The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…

This book contains 15 essays written between 1969 through 1983. The essays included are: (1) "Semantic Analysis of Verbs in Terms of Conceptual Situations"; (2) "'Because' and the Concepts of Causation"; (3) "The Development of Language as Purposive Behavior"; (4) "Adaptation and Viability"; (5) "On the…

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

Proposes the hypothesis that preschoolers have number concepts based on the numbers 1-5 rather than on the decimal structure. Results suggest that children understand numbers to 5 as a privileged anchor. Proposes a new model for a representational system of numbers. (Author/DR)

Discussed are the results of interviews with 63 Australian children (interviewed in English) and 62 Nigerian children (62 interviewed in English and 60 interviewed in Yoruba) to determine how they used number concepts in discussing five demonstrations manipulating physical matter. Differences between the two groups are considered. (RH)

The study compared two methods of teaching an initial place value skill: a concrete, semiconcrete, abstract teaching sequence and an abstract-only presentation. Learning-disabled elementary and middle school students (N=24) using the concrete to abstract teaching sequence performed significantly better on three posttests than students taught the…

The goal of this study was to describe characteristic stages in the development of children's understanding of place value. Sixty children (15 in each grade, 2 through 5) at 5 elementary schools in Butte County, California, were individually administered 18 tasks designed to reveal their thinking about place value and part-whole relations. On six…

The principles of cognitive psychology as they relate to rational number learning and instruction are discussed. Issues of knowledge acquisition, organization, retrieval and transfer are reviewed as they affect this area of the elementary school curriculum. Specific problems in learning about rational numbers and systematic student errors are…

Presented is a report on four 45-minute sessions with a group of 17-year-old students in Poland. Sessions were the first of a series organized with aim of exploring the possibilities of elaborating didactical situations that would help students overcome epistemological obstacles related to limits. Students' attitudes pertinent to the development…

Compares the Genevan and Cattell-Horn theories of intelligence and describes both similarities and differences. Describes a study investigating the relation of the Piagetian operative level to the child's ability to use crystallized solution procedures (aids) in making elementary numerical comparisons. (HOD)

The article suggests that Belcastro rods, which retain the basic properties of Cuisenaire rods but allow instant identification by touch, may be useful in teaching mathematical concepts to blind children. Drawings illustrate use of the rods in teaching such concepts as addition and subtraction. (Author/DB)

Reports on a study to determine the development of children's understanding of seven properties of the arithmetic mean and to assess the effects of material used in the testing and the medium of presentation. Some differences were found in children's reasoning. No significant differences were found for materials or medium of presentation. (PK)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

What makes a fraction meaningful and a definition of the quantitative notion of fractions are discussed. Then observations from teaching experiments are presented. (MNS)

Studies five-year-olds' relative number judgements of small and large number displays with and without perceptual aids. Children were found to respond to local rather than global density differences and to benefit from the provision of perceptual aids on both small and large number displays. (Author/AS)