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, 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…

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…

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…

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;…

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…

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…

A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (M[subscript age] = 3.86 years; N = 216; 99 males; 80.8%…

Understanding large number data is essential for making sense of real-world problems. For the research reported here, our intent was to find connections between quantitative cognitive science studies and our prior qualitative study about participants' understanding of the relative size of large numbers. While all 23 cognitive science research…

The conceptual development of natural number in preschoolers is well-researched. However, less is known about the conceptual development of zero. Recent studies suggest that children develop an understanding of zero after learning to count. It remains unclear, when a conceptual understanding of "zero" as number word for an empty set…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…