Mathematics And Cognition

Author : Camilla Gilmore,Silke M. Göbel,Matthew Inglis
Publisher : Taylor & Francis
Page : 