This article reconsiders Case's theory of central conceptual structures (CCS), examining the relation between working memory and the acquisition of quantitative CCS. The lead hypothesis is that the development of working memory capacity shapes the development of quantitative concepts (whole and rational numbers). Study I, with 779 children from…

Children's first mathematics concept is their understanding of the quantities represented by number words (cardinal value), and the age at which they achieve this insight predicts their readiness for mathematics learning in school. We provide the first exploration of the factors that influence the age of becoming a cardinal principle knower (CPK),…

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

Research Findings: A total of 72 Head Start children (M age = 53.26 months, SD = 5.07) were randomly assigned to 4 conditions. Some were taught the oddity principle (choosing the object that differs from others in a group) and seriation (ordering objects on a dimension and inserting new objects into such orders), which are forms of thinking that…

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and…

To date, a number of studies have demonstrated the existence of mismatches between children's "implicit" and "explicit" knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to…

Presents experimental findings that indicate that some number capacity is present in 22-week old infants, long before the onset of verbal counting. Suggests that verbal counting may have precursors present during infancy. (CS)

Adapted Keil's predictability method to examine adults' and preschoolers' conceptions of numbers, focusing on the ontological distinction between numbers and sets of objects. Found that children, like adults, attribute spatial-arrangement properties to collections much more than to numbers, although both are considered to have quantitative…

The author argues on theoretical grounds that not all "logical" pre-number activities are equally relevant for numeracy, and concludes with a practical suggestion for the kind of activity which does have particular relevance. (MN)

A teaching experiment with six third graders to analyze their ways of operating while solving fraction tasks. Children's quantitative reasoning with fractions was based on their quantitative reasoning with natural numbers. Presents the constructive itinerary of one of the most advanced children in the group. (Contains 44 references.) (Author/MDH)

The purpose of the study was to determine whether kindergarten children could perform successfully on Piagetian class inclusion tasks and whether their performance was a function of the types of conditions under which the task was presented. Children were asked to classify items based on a physical attribute not visually perceptible (painted…

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 the ability to associate numerals with sets of appropriate size was studied in children, ages 4 to 5-1/2. (ST)

Study supported by grant number 00870-05 from the National Institute of Child Health and Human Development.

Three- to 7-year-old children were trained through reinforcement to select the more or less numerous of two rows of squares. All children successfully judged relative numerosity when number covaried with length or density, but only concrete operational children were successful when numbers did not covary with other dimensions. (Author/DB)