Previous research has demonstrated a link between children's ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved.…

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…

The development of numerical concepts is described from infancy to preschool age. Infants a few days old exhibit an early sensitivity for numerosities. In the course of development, nonverbal mental models allow for the exact representation of small quantities as well as changes in these quantities. Subitising, as the accurate recognition of small…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing…

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…

The arithmetic portion of the Developing Mathematical Processes (DMP) program, as it applies to children of ages 5 to 8, is described in some detail. The terminal objective of the number program of the primary segment of DMP is the ability of the child to correctly write, read and validate mathematical sentences of the form A = B plus or minus X.…

Studies of young children's sequence of development from counting to the beginnings of formal arithmetic are reviewed. Four essential basic skills are identified: use of counting words, enumeration, the cardinality rule, and quantitative comparison. The contribution of counting to the development of arithmetical proficiency is stressed. (JDD)

Examines the concept of number sense in mathematics learning, compares this concept to that of phonological awareness in reading, and urges application of existing research to improving mathematics instruction for students with mathematical disabilities. Reviews research on building automaticity with basic facts, adjusting instruction to address…

Six tests were constructed, four on a pictorial level and two on a symbolic level, to measure the performance of fourth-, fifth-, and sixth-grade children, in three different ability groups, on problems concerning ratios or fractions. Two variables were of interest in the four tests on a pictorial level: (a) "equal" ratio situations vs.…

Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

In this paper four programs are described in which children learn multidigit number concepts and operations with understanding: (1) the Supporting Ten-Structured Thinking projects, (2) the Conceptually Based Instruction project, (3) Cognitively Guided Instruction projects, and (4) the Problem Centered Mathematics Project. The diversity in these…

This study showed that Oksapmin children not only spontaneously use the indigenous numerical system of their nontechnical culture but also have created new forms of numerical symbolization and calculation to deal with schooling arithmetic problems. Novel conceptual developments, factors mediating the schools effect, and the influence of prior…