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;…

Place value concepts were measured longitudinally from kindergarten (2017) to first grade (2018) in a diverse sample (n = 279; M[subscript age] = 5.76 years, SD = 0.55; 135 females; 41% Black, 38% White, 8% Asian, 12% Latino). Children completed three syntactic tasks that required an explicit understanding of base-10 symbols and three approximate…

Infants and toddlers experience the world in interaction with others. Likewise, social interactions are important in learning about math--concepts of number ("one," "two," "three"), space ("on top," "upside-down," "round"), and magnitude ("more," "big,"…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

We review recently published papers that have contributed to our understanding of how the preverbal infant represents number, area and time. We review evidence that infants rely on two distinct systems to represent number nonverbally and highlight the similarities in the ratio-dependent discrimination of number, time and area. Contrary to earlier…

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…

The development of ordering and correspondence operations, under varying degrees of the presence of length cues to number, was studied in 91 preschool children. Findings are interpreted in terms of the young child's difficulty in separating and coordinating the dimensions of length and number. (Author/ED)

Provides data incongruent with Piaget's idea of a concrete operational stage. Shows no clear-cut termination of preconceptual thinking and no simultaneous conceptual development in the three content areas (number, space, and time). (Author/RL)

Discusses the relationship between geometrical and numerical concepts in the mathematical development of young children. Based upon a longitudinal field study of 224 children, findings suggest that memorization ability facilitates understanding of numerical concepts but that subsequent mathematical development is restricted until basic geometry is…

Research supported by a grant form the U.S. Office of Education, Bureau of Research

A 7-month longitudinal study of 20 2- and 3-year-old children shows that children at an early age already know that counting words each refer to a distinct numerosity, although they do not know to which numerosity. It takes children a long time to learn the latter. (SLD)

A project conducted several years ago to develop informal mathematical learning experiences at kindergarten level is compared with the results of the work-book type (formal) program being used at that time. It is hypothesized that kindergarten pupils who study mathematical concepts in a planned, sequential, systematic, but non-workbook (informal)…

Two sections in this survey of research on conceptualization are devoted to "Recent Conceptual Studies in the Behaviourist Mould" and "Main Stream of Ontogenetic Studies of Conceptualization." Under Section I, topics investigated are behaviourist approaches to the conceptual process, conceptual problems, and developmental…