Foundations Of Geometric Cognition

Foundations Of Geometric Cognition Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Foundations Of Geometric Cognition book. This book definitely worth reading, it is an incredibly well-written.

Foundations of Geometric Cognition

Mateusz Hohol
Foundations of Geometric Cognition Book PDF

Author : Mateusz Hohol
Publisher : Routledge
Page : 188 pages
File Size : 50,5 Mb
Release : 2019-09-12
Category : Psychology
ISBN : 9780429508592

Get Book

Foundations of Geometric Cognition by Mateusz Hohol Pdf

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.

Foundations of Geometric Cognition

Mateusz Hohol
Foundations of Geometric Cognition Book PDF

Author : Mateusz Hohol
Publisher : Routledge
Page : 315 pages
File Size : 46,7 Mb
Release : 2019-09-12
Category : Psychology
ISBN : 9780429509216

Get Book

Foundations of Geometric Cognition by Mateusz Hohol Pdf

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.

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

George Lakoff,Rafael E. Nunez
Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being Book PDF

Author : George Lakoff,Rafael E. Nunez
Publisher : Unknown
Page : 520 pages
File Size : 42,9 Mb
Release : 2000-11-02
Category : Mathematics
ISBN : UOM:39015049551552

Get Book

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being by George Lakoff,Rafael E. Nunez Pdf

A study of the cognitive science of mathematical ideas.

Conceptual Spaces

Peter Gardenfors
Conceptual Spaces Book PDF

Author : Peter Gardenfors
Publisher : MIT Press
Page : 324 pages
File Size : 40,6 Mb
Release : 2004-01-30
Category : Psychology
ISBN : 0262572192

Get Book

Conceptual Spaces by Peter Gardenfors Pdf

Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.

Cognitive Foundations for Improving Mathematical Learning

David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Cognitive Foundations for Improving Mathematical Learning Book PDF

Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Page : 377 pages
File Size : 40,8 Mb
Release : 2019-01-03
Category : Psychology
ISBN : 9780128159538

Get Book

Cognitive Foundations for Improving Mathematical Learning by David C. Geary,Daniel B. Berch,Kathleen Mann Koepke Pdf

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

Mathematics Learning in Early Childhood

National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Mathematics Learning in Early Childhood Book PDF

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Publisher : National Academies Press
Page : 399 pages
File Size : 45,5 Mb
Release : 2009-11-13
Category : Education
ISBN : 9780309147439

Get Book

Mathematics Learning in Early Childhood by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics Pdf

Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

Space, Time and Number in the Brain

Elizabeth Brannon
Space Time and Number in the Brain Book PDF

Author : Elizabeth Brannon
Publisher : Academic Press
Page : 375 pages
File Size : 53,7 Mb
Release : 2011-05-31
Category : Mathematics
ISBN : 9780123859488

Get Book

Space, Time and Number in the Brain by Elizabeth Brannon Pdf

The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts

David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke
Acquisition of Complex Arithmetic Skills and Higher Order Mathematics Concepts Book PDF

Author : David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke
Publisher : Academic Press
Page : 360 pages
File Size : 55,7 Mb
Release : 2017-02-08
Category : Psychology
ISBN : 9780128133682

Get Book

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts by David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke Pdf

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

Exploiting Mental Imagery with Computers in Mathematics Education

Rosamund Sutherland,John Mason
Exploiting Mental Imagery with Computers in Mathematics Education Book PDF

Author : Rosamund Sutherland,John Mason
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642577710

Get Book

Exploiting Mental Imagery with Computers in Mathematics Education by Rosamund Sutherland,John Mason Pdf

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

Digital Geometry Algorithms

Valentin E. Brimkov,Reneta P. Barneva
Digital Geometry Algorithms Book PDF

Author : Valentin E. Brimkov,Reneta P. Barneva
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 50,8 Mb
Release : 2012-05-20
Category : Technology & Engineering
ISBN : 9789400741744

