The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

A critical examination of two key aspects of Piaget's account of how small children come to understand basic number concepts. (Author/CS)

Two experiments examined the ability of preschool children to reason about the numerical relations greater than and less than. Results showed that children as young as 21/2 years of age could make number-based relational judgments and compare two number pairs on the basis of a common ordering relation. (Author/JMB)

A multiple baseline design was used to demonstrate the effectiveness of a self-instruction training sequence across three groups of three preschool handicapped students to improve their ability to count a requested number of objects from one to ten. Eight of nine students showed improved accuracy in counting objects and generalized these gains to…

Students who discover how to count by tens starting at a number other than 10 learn about the basic structure of the decimal system in addition. (CL)

Investigates the ability of 24 children ages two, three, and four to discriminate between two small object collections on the basis of numerosity and to maintain that discrimination across changes in number-related cues. Most children learned the discrimination and transferred their learning on the basis of relational cues. (Author/CI)

A "proof" is given to show that the set of natural numbers is not countable. (DT)

Examples of unrealistic'' mathematics and mathematical reasoning are presented and discussed. (DT)