Initial acquisition of the first symbolic numbers is measured with the Give a Number (GaN) task. According to the classic method, it is assumed that children who know only 1, 2, 3, or 4 in the GaN task, (termed separately one-, two-, three-, and four-knowers, or collectively subset-knowers) have only a limited conceptual understanding of numbers.…

Understanding numerical magnitude is critical to the development of mathematics proficiency. Math interventions targeting magnitude knowledge have been shown to improve outcomes for students with math learning difficulties across grade levels. However, while recent studies have found that growth in magnitude knowledge mediates fractions…

Understanding numerical magnitude is critical to the development of mathematics proficiency, and math interventions targeting magnitude knowledge have been shown to improve outcomes for students with math learning difficulties across grade levels. While recent studies have found that growth in magnitude knowledge mediates fractions intervention…

This study aimed to examine kindergarten children's performance and strategies when answering different types of numerosity estimation questions. To this end, interviews were conducted with 44 children (aged 61-80 months) in an online setting, during which they were asked nine estimation questions of three types. These questions (open-ended,…

Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a…

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…

Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…

Playing board games and other math activities can provide young children with opportunities to develop their math skills. However, it is critical to understand for whom these activities may be most beneficial. In two studies, we examine the extent to which foundational cognitive skills moderate the effects of playing math games on math skills. In…

Researchers have long been interested in the origins of humans' understanding of symbolic number, focusing primarily on how children learn the meanings of number words (e.g., "one", "two", etc.). However, recent evidence indicates that children learn the meanings of number gestures before learning number words. In the present…

How do children construct a concept of natural numbers? Past research addressing this question has mainly focused on understanding how children come to acquire the cardinality principle. However, at that point children already understand the first number words and have a rudimentary natural number concept in place. The question therefore remains;…

The study investigates the knowledge profiles of elementary pre-service teachers (PST) concerning numbers and operations before their professional classroom practice. By validating an instrument through exploratory and confirmatory factor analyses, it identifies and categorizes the PST' performance into distinct profiles based on the mathematical…

The current research aimed to unpack teachers' knowledge of integers by investigating how they used the number line and counter models to represent the two meanings of division (i.e., partitive and measurement). The participants were three middle school mathematics teachers working in different cities in Türkiye. Data consisted of teachers'…

Which dimension of a set of objects is more salient to young children: number or size? The "Build-A-Train" task was developed and used to examine whether children spontaneously use a number or physical size approach on an un-cued matching task. In the Build-A-Train task, an experimenter assembles a train using one to five blocks of a…

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…

There is growing interest in mathematics learning progressions in early childhood education. Counting is a skill usually developed early in life. The application of the counting principles in early childhood typically entails counting objects. This poses challenges for learning about zero. Indeed, the word "zero" is seldom used in the…