A Systemic Perspective On Cognition And Mathematics
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A Systemic Perspective On Cognition And Mathematics
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Author : Jeffrey Yi-Lin Forrest
language : en
Publisher: CRC Press
Release Date : 2013-02-28
A Systemic Perspective On Cognition And Mathematics written by Jeffrey Yi-Lin Forrest and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Computers categories.
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 deve
A Systemic Perspective On Cognition And Mathematics
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Author : Jeffrey Yi-Lin Forrest
language : en
Publisher: CRC Press
Release Date : 2013-02-28
A Systemic Perspective On Cognition And Mathematics written by Jeffrey Yi-Lin Forrest and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Computers categories.
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
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Author : John Adams
language : en
Publisher: Routledge
Release Date : 2017-04-21
The Nature And Development Of Mathematics written by John Adams and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-21 with Education categories.
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
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Author : Camilla Gilmore
language : en
Publisher: Routledge
Release Date : 2018-06-13
An Introduction To Mathematical Cognition written by Camilla Gilmore and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Psychology categories.
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.
Affect And Mathematical Problem Solving
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Author : Douglas B. McLeod
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Affect And Mathematical Problem Solving written by Douglas B. McLeod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Research on cognitive aspects of mathematical problem solving has made great progress in recent years, but the relationship of affective factors to problem-solving performance has been a neglected research area. The purpose of Affect and Mathematical Problem Solving: A New Perspective is to show how the theories and methods of cognitive science can be extended to include the role of affect in mathematical problem solving. The book presents Mandler's theory of emotion and explores its implications for the learning and teaching of mathematical problem solving. Also, leading researchers from mathematics, education, and psychology report how they have integrated affect into their own cognitive research. The studies focus on metacognitive processes, aesthetic influences on expert problem solvers, teacher decision-making, technology and teaching problem solving, and beliefs about mathematics. The results suggest how emotional factors like anxiety, frustration, joy, and satisfaction can help or hinder performance in problem solving.
Situated Cognition
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Author : David Kirshner
language : en
Publisher: Taylor & Francis
Release Date : 2021-12-16
Situated Cognition written by David Kirshner and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Psychology categories.
This book is a result of a symposium at a recent annual meeting of the American Educational Research Association that explored foundational issues relative to situated cognition theory. Its chapters contribute to discourse about repositioning situated cognition theory within the broader supporting disciplines and to resolving the problematics addressed within the book. There is a cumulative vision to the book -- its theme is that the notion of the individual in situated cognition theory needs to be fundamentally reformulated. No theoretical reconfiguration of the social world or of social practices can overcome an individual cast in the dualist tradition. This reformulation probes the physiological, psychoanalytic, and semiotic constitution of persons. Chapters authors cover a wide range of topics including: * transfer of training -- arguing that traditional cognitive psychology has found precious little evidence of people's ability to apply knowledge gained in one context to the problems encountered in another; * ecosocial systems -- a new object of inquiry for situated cognition theory in which the primary units of analysis are not things or people, but processes and practices; * how linkages between discursive practices are manifested as semiotic chaining of signifiers for individuals engaged in everyday activities at home or at school; * how the ability to function in ways that are consistent with logic emerges not through reflective abstraction on actions, but through an enhanced sense of agency as more responsible roles are adopted in daily life practices; * the mutual constitution of social and individual knowledge -- familiar terms and concepts normally available through linguistic labels are cultural models, to be distinguished from the variegated and hidden mid-level meanings that reflect their situated uses in social activity; * the material (neurological) substrate through which cultural models and mid-level meanings emerge; and * how learning environments can be structured to take advantage of the perceptual underpinnings of cognition.
Development Of Mathematical Cognition
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Author : Daniel B. Berch
language : en
Publisher: Academic Press
Release Date : 2015-10-03
Development Of Mathematical Cognition written by Daniel B. Berch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-03 with Psychology categories.
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
Handbook Of Cognitive Mathematics
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Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2022-10-31
Handbook Of Cognitive Mathematics written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-31 with Mathematics categories.
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.
Computation Dynamics And Cognition
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Author : Marco Giunti
language : en
Publisher: Oxford University Press
Release Date : 1997-06-26
Computation Dynamics And Cognition written by Marco Giunti and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-26 with Philosophy categories.
Currently there is growing interest in the application of dynamical methods to the study of cognition. Computation, Dynamics, and Cognition investigates this convergence from a theoretical and philosophical perspective, generating a provocative new view of the aims and methods of cognitive science. 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. In chapter one Giunti employs a dynamical viewpoint to explore foundational issues in computation theory. Using the concept of Turing computability, he precisely and originally defines the nature of a computational system, sharpening our understanding of computation theory and its applications. In chapter two he generalizes his definition of a computational system, arguing that the concept of Turing computability itself is relative to the kind of support on which Turing machine operate. Chapter three completes the book's conceptual foundation, discussing a form of scientific explanation for real dynamical systems that Giunti calls "Galilean explanation." The book's fourth and final chapter develops the methodological thesis that all cognitive systems are dynamical systems. On Giunti's view, a dynamical approach is likely to benefit even those scientific explanations of cognition which are based on symbolic models. Giunti concludes by proposing a new modeling practice for cognitive science, one based on "Galilean models" of cognitive systems. Innovative, lucidly-written, and broad-ranging in its analysis, Computation, Dynamics, and Cognition will interest philosophers of science and mind, as well as cognitive scientists, computer scientists, and theorists of dynamical systems. This book elaborates a comprehensive picture of the application of dynamical methods to the study of cognition. Giunti argues that both computational systems and connectionist networks are special types of dynamical systems. He shows how this dynamical approach can be applied to problems of cognition, information processing, consciousness, meaning, and the relation between body and mind.
Foundations Of Geometric Cognition
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Author : Mateusz Hohol
language : en
Publisher: Routledge
Release Date : 2019-09-12
Foundations Of Geometric Cognition written by Mateusz Hohol and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Psychology categories.
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.