Get Book

Digital Geometry Algorithms by Valentin E. Brimkov,Reneta P. Barneva Pdf

Digital geometry emerged as an independent discipline in the second half of the last century. It deals with geometric properties of digital objects and is developed with the unambiguous goal to provide rigorous theoretical foundations for devising new advanced approaches and algorithms for various problems of visual computing. Different aspects of digital geometry have been addressed in the literature. This book is the first one that explicitly focuses on the presentation of the most important digital geometry algorithms. Each chapter provides a brief survey on a major research area related to the general volume theme, description and analysis of related fundamental algorithms, as well as new original contributions by the authors. Every chapter contains a section in which interesting open problems are addressed.

Mind, Body, World

Michael R. W. Dawson
Mind Body World Book PDF

Author : Michael R. W. Dawson
Publisher : Athabasca University Press
Page : 506 pages
File Size : 55,8 Mb
Release : 2013
Category : Computers
ISBN : 9781927356173

Get Book

Mind, Body, World by Michael R. W. Dawson Pdf

Cognitive science arose in the 1950s when it became apparent that a number of disciplines, including psychology, computer science, linguistics, and philosophy, were fragmenting. Perhaps owing to the field's immediate origins in cybernetics, as well as to the foundational assumption that cognition is information processing, cognitive science initially seemed more unified than psychology. However, as a result of differing interpretations of the foundational assumption and dramatically divergent views of the meaning of the term information processing, three separate schools emerged: classical cognitive science, connectionist cognitive science, and embodied cognitive science. Examples, cases, and research findings taken from the wide range of phenomena studied by cognitive scientists effectively explain and explore the relationship among the three perspectives. Intended to introduce both graduate and senior undergraduate students to the foundations of cognitive science, Mind, Body, World addresses a number of questions currently being asked by those practicing in the field: What are the core assumptions of the three different schools? What are the relationships between these different sets of core assumptions? Is there only one cognitive science, or are there many different cognitive sciences? Giving the schools equal treatment and displaying a broad and deep understanding of the field, Dawson highlights the fundamental tensions and lines of fragmentation that exist among the schools and provides a refreshing and unifying framework for students of cognitive science.

The Topos of Music

Guerino Mazzola
The Topos of Music Book PDF

Author : Guerino Mazzola
Publisher : Birkhäuser
Page : 1310 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881418

Get Book

The Topos of Music by Guerino Mazzola Pdf

With contributions by numerous experts

Interdisciplinary Perspectives on Math Cognition

Marcel Danesi
Interdisciplinary Perspectives on Math Cognition Book PDF

Author : Marcel Danesi
Publisher : Springer Nature
Page : 344 pages
File Size : 43,9 Mb
Release : 2019-09-14
Category : Mathematics
ISBN : 9783030225377

Get Book

Interdisciplinary Perspectives on Math Cognition by Marcel Danesi Pdf

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.

Quantum Models of Cognition and Decision

Jerome R. Busemeyer,Peter D. Bruza
Quantum Models of Cognition and Decision Book PDF

Author : Jerome R. Busemeyer,Peter D. Bruza
Publisher : Cambridge University Press
Page : 425 pages
File Size : 48,6 Mb
Release : 2012-07-26
Category : Psychology
ISBN : 9781139536486

Get Book

Quantum Models of Cognition and Decision by Jerome R. Busemeyer,Peter D. Bruza Pdf

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

Geometric Structures of Statistical Physics, Information Geometry, and Learning

Frédéric Barbaresco,Frank Nielsen
Geometric Structures of Statistical Physics Information Geometry and Learning Book PDF

Author : Frédéric Barbaresco,Frank Nielsen
Publisher : Springer Nature
Page : 466 pages
File Size : 43,5 Mb
Release : 2021-06-27
Category : Mathematics
ISBN : 9783030779573

Get Book

Geometric Structures of Statistical Physics, Information Geometry, and Learning by Frédéric Barbaresco,Frank Nielsen Pdf

Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.