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 integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research…

Deficits in basic numerical processing have been identified as a central and potentially causal problem in developmental dyscalculia; however, so far not much is known about the typical and atypical development of such skills. This study assessed basic number skills cross-sectionally in 262 typically developing and 51 dyscalculic children in…

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltesz et al., 2007) here our objective was to identify and compare…

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 relationship between the development of reversible thought and performance in arithmetic equations among children was investigated. Subjects were 86 second grade boys and girls. Two reversibility tasks and 20 addition and subtraction equations were administered. Results indicated significant correlations between the two variables only among…

Described in the context of a computer simulation are highlights of a program of research focusing on the storage of mathematics problem solving information in young children's memory and the development of such knowledge structures in older children. Specifically discussed are the problem size effect, the network nature of the memory…

Presents a three-component model of arithmetical development in young children. Applies this model as a basis for analysis of developmental processes in early mathematics learning that may be universal. (RJC)

Children appear to interpret the "equals" sign as an operator ("adds up to") not a relational ("the same as") symbol--e.g., viewing equations like 13 = 7 + 6 or 8 = 8 as senseless. This study, a natural experiment, examined the effects of long-term instruction emphasizing a relational definition of "equals."…

This study investigated a theoretical structure which attempts to explain the problem-solving strategies used by first-grade students who are successful in solving simple arithmetic story problems. The structure used describes the problem-solving procedure as consisting of a three-stage model building process: (1) comprehending the story, (2)…

This investigation used a clinical interview technique to identify the difficulties of kindergarten children who are unable to develop models or representations of simple arithmetic story problems. It is hypothesized that effective human problem solvers first generate some type of "physical model" and use this model to create a…

Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and…