The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…

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…

It is over 25 years since Wood, Bruner and Ross (1976, "Journal of Child Psychology and Psychiatry," 17, 89-100) introduced the idea of "scaffolding" to represent the way children's learning can be supported. Despite problems, this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing…

In this article, the authors offer three definitions of dyscalculia, then describe the background and initial progress of the Harrow Dyscalculia Project. Their project in Harrow is associated with ongoing research into numeracy and brain development led by Brian Butterworth, Professor of Cognitive Neuropsychology at UCL. Pupils from Harrow schools…

Problem-posing abilities of 54 third graders who displayed different patterns of achievement in number concepts and novel problem solving were investigated in this paper. The children were administered a problem-posing pretest followed by an instructional program (for half the sample) and a delayed posttest. Among the findings are the limited…

This book contains activities and projects designed to be congruent with three underlying philosophies: the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards; Howard Gardner's multiple intelligences; and manipulatives, activities, and projects. The introduction contains information about educational reforms; multiple…

Defining better implicit models of children's actions in a series of situations is of paramount importance to understanding how knowledge is constructed. The objective of this study was to analyze the implicit mental models used by children in complex change problems to understand the stability of the models and their evolution with the child's…

Equivalent fractions are usually introduced in fourth grade and reviewed repeatedly in the subsequent grades as the four arithmetical operations are taught. In spite of this repeated instruction, the results are disappointing. This paper reviews some data from previous research documenting the difficulty of equivalent fractions, explains this…

A series of puzzle-type activities combining arithmetic reasoning and geometric figures is described and illustrated. (SD)

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

Chapters 11 through 14 of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

On the basis of implications drawn from Piagetian theory, an approach to first-grade arithmetic which eliminated instruction and used only two kinds of activities (situations in daily living and group games) was implemented in an experimental context. Situations in daily living and group games, in contrast to "mechanical" worksheet…

A study was conducted to: (1) observe through a case study approach the exploratory behavior exhibited by 8-year-old boys and girls when calculators were made available in problem-solving situations; (2) investigate changes that occur in the kinds of arithmetical problems children construct following the introduction of calculators; and (3)…