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Arithmetic is still hugely important in many aspects of modern life, but our personal attitudes to it differ greatly. Many people struggle with the basic principles of arithmetic, whilst others love it and feel confident in their arithmetical abilities. Why are there so many individual differences in people’s performance in, and feelings about, arithmetic? Individual Differences in Arithmetic explores the idea that there is no such thing as arithmetical ability, only arithmetical abilities. The book discusses several important components of arithmetic, from counting principles and procedures to arithmetical estimation, alongside emotional and cognitive components of arithmetical performance. This edition has been extensively revised to include the latest research, including recent cross-cultural and cross-linguistic research, the development of new interventions for children with difficulties and studies of early foundations of mathematical abilities. Drawing on developmental, educational, cognitive and neuropsychological studies, this book will be essential reading for all researchers of mathematical cognition. It will also be of interest to educators and other professionals working within individuals with arithmetic deficits.
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.
This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.
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.
This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars, past and present, have suggested. The results of psychological, educational, and clinical studies using a wide range of arithmetic tasks and populations (including "normally" and atypically developing children, non-injured and brain-injured adults, and savants) all point to the same conclusion: The heart of arithmetic fluency, in general, and the flexible and creative use of strategies, in particular, is what is termed "adaptive expertise" (meaningful or conceptually based knowledge). The construction of adaptive expertise in mathematics is, for the first time, examined across various arithmetic topics and age groups. This book will be an invaluable resource for researchers and graduate students interested in mathematical cognition and learning (including mathematics educators, developmental and educational psychologists, and neuropsychologists), educators (including teachers, curriculum supervisors, and school administrators), and others interested in improving arithmetic instruction (including officials in national and local education departments, the media, and parents).
Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. - Covers methodologies in studying emotion in mathematical knowledge - Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition - Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches - Explores the role of anxiety in mathematical learning - Synthesizes unifies the work of multiple sub-disciplines in one place
Published in 1981, Psychology of Mathematics for Instruction is a valuable contribution to the field of Education.
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.