Numerical Cognition And The Epistemology Of Arithmetic
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Numerical Cognition And The Epistemology Of Arithmetic
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Author : Markus Pantsar
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-31
Numerical Cognition And The Epistemology Of Arithmetic written by Markus Pantsar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-31 with Science categories.
The first book-length philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition.
Dual Process Theories Of Numerical Cognition
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Author : Mario Graziano
language : en
Publisher: Springer
Release Date : 2018-08-12
Dual Process Theories Of Numerical Cognition written by Mario Graziano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-12 with Science categories.
This book presents a philosophical interpretation to numerical cognition based on dual process theories and heuristics. It shows how investigations in cognitive science can shed light on issues traditionally raised by philosophers of mathematics. The analysis will also help readers to better understand the relationship between current neuroscientific research and the philosophical reflection on mathematics. The author seeks to explain the acquisition of mathematical concepts. To accomplish this, he needs to answer two questions. How can the concepts of approximate numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills. However, the author details a solution to this problem: dual process theories. It is an approach widely used by theorists focusing on reasoning, decision making, social cognition, and consciousness. Here, he applies this approach to the studies on mathematical knowledge. He details the results brought about by psychological and neuroscientific studies conducted on numerical cognition by key neuroscientists. In the process, he develops the foundations of a new, potential philosophical explanation on mathematical knowledge.
Mathematical Cognition
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Author : Brian Butterworth
language : en
Publisher: Psychology Press
Release Date : 1996
Mathematical Cognition written by Brian Butterworth and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Cognition categories.
This volume is a collection of all papers published in Volume One of the journal "Mathematical Cognition". The aim of the journal is to provide a forum for explorations of how we understand mathematics and how we acquire and use mathematical concepts. The journal encourages an interdisciplinary approach to the field, and publishes advances in the study of the mental representation and use of mathematical concepts from a range of disciplines.; This first volume features contributions from cognitive psychology, developmental psychology, philosophy, neuroscience, education, computational modelling, and neuropsychology.
Naturalizing Logico Mathematical Knowledge
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Author : Sorin Bangu
language : en
Publisher: Routledge
Release Date : 2018-02-01
Naturalizing Logico Mathematical Knowledge written by Sorin Bangu and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Mathematics categories.
This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.
Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Clarendon Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Philosophy categories.
Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquintoargues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition,Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures.Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
The Oxford Handbook Of Numerical Cognition
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Author : Roi Kadosh
language : en
Publisher: OUP Oxford
Release Date : 2015-07-30
The Oxford Handbook Of Numerical Cognition written by Roi Kadosh and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Psychology categories.
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.
The Oxford Handbook Of Numerical Cognition
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Author : Roi Kadosh
language : en
Publisher: Oxford University Press
Release Date : 2015-07-30
The Oxford Handbook Of Numerical Cognition written by Roi Kadosh 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 2015-07-30 with Psychology categories.
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.
Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Clarendon Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Philosophy categories.
Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
Abstraction And Representation
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Author : Peter Damerow
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Abstraction And Representation written by Peter Damerow 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 2013-06-29 with History categories.
This book deals with the development of thinking under different cultural conditions, focusing on the evolution of mathematical thinking in the history of science and education. Starting from Piaget's genetic epistemology, it provides a conceptual framework for describing and explaining the development of cognition by reflective abstractions from systems of actions.
Heterogeneous Contributions To Numerical Cognition
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Author : Wim Fias
language : en
Publisher: Academic Press
Release Date : 2021-05-28
Heterogeneous Contributions To Numerical Cognition written by Wim Fias and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Medical categories.
Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, neuropsychological, behavioral, and interactional levels. Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical Cognition examines research in mathematical education methods and their neurodevelopmental basis, focusing on the underlying neurodevelopmental features that must be taken into account when teaching and learning mathematics. Cognitive domains and functions such as executive functions, memory, attention, and language contribute to numerical cognition and are essential for its proper development. These lines of research and thinking in neuroscience are discussed in this book to further the understanding of the neurodevelopmental and cognitive basis of more complex forms of mathematics – and how to best teach them. By unravelling the basic building blocks of numerical thinking and the developmental basis of human capacity for arithmetic, this book and the discussions within are important for the achievement of a comprehensive understanding of numerical cognition, its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. A novel innovative reference on the emerging field of numerical cognition and neurodevelopment underlying mathematical education Includes an overview of the multiple disciplines that comprise numerical cognition written by world-leading researchers in the numerical cognition and neurodevelopment fields Features an innovative organization with each section providing a general overview, developmental research, neurocognitive mechanisms, and discussion about relevant studies