Historically there has always been a lively research discussion on whether the development of number concept should be considered as innate, or whether the catalyst for the development of the number concept -- and for counting -- is hearing number words combined with seeing concrete examples. One can recognize these theories as the nativist view…

There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing…

Previous research has reported that children's numerical equivalence judgments are affected by surface similarity and counting ability (e.g. Mix, Huttenlocher, & Levine, 1996; Siegel, 1973), a pattern that suggests categorization processes play a role in numerical development. However, because these studies involved memory for sets, large set…

Based on close observations of two 4-year-old children responding to their parents' requests for quantitative comparisons, we offer a "participationist" account of the origins and development of numerical thinking, one that portrays numbers as a product rather than a pregiven object of human communication. In parallel, we propose a…

This paper examines what children believe about unmapped number words--those number words whose exact meanings children have not yet learned. In Study one, 31 children (ages 2-10 to 4-2) judged that the application of "five" and "six" changes when numerosity changes, although they did not know that equal sets must have the same number word. In…

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…

Two samples of kindergarten children's representation and understanding of written number symbols were examined in two time points in one academic year. About 85% of Chinese five year olds (mean = 5 years 10 months) were able to use conventional number symbols to represent the quantity of 30 or larger. At the end of the kindergarten year, 94% of…

Developmental research suggests that some of the mechanisms that underlie numerical cognition are present and functional in human infancy. To investigate these mechanisms and their developmental course, psychologists have turned to behavioral and electrophysiological methods using briefly presented displays. These methods, however, depend on the…

Two samples of preschool children's representation and understanding of written number symbols was examined in two time points in one academic year. About 40% of Chinese four year olds (mean=4:7) were able to use conventional number symbols to represent the quantity of ten, on average. The majority of these children (85%) could represent written…

Number sense is easy to recognize but difficult to define and hence, to teach. In this article, number sense is defined in terms of the knowledge known to underline it, as identified in cognitive developmental theory and research. A preK-2 mathematics program, called Number Worlds, that was specifically developed to teach this knowledge is…

This paper reports on a study of nursery children's responses to number focused activities. Responses were analysed in terms of cognitive, physical, emotional and social aspects in order to gain insights into what engaged children in number learning opportunities. "Cognitive-emotional hooks" for number activities were identified, involving…

Efforts to improve the educational achievement of children, especially those from disadvantaged backgrounds, are at the heart of current government policies in the United Kingdom. The Peers Early Education Partnership (PEEP) is an intervention that, since 1995, has worked directly with parents and caregivers of children from infancy to 5 years of…