This paper reports part of an ongoing investigation into the understanding of irrational numbers by prospective secondary school teachers. It focuses on the representation of irrational numbers as points on a number line. In a written questionnaire, followed by a clinical interview, participants were asked to indicate the exact location of the…

This article presents a story of Robert Andrew's mental engagement with mathematics. It has been jointly written by Robert, who is a Y8 student, and his father, Paul Andrews, who is a mathematics educator. It starts with Robert who presents the context for the story and is followed by Paul's commentary which draws on what Robert has written.…

Many middle-school students struggle with decimals and fractions, even if they do not have a mathematical learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

"Numeracy," so-called on analogy with literacy, is essential for making health and other social judgments in everyday life [Reyna, V. F., & Brainerd, C. J. (in press). The importance of mathematics in health and human judgment: Numeracy, risk communication, and medical decision making. "Learning and Individual Differences."]. Recent research on…

David Schwartz's classic book "How Much Is a Million?" can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2-5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of…

Given the vital importance of using a scientific approach for curriculum development, the authors employed a design experiment methodology (Brown, 1992; Shavelson et al., 2003) to develop and evaluate, FUSION, a first grade mathematics intervention intended for students with or at-risk for mathematics disabilities. FUSION, funded through IES…

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)