Abstract Mathematical Cognition
Abstract Mathematical Cognition

Author: Wolfgang Grodd

Publisher: Frontiers Media SA

Published: 2016-08-09

Total Pages: 113

ISBN-13: 2889198162

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Despite the importance of mathematics in our educational systems little is known about how abstract mathematical thinking emerges. Under the uniting thread of mathematical development, we hope to connect researchers from various backgrounds to provide an integrated view of abstract mathematical cognition. Much progress has been made in the last 20 years on how numeracy is acquired. Experimental psychology has brought to light the fact that numerical cognition stems from spatial cognition. The findings from neuroimaging and single cell recording experiments converge to show that numerical representations take place in the intraparietal sulcus. Further research has demonstrated that supplementary neural networks might be recruited to carry out subtasks; for example, the retrieval of arithmetic facts is done by the angular gyrus. Now that the neural networks in charge of basic mathematical cognition are identified, we can move onto the stage where we seek to understand how these basics skills are used to support the acquisition and use of abstract mathematical concepts.

An Introduction to Mathematical Cognition
An Introduction to Mathematical Cognition

Author: Camilla Gilmore

Publisher: Taylor & Francis

Published: 2018-06-13

Total Pages: 265

ISBN-13: 1317410114

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The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.

Development of Mathematical Cognition
Development of Mathematical Cognition

Author: Daniel B. Berch

Publisher: Academic Press

Published: 2015-10-03

Total Pages: 418

ISBN-13: 0128019093

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Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities. Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field. Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition Addresses recent work in quantitative and molecular genetics Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning Informs policy to help increase the level of mathematical proficiency among the general public

Interdisciplinary Perspectives on Math Cognition
Interdisciplinary Perspectives on Math Cognition

Author: Marcel Danesi

Publisher: Springer Nature

Published: 2019-09-14

Total Pages: 344

ISBN-13: 3030225372

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This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.

The Handbook of Mathematical Cognition
The Handbook of Mathematical Cognition

Author: Jamie I.D. Campbell

Publisher: Psychology Press

Published: 2005-08-15

Total Pages: 527

ISBN-13: 1135423660

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How does the brain represent number and make mathematical calculations? What underlies the development of numerical and mathematical abilities? What factors affect the learning of numerical concepts and skills? What are the biological bases of number knowledge? Do humans and other animals share similar numerical representations and processes? What underlies numerical and mathematical disabilities and disorders, and what is the prognosis for rehabilitation? These questions are the domain of mathematical cognition, the field of research concerned with the cognitive and neurological processes that underlie numerical and mathematical abilities. TheHandbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field.

Foundations of Geometric Cognition
Foundations of Geometric Cognition

Author: Mateusz Hohol

Publisher: Routledge

Published: 2019-09-12

Total Pages: 315

ISBN-13: 0429509219

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The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts
Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts

Author: David C. Geary

Publisher: Academic Press

Published: 2017-08-01

Total Pages: 362

ISBN-13: 0128133686

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Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public

How Our Emotions and Bodies are Vital for Abstract Thought
How Our Emotions and Bodies are Vital for Abstract Thought

Author: Anna Sverdlik

Publisher: Routledge

Published: 2018-06-18

Total Pages: 384

ISBN-13: 1351344757

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If mathematics is the purest form of knowledge, the perfect foundation of all the hard sciences, and a uniquely precise discipline, then how can the human brain, an imperfect and imprecise organ, process mathematical ideas? Is mathematics made up of eternal, universal truths? Or, as some have claimed, could mathematics simply be a human invention, a kind of tool or metaphor? These questions are among the greatest enigmas of science and epistemology, discussed at length by mathematicians, physicians, and philosophers. But, curiously enough, neuroscientists have been absent in the debate, even though it is precisely the field of neuroscience—which studies the brain’s mechanisms for thinking and reasoning—that ought to be at the very center of these discussions. How our Emotions and Bodies are Vital for Abstract Thought explores the unique mechanisms of cooperation between the body, emotions, and the cortex, based on fundamental physical principles. It is these mechanisms that help us to overcome the limitations of our physiology and allow our imperfect, human brains to make transcendent mathematical discoveries. This book is written for anyone who is interested in the nature of abstract thought, including mathematicians, physicists, computer scientists, psychologists, and psychiatrists.