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 : 2024-03-28
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 2024-03-28 with Science categories.
Arithmetic is one of the foundations of our educational systems, but what exactly is it? This book provides a philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition. It explains how humans have developed arithmetic from humble origins to its modern status.
The Oxford Handbook Of Epistemology
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Author : Paul K. Moser
language : en
Publisher: Oxford University Press
Release Date : 2005-10-27
The Oxford Handbook Of Epistemology written by Paul K. Moser 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 2005-10-27 with Philosophy categories.
The Oxford Handbook of Epistemology contains 19 previously unpublished chapters by today's leading figures in the field. These chapters function not only as a survey of key areas, but as original scholarship on a range of vital topics. Written accessibly for advanced undergraduates, graduate students, and professional philosophers, the Handbook explains the main ideas and problems of contemporary epistemology while avoiding overly technical detail.
Numbers As Cognitive Tools
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Author : César Frederico dos Santos
language : en
Publisher: Springer Nature
Release Date : 2025-08-19
Numbers As Cognitive Tools written by César Frederico dos Santos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-19 with Mathematics categories.
This books offers a novel account of the nature of numbers firmly grounded in results from numerical cognition and the philosophy of mathematics. Drawing on empirical data on the human experience of what we call “numbers,” the author shows that numbers do not exist as abstract objects, but that the idea that they do is a useful cognitive tool. Contrary to the platonist view, according to which arithmetic is true of a realm of abstract entities, the nominalistic account presented in this book shows arithmetic to be true of descriptions of structural properties of techniques such as counting and calculating procedures. This book is of interest to both philosophers and cognitive scientists who want to have a deeper understanding of what numbers are.
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.
An Introduction To Mathematical Cognition
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Author : Camilla Gilmore
language : en
Publisher: Taylor & Francis
Release Date : 2018-06-13
An Introduction To Mathematical Cognition written by Camilla Gilmore and has been published by Taylor & Francis 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.
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 Psychology 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.
Advances In Experimental Philosophy Of Logic And Mathematics
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Author : Andrew Aberdein
language : en
Publisher: Bloomsbury Publishing
Release Date : 2019-05-02
Advances In Experimental Philosophy Of Logic And Mathematics written by Andrew Aberdein and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Philosophy categories.
This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition.
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.
Ongoing Advancements In Philosophy Of Mathematics Education
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Author : Maria Aparecida Viggiani Bicudo
language : en
Publisher: Springer Nature
Release Date : 2023-09-30
Ongoing Advancements In Philosophy Of Mathematics Education written by Maria Aparecida Viggiani Bicudo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-30 with Education categories.
Ongoing Advancements in Philosophy of Mathematics Education approaches the philosophy of mathematics education in a forward movement, analyzing, reflecting, and proposing significant contemporary themes in the field of mathematics education. The theme that gives life to the book is philosophy of mathematics education understood as arising from the intertwining between philosophy of mathematics and philosophy of education which, through constant analytical and reflective work regarding teaching and learning practices in mathematics, is materialized in its own discipline, philosophy of mathematics education. This is the field of investigation of the chapters in the book. The chapters are written by an international cohort of authors, from a variety of countries, regions, and continents. Some of these authors work with philosophical and psychological foundations traditionally accepted by Western civilization. Others expose theoretical foundations based on a new vision and comprising innovative approaches to historical and present-day issues in educational philosophy. The final third of the book is devoted to these unique and innovative research stances towards important and change resistant societal topics such as racism, technology gaps, or the promotion of creativity in the field of mathematics education.
Number Theory In Mathematics Education
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Author : Rina Zazkis
language : en
Publisher: Routledge
Release Date : 2012-10-12
Number Theory In Mathematics Education written by Rina Zazkis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-12 with Education categories.
This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: *understanding particular concepts related to numerical structure and number theory; *elaborating on the historical and psychological relevance of number theory in concept development; *attaining a smooth transition and extension from pattern recognition to formative principles; *appreciating the aesthetics of number structure; *exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; *reexamining previously constructed knowledge from a novel angle; *investigating connections between technique and theory; *utilizing computers and calculators as pedagogical tools; and *generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.