A Systemic Perspective On Cognition And Mathematics

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A Systemic Perspective on Cognition and Mathematics

Author : Jeffrey Yi-Lin Forrest
Publisher : CRC Press
ISBN 13 : 1138000167
Total Pages : 444 pages
Book Rating : 4.1/5 (38 download)

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Book Synopsis A Systemic Perspective on Cognition and Mathematics by : Jeffrey Yi-Lin Forrest

Download or read book A Systemic Perspective on Cognition and Mathematics written by Jeffrey Yi-Lin Forrest and published by CRC Press. This book was released on 2013-02-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of human thought, its systemic structure, and the historical development of mathematics both as a product of thought and as a fascinating case analysis. After demonstrating that systems research constitutes the second dimension of modern science, the monograph discusses the yoyo model, a recent ground-breaking development of systems research, which has brought forward revolutionary applications of systems research in various areas of the traditional disciplines, the first dimension of science. After the systemic structure of thought is factually revealed, mathematics, as a product of thought, is analyzed by using the age-old concepts of actual and potential infinities. In an attempt to rebuild the system of mathematics, this volume first provides a new look at some of the most important paradoxes, which have played a crucial role in the development of mathematics, in proving what these paradoxes really entail. Attention is then turned to constructing the logical foundation of two different systems of mathematics, one assuming that actual infinity is different than potential infinity, and the other that these infinities are the same. This volume will be of interest to academic researchers, students and professionals in the areas of systems science, mathematics, philosophy of mathematics, and philosophy of science.

The Nature and Development of Mathematics

Author : John Adams
Publisher : Routledge
ISBN 13 : 1317300181
Total Pages : 348 pages
Book Rating : 4.3/5 (173 download)

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Book Synopsis The Nature and Development of Mathematics by : John Adams

Download or read book The Nature and Development of Mathematics written by John Adams and published by Routledge. This book was released on 2017-04-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: From an infant’s first grasp of quantity to Einstein’s theory of relativity, the human experience of number has intrigued researchers for centuries. Numeracy and mathematics have played fundamental roles in the development of societies and civilisations, and yet there is an essential mystery to these concepts, evidenced by the fear many people still feel when confronted by apparently simple sums. Including perspectives from anthropology, education and psychology, The Nature and Development of Mathematics addresses three core questions: Is maths natural? What is the impact of our culture and environment on mathematical thinking? And how can we improve our mathematical ability? Examining the cognitive processes that we use, the origins of these skills and their cultural context, and how learning and teaching can be supported in the classroom, the book contextualises each issue within the wider field, arguing that only by taking a cross-disciplinary perspective can we fully understand what it means to be numerate, as well as how we become numerate in our modern world. This is a unique collection including contributions from a range of renowned international researchers. It will be of interest to students and researchers across cognitive psychology, cultural anthropology and educational research.

An Introduction to Mathematical Cognition

Author : Camilla Gilmore
Publisher : Routledge
ISBN 13 : 1317410106
Total Pages : 248 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis An Introduction to Mathematical Cognition by : Camilla Gilmore

Download or read book An Introduction to Mathematical Cognition written by Camilla Gilmore and published by Routledge. This book was released on 2018-06-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cognition in Practice

Author : Jean Lave
Publisher : Cambridge University Press
ISBN 13 : 9780521357340
Total Pages : 236 pages
Book Rating : 4.3/5 (573 download)

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Book Synopsis Cognition in Practice by : Jean Lave

Download or read book Cognition in Practice written by Jean Lave and published by Cambridge University Press. This book was released on 1988-07-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most previous research on human cognition has focused on problem-solving, and has confined its investigations to the laboratory. As a result, it has been difficult to account for complex mental processes and their place in culture and history. In this startling - indeed, disco in forting - study, Jean Lave moves the analysis of one particular form of cognitive activity, - arithmetic problem-solving - out of the laboratory into the domain of everyday life. In so doing, she shows how mathematics in the 'real world', like all thinking, is shaped by the dynamic encounter between the culturally endowed mind and its total context, a subtle interaction that shapes 1) Both tile human subject and the world within which it acts. The study is focused on mundane daily, activities, such as grocery shopping for 'best buys' in the supermarket, dieting, and so on. Innovative in its method, fascinating in its findings, the research is above all significant in its theoretical contributions. Have offers a cogent critique of conventional cognitive theory, turning for an alternative to recent social theory, and weaving a compelling synthesis from elements of culture theory, theories of practice, and Marxist discourse. The result is a new way of understanding human thought processes, a vision of cognition as the dialectic between persons-acting, and the settings in which their activity is constituted. The book will appeal to anthropologists, for its novel theory of the relation of cognition to culture and context; to cognitive scientists and educational theorists; and to the 'plain folks' who form its subject, and who will recognize themselves in it, a rare accomplishment in the modern social sciences.

