Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…

For learning math, non-symbolic quantity skills, symbolic skills and the mapping between number symbols and non-symbolic quantities are all important precursors. Little is known, however, about the interrelated development of these skills. The current study focuses on numerical development by: (a) investigating the structure of non-symbolic,…

The impulse to investigate the natural world is deeply rooted in our earliest childhood experiences. This notion has long guided researchers to uncover the cognitive mechanisms underlying the development of scientific reasoning in children. Until recently, however, research in cognitive development and education followed largely independent…

The authors explore how children's play can support the development of the foundations of mathematics learning and how adults can support children's representation of--and thus the "mathematization" of--their play. The authors review research about the amount and nature of mathematics found in the free play of children. They briefly…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

Investigates numerical competence in five-month-old infants using a violation-of-expectation paradigm. Supports previous findings that young children possess not only the competence for limited numerical abstraction, but also the ability to carry out addition and subtraction operations. An alternative explanation, that infants' responses are based…

Conservation of a property is the ability to recognize that the property in question hasn't altered, even though other properties have been varied. It is Piaget's view, confirmed by empirical evidence that children are not able to conserve length until age 7 or 8. Recent concern over confounding variables led to the present study in which the…

This study sought to determine whether a number of specific counting and numeration behaviors emerge within children in a fixed developmental sequence; at what point in the development of mathematical behavior the use of numerical representations normally appears; and what relationship holds between development of counting skills and development…

Explored whether a system between written place-value system and base-10 manipulatives helped children understand place-value. Found evidence that the intermediate system helped children differentiate between face values and complete values of digits in multidigit place-value number representations, and to grasp that the sum of the digits'…

"More" and "less" were analyzed into two meaning dimensions, "occurence" and "quantity", which were hypothesized to be developmentally related to acts of addition and subtraction. (SBT)

To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of five to seven years, children were tested on nonnumerical function tasks, numerical tasks, and aspects of logical reasoning. (PCB)

Investigates the development of understanding of quantity in 36 children with Down's Syndrome. Findings confirmed similarities in sequence of development between Down's Syndrome children and nonretarded children. Down's children who received training recognized conservation of continuous and discontinuous quantity. (RJC)

Arguing that cognitive development involves both conceptual and semiotic achievements, the authors emphasize the distinctness of semiotic issues and develop a differentiated appreciation of semiotic aspects of cognition, particularly in elementary mathematics cognition. Semiotic analyses are provided of differences between counting, adding, and…

This article states that children in the first grade have usually not developed the thought processes which would enable them to understand the typical first-grade math curriculum. (CD)

Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…