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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 book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.
Written by an experienced teacher and teacher educator with widespread experience of teaching mathematics in the UK and internationally, Understanding and Teaching Primary Mathematics combines pedagogy and subject knowledge to build confidence and equip you with all the skills and know-how you need to successfully teach mathematics to children of any age. This fourth edition has been fully updated to reflect the latest research developments and initiatives in the field, including a brand-new chapter on ‘Mastery and mathematics’ and ‘The Singapore approach’ which reflects the current international interest in these approaches to learning and teaching mathematics. Extra features also include helpful callouts to the book’s revised and updated companion website, which offers a shared site with a range of resources relevant to both this book and its companion volume, Teaching for Mathematical Understanding. Stimulating, accessible and well-illustrated, with comprehensive coverage of subject knowledge and pedagogy, Understanding and Teaching Primary Mathematics is an essential purchase for trainee and practising teachers alike.
This book addresses the particular areas of mathematics within the primary curriculum that teachers find difficult to teach and in which children struggle to achieve.. .It begins with introductory sections on how children learn mathematics and is then organised on a subject area basis, dealing with the teaching of particular maths topics. Key topics addressed include rounding and measuring, means and medians, fractions, negative numbers, commutative and associative laws in number operations, and shape and space. .Within each chapter, the authors examine the themes of representing, reasoning and communicating, drawing out both the subject knowledge and ways of teaching each topic. A reference section for studies drawn upon is provided at the end of each chapter.....
Originally published in 1966, the two authors combined skill in their subject with experience of teaching it to students in Africa and elsewhere. Their aim was threefold. First and most important to emphasise to teachers in training how essential it is to regard children as individuals, each with a character and problems resulting from heredity and environment. Secondly, to give the teacher enough knowledge of psychology to help him to understand each pupil’s learning process and behaviour. Thirdly, to stimulate the teacher to observation, enquiry and thought. Each chapter ends with suggested exercises, discussion points and reading references. The book was one of a series offered to Africa teachers in training. The series was designed to help those who were called upon to teach the many subjects of the primary school curriculum or two or more subjects with junior forms of secondary schools. It was dedicated to the proposition that giving a good basic education to a country’s children is vital to its development programme.
Sibling relationships are both patterned and diverse. This report provides an 'insider' perspective on these relationships and highlights their complexity. This book draws on research which explores the views of children in middle childhood, aged between 7 and 13. It shows that relationships varying according to context, with gender and the age hierarchy as important features.
This state-of-the-art review of research covers children's understanding of the school, economics, politics, the law and legal processes, gender roles, social class and occupational groupings, racial groups, ethnic groups and national groups.