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

Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children.

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

What is Thinking? – Trying to Define an Equally Fascinating and Elusive Phenomenon Human thinking is probably the most complex phenomenon that evolution has come up with until now. There exists a broad spectrum of definitions, from subs- ing almost all processes of cognition to limiting it to language-based, sometimes even only to formalizable reasoning processes. We work with a “medium sized” definition according to which thinking encompasses all operations by which cog- tive agents link mental content in order to gain new insights or perspectives. Mental content is, thus, a prerequisite for and the substrate on which thinking operations are executed. The largely unconscious acts of perceptual object stabilization, ca- gorization, emotional evaluation – and retrieving all the above from memory inscriptions – are the processes by which mental content is generated, and are, therefore, seen as prerequisites for thinking operations. In terms of a differentia specifica, the notion of “thinking” is seen as narrower than the notion of “cognition” and as wider than the notion of “reasoning”. Thinking is, thus, seen as a subset of cognition processes; and reasoning processes are seen as a subset of thinking. Besides reasoning, the notion of thinking includes also nonexplicit, intuitive, and associative processes of linking mental content. According to this definition, thinking is not dependant on language, i. e. also many animals and certainly all mammals show early forms of thinking.

This book provides a thrilling description of preliterate children's developing ideas about writing and numerals, and it illustrates well the many ways in which cultural artifacts influence the mind and vice versa. Remarkably, children treat writing and numerals as distinct even before they have received any formal training on the topic, and well before they learn how to use writing to represent messages and numerals to represent quantities. In this revolutionary new book, Liliana Tolchinsky argues that preliterate children's experiences with writing and numerals play an essential and previously unsuspected role in children's subsequent development. In this view, learning notations, such as writing is not just a matter of acquiring new instruments for communicating existing knowledge. Rather, there is a continual interaction between children's understanding of the features of a notational system and their understanding of the corresponding domain of knowledge. The acquisition of an alphabetic writing system transforms children's view of language, and the acquisition of a formal system of enumeration transforms children's understanding of numbers. Written in an engaging narrative style, and richly illustrated with historical examples, case studies, and charming descriptions of children's behavior, this book is aimed not only at cognitive scientists, but also at educators, parents, and anyone interested in how children develop in a cultural context.