This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bücchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation. The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory

Problem-solving in mathematics is seen by many students as a struggle. Since the capacity to count and understand basic arithmetical concepts (adding, taking away, etc.) is innate and emerges effortlessly in childhood, why does this negative perception and fear of problem-solving exist? This book counteracts this perception by providing a semiotic analysis of problem-solving and, from this analysis, constructing a pedagogical framework for teaching problem-solving that is consistent with the psychology of how humans learn to use signs and symbols. It is based on an experimental math course designed to impart fluency in problem-solving through semiotic training. The positive results of that course inspired the writing of this book.

Standards in numeracy are a constant concern to educational policy-makers. However, why are differences in arithmetical performance so marked? In Individual Differences in Arithmetic, Ann Dowker seeks to provide a better understanding of why these differences in ability exist, encouraging a more informed approach to tackling numeracy difficulties. This book reviews existing research by the author and by others on the subject of arithmetical ability and presents strong evidence to support a componential view of arithmetic. Focusing primarily on children, but including discussion of arithmetical cognition in healthy adults and neuropsychological patients, each of the central components of arithmetic is covered. Within this volume, findings from developmental, educational, cognitive and neuropsychological studies are integrated in a unique approach. This book covers subjects such as: Counting and the importance of individual differences. Arithmetic facts, procedures and different forms of memory. Causes of, and interventions with, mathematical difficulties. The effects of culture, language and experience. The educational implications of these findings are discussed in detail, revealing original insights that will be of great interest to those studying or researching in the areas of education, neuroscience and developmental and cognitive psychology.

DigiCat Publishing presents to you this special edition of "The Psychology of Arithmetic" by Edward L. Thorndike. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.

How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. 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 in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.

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Educational resource for teachers, parents and kids!