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date: 14 December 2019

(p. vii) Preface

(p. vii) Preface

Numbers are crucial and pervasive in many areas: science, economics, sports, education, and everyday life. The human ability to represent and understand numbers is a puzzling paradox: in some ways universal; in other ways subject to huge individual and cultural differences, with many people experiencing difficulties that seriously affect them in everyday life.

Numerical cognition, which in this book refers to basic numerical skills as well as mathematical abilities and learning, has in recent years become a vibrant area that brings together scientists from different and diverse research areas (e.g. neuropsychology, cognitive psychology, neuroscience, developmental psychology, comparative psychology, anthropology, education, computer science, and philosophy) using different methodological approaches (e.g. behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; physiology and lesion studies in non-human primates, habituation studies in human infants and animals, and computational modeling).

Despite its importance, the study of numerical cognition had been relatively neglected for a long time. However, especially during the last decade there has been an explosion of studies and new findings, due partly to technological advances enabling sophisticated human neuroimaging techniques and neurophysiological studies of monkeys, and partly to advances in more traditional psychological and educational research. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils’ mathematical achievement, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties.

The primary goal of this handbook is to bring together the different research areas that constitute contemporary research in the field of numerical cognition to one comprehensive and authoritative volume. This provides a broad and extensive review of this field that is written in an accessible form for scholars and students, as well as educationists and policy makers. The book covers the most important aspects of numerical cognition research from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal neuroscience, computational modeling, education and individual differences, and philosophy in fifty-three chapters and seven overview chapters that provide a state-of-the-art review of the current literature.

The book is divided into eight sections. The first section provides a general introduction including a chapter on how mathematics can be communicated to a general audience and a chapter that discusses numerical cognition from a philosophical perspective.

The section after the introduction introduces the major theoretical accounts that have been formulated in the field of cognitive psychology based primarily on behavioral research in humans. The following two sections cover empirical findings on the ontogeny and phylogeny of numerical understanding, and the effect of culture and language on numerical (p. viii) competence and mathematical understanding. These sections are followed by a section on neuroscience and mathematics, which deals with neuronal and neural mechanisms that are involved in mathematical understanding in monkeys and humans, and a chapter that relates some of these empirical findings to computational models.

After the sections on typical numerical understanding with regard to its development, cognitive mechanisms, and neural architecture, we provide a section that deals with numerical disabilities of congenital or acquired origin, and methods for rehabilitation and intervention.

The last two sections discuss mathematics from the perspective of education and individual differences. These sections provide a useful way to link the research discussed up to that point with its practical and social applications, e.g. improving classroom mathematics education.

A special feature of this book is the ‘navigator’ chapters. The role of these chapters, which appear at the beginning of each section (aside from the Introduction) is to provide an integration of the section, together with the future direction that the field needs to go (therefore navigating the field). We chose to include this type of chapter in order that the non-specialist could read an overview on the field, and decide if they would like to read part or the whole of the section, or just use the navigator for a quick update. This will make it more likely that readers will gain a comprehensive overview of the area, even if they choose not to engage in a detailed reading of sections that do not relate to their work (albeit they are encouraged!). We hope that these navigator chapters will also be useful to people who are actively seeking brief reviews of specific fields.

This book could have not been produced by ourselves alone, and we are honored and privileged to have engaged scientists and researchers whose valuable contributions have advanced and elucidated these areas of research. These authors have paved the way to several of the most relevant discoveries in the field, and have provided excellent chapters that provide state-of-the-art knowledge. Undoubtedly, as much as we wanted to, we could not cover all topics or involve all researchers in the field in this volume, and some of those who did not contribute to this book as authors were courteous enough to serve as reviewers and provide excellent feedback that improved the chapters in this book.

We wish to thank all the authors for their contributions, which have also increased our own knowledge of the field. We would also like to thank the reviewers who gave time to providing such useful feedback for the various chapters. We are grateful to Martin Baum, the acquisitions editor, and to Charlotte Green, the Senior Assistant Commissioning Editor, for all their support during the various stages of this project. Thanks are due to the Wellcome Trust for their support of Roi, and to the Esmee Fairbairn Foundation, the Caxton Trust and the Education Endowment Fund for financial support to Ann, which enabled them to complete this book. Last, Roi would like to thank Kathrin, his wife, Jonathan and Itamar, his children, and his students for their patience and support. Ann would like to thank all who have helped and supported her over the years.

We trust that this book will provide a valuable contribution in promoting future discoveries, providing material for critical discussions, and educating readers about this fascinating and promising field.