With a focus on examining two areas of quantitative literacy, number knowledge and counting (Jordan, Kaplan, and Locuniak 2007) we seek to explore how educators, within an early childhood setting, used a project…

Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and…

We identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on the practical uses of mathematics and an increased emphasis on verbalizations as opposed to numerical and computational skills. With tools provided by John Dewey, an early advocate of contextual and practical…

Children's spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children's focus on numerosity, may reveal whether task materials can implicitly prompt children to…

In this paper we describe the development of an online tool for assessing the foundational knowledge and competencies essential to understanding money and building financial literacy. We present findings from an initial study using the tool to (i) measure basic skills with money among secondary students with intellectual disability (N = 85) and…