Mathematical Cognition

Author : James M. Royer
Publisher : IAP
ISBN 13 : 1607527960
Total Pages : 273 pages
Book Rating : 4.6/5 (75 download)

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Book Synopsis Mathematical Cognition by : James M. Royer

Download or read book Mathematical Cognition written by James M. Royer and published by IAP. This book was released on 2003-01-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Logic and Information

Author : Keith J. Devlin
Publisher : Cambridge University Press
ISBN 13 : 9780521499712
Total Pages : 334 pages
Book Rating : 4.4/5 (997 download)

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Book Synopsis Logic and Information by : Keith J. Devlin

Download or read book Logic and Information written by Keith J. Devlin and published by Cambridge University Press. This book was released on 1995-09-29 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paperback edition of ground-breaking new theory of information processing.

Development of Mathematical Cognition

Author : Daniel B. Berch
Publisher : Academic Press
ISBN 13 : 0128019093
Total Pages : 414 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Development of Mathematical Cognition by : Daniel B. Berch

Download or read book Development of Mathematical Cognition written by Daniel B. Berch and published by Academic Press. This book was released on 2015-10-03 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

Author : George Lakoff
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being by : George Lakoff

Download or read book Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and published by . This book was released on 2000-11-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the cognitive science of mathematical ideas.

General Systems Theory

Author : Jeffrey Yi-Lin Forrest
Publisher : Springer
ISBN 13 : 3030045587
Total Pages : 370 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis General Systems Theory by : Jeffrey Yi-Lin Forrest

Download or read book General Systems Theory written by Jeffrey Yi-Lin Forrest and published by Springer. This book was released on 2018-12-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the theoretical value and practical significance of systems science and its logic of thinking by presenting a rigorously developed foundation—a tool for intuitive reasoning, which is supported by both theory and empirical evidence, as well as practical applications in business decision making. Following a foundation of general systems theory, the book presents an applied method to intuitively learn system-sciences fundamentals. The third and final part examines applications of the yoyo model and the theoretical results developed earlier within the context of problems facing business decision makers by organically combining methods of traditional science, the first dimension of science, with those of systems science, the second dimension, as argued by George Klir in the 1990s. This text would benefit graduate students, researchers, or practitioners in the areas of mathematics, systems science or engineering, economics, and business decision science.

A New Foundation for Representation in Cognitive and Brain Science

Author : Jaime Gómez-Ramirez
Publisher : Springer Science & Business Media
ISBN 13 : 9400777388
Total Pages : 193 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis A New Foundation for Representation in Cognitive and Brain Science by : Jaime Gómez-Ramirez

Download or read book A New Foundation for Representation in Cognitive and Brain Science written by Jaime Gómez-Ramirez and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus. The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks. The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.

Memory Evolutive Systems; Hierarchy, Emergence, Cognition

Author : A C Ehresmann
Publisher : Elsevier
ISBN 13 : 9780080555416
Total Pages : 402 pages
Book Rating : 4.5/5 (554 download)

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Book Synopsis Memory Evolutive Systems; Hierarchy, Emergence, Cognition by : A C Ehresmann

Download or read book Memory Evolutive Systems; Hierarchy, Emergence, Cognition written by A C Ehresmann and published by Elsevier. This book was released on 2007-05-25 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Memory Evolutive Systems; Hierarchy, Emergence, Cognition provides comprehensive and comprehensible coverage of Memory Evolutive Systems (MEM). Written by the developers of the MEM, the book proposes a mathematical model for autonomous evolutionary systems based on the Category Theory of mathematics. It describes a framework to study and possibly simulate the structure of living systems and their dynamic behavior. This book contributes to understanding the multidisciplinary interfaces between mathematics, cognition, consciousness, biology and the study of complexity. It is organized into three parts. Part A deals with hierarchy and emergence and covers such topics as net of interactions and categories; the binding problem; and complexifications and emergence. Part B is about MEM while Part C discusses MEM applications to cognition and consciousness. The book explores the characteristics of a complex evolutionary system, its differences from inanimate physical systems, and its functioning and evolution in time, from its birth to its death. This book is an ideal reference for researchers, teachers and students in pure mathematics, computer science, cognitive science, study of complexity and systems theory, Category Theory, biological systems theory, and consciousness theory. It would also be of interest to both individuals and institutional libraries. Comprehensive and comprehensible coverage of Memory Evolutive System Written by the developers of the Memory Evolutive Systems Designed to explore the common language between sciences

