The authors report the results of some half dozen years of research into when and how children acquire numerical skills. They provide a new set of answers to these questions, and overturn much of the traditional wisdom on the subject. Table of Contents: 1. Focus on the Preschooler 2. Training Studies Reconsidered 3. More Capacity Than Meets the Eye: Direct Evidence 4. Number Concepts in the Preschooler? 5. What Numerosities Can the Young Child Represent? 6. How Do Young Children Obtain Their Representations of Numerosity? 7. The Counting Model 8. The Development of the How-To-Count Principles 9. The Abstraction and Order-Irrelevance Counting Principles 10. Reasoning about Number 11. Formal Arithmetic and the Young Child's Understanding of Number 12. What Develops and How Conclusions References Index Reviews of this book: The publication of this book may mark a sea change in the way that we think about cognitive development. For the past two decades, the emphasis has been on young children's limitations... Now a new trend is emerging: to challenge the original assumption of young children's cognitive incapacity. The Child's Understanding of Number represents the most original and provocative manifestation to date of this new trend. --Contemporary Psychology Reviews of this book: Here at last is the book we have been waiting for, or at any rate known we needed, on the young child and number. The authors are at once sophisticated in their own understanding of number and rich in psychological intuition. They present a wealth of good experiments to support and guide their intuitions. And all is told in so simple and unalarming a manner that even the most pusillanimous will be able to read with enjoyment. --Canadian Journal of Psychology

The authors report the results of some half dozen years of research into when and how children acquire numerical skills. They provide a new set of answers to these questions, and overturn much of the traditional wisdom on the subject.

For some time now, the study of cognitive development has been far and away the most active discipline within developmental psychology. Although there would be much disagreement as to the exact proportion of papers published in developmental journals that could be considered cognitive, 50% seems like a conservative estimate. Hence, a series of scholary books to be devoted to work in cognitive development is especially appropriate at this time. The Springer Series in Cognitive Development contains two basic types of books, namely, edited collections of original chapters by several authors, and original volumes written by one author or a small group of authors. The flagship for the Springer Series is a serial publication of the "advances" type, carrying the subtitle Progress in Cognitive Development Research. Volumes in the Progress sequence are strongly thematic, in that each is limited to some well-defined domain of cognitive developmental research (e. g. , logical and mathematical development, semantic development). All Progress volumes are edited collections. Editors of such books, upon consultation with the Series Editor, may elect to have their works published either as contributions to the Progress sequence or as separate volumes. All books written by one author or a small group of authors will be published as separate volumes within the series. is being used in the selec A fairly broad definition of cognitive development tion of books for this series.

This work argues that cognitive development is experience driven, and processes entailed in acquiring information about the world are analyzed based on recent models of learning and induction. The way information is represented and accessed when performing cognitive tasks is considered paying particular attention to the implications of Parallel Distributed Processing (PDP) models for cognitive development. The first half of the book contains analyses of human reasoning processes (drawing on PDP models of analogy), development of strategies, and task complexity -- all based on aspects of PDP representations. It is proposed that PDP representations become more differentiated with age, so more vectors can be processed in parallel, with the result that structures of greater complexity can be processed. This model gives an account of previously unexplained difficulties in children's reasoning, including some which were influential in stage theories. The second half of the book examines processes entailed in some representative cognitive developmental tasks, including transitive inference, deductive inference (categorical syllogisms), hypothesis testing, learning set acquisition, acquisition and transfer of relational structures, humor, hierarchical classification and inclusion, understanding of quantity, arithmetic word problems, algebra, conservation, mechanics, and the concept of mind. Process accounts of tasks are emphasized, based on applications of recent developments in cognitive science.

This volume celebrates the 50th anniversary of the famous and influential work of Jean Piaget and Alina Szeminska, The Child's Conception of Number. It is a tribute to those two authors as well as to the entire Geneva school that pioneered the genetic study of cognitive structures in children. Dealing with the process of the child's construction of the notion of number -- a very important subject for the child as well as for the teacher, the researcher, and the practicing psychologist -- it summarizes the progress that has been made and outlines new research directions in this area. The book is a compilation of the work of the foremost international researchers in this area and includes a wide spectrum of viewpoints and schools of thought. It also introduces several new authors from Europe, including students of Piaget, to the American academic community.

Children’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.

Rapport fra projektet: Numerosity and the development of arithmetic skills among visual impaired children, hearing impaired children and children without these impairments