Interdisciplinary Perspectives on Math Cognition

Author : Marcel Danesi
Publisher : Springer
ISBN 13 : 9783030225360
Total Pages : 0 pages
Book Rating : 4.2/5 (253 download)

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Book Synopsis Interdisciplinary Perspectives on Math Cognition by : Marcel Danesi

Download or read book Interdisciplinary Perspectives on Math Cognition written by Marcel Danesi and published by Springer. This book was released on 2019-09-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Cognitive Mathematics

Author : Marcel Danesi
Publisher : Springer Nature
ISBN 13 : 3031039459
Total Pages : 1392 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Handbook of Cognitive Mathematics by : Marcel Danesi

Download or read book Handbook of Cognitive Mathematics written by Marcel Danesi and published by Springer Nature. This book was released on 2022-10-31 with total page 1392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cognitive mathematics provides insights into how mathematics works inside the brain and how it is interconnected with other faculties through so-called blending and other associative processes. This handbook is the first large collection of various aspects of cognitive mathematics to be amassed into a single title, covering decades of connection between mathematics and other figurative processes as they manifest themselves in language, art, and even algorithms. It will be of use to anyone working in math cognition and education, with each section of the handbook edited by an international leader in that field.

Enhancing Thinking Skills in the Sciences and Mathematics

Author : Diane F. Halpern
Publisher : Psychology Press
ISBN 13 : 9780805810530
Total Pages : 172 pages
Book Rating : 4.8/5 (15 download)

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Book Synopsis Enhancing Thinking Skills in the Sciences and Mathematics by : Diane F. Halpern

Download or read book Enhancing Thinking Skills in the Sciences and Mathematics written by Diane F. Halpern and published by Psychology Press. This book was released on 1992 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years national and international reports have been issued that speak of the sad state of the educational system in the United States and the desperate need for reform in teaching science and mathematics. Cognitive psychologists and mathematics and science educators have responded to this need by designing instructional programs that are more compatible with our knowledge of how people acquire, use, and retain knowledge. Many of the guiding principles that underlie these programs are presented in this volume such as teaching comprehension of scientific text through a problem-solving approach: problem planning and representation, selection of relevant information, and simultaneous monitoring of both the specifics of the problem and the mental processes being used to solve it.

Computation, Dynamics, and Cognition

Author : Marco Giunti
Publisher : Oxford University Press, USA
ISBN 13 : 0195090098
Total Pages : 192 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Computation, Dynamics, and Cognition by : Marco Giunti

Download or read book Computation, Dynamics, and Cognition written by Marco Giunti and published by Oxford University Press, USA. This book was released on 1997-07-24 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advancing the dynamical approach as the methodological frame best equipped to guide inquiry in the field's two main research programs - the symbolic and connectionist approaches - Marco Giunti engages a host of questions crucial not only to the science of cognition, but also to computation theory, dynamical systems theory, philosophy of mind, and philosophy of science.

Cognitive Foundations for Improving Mathematical Learning

Author : David C. Geary
Publisher : Academic Press
ISBN 13 : 0128159537
Total Pages : 377 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Cognitive Foundations for Improving Mathematical Learning by : David C. Geary

Download or read book Cognitive Foundations for Improving Mathematical Learning written by David C. Geary and published by Academic Press. This book was released on 2019-01-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. Identifies the relative influence of school and family on math learning Discusses the efficacy of numerical play for improvement in math Features learning trajectories in math Examines the role of math language in numeracy skills Includes assessments of math skills Explores the role of cognition in treating math-based learning difficulties

Interdisciplinary Perspectives on Math Cognition

Author : Marcel Danesi
Publisher : Springer Nature
ISBN 13 : 3030225372
Total Pages : 344 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Interdisciplinary Perspectives on Math Cognition by : Marcel Danesi

Download or read book Interdisciplinary Perspectives on Math Cognition written by Marcel Danesi and published by Springer Nature. This book was released on 2019-09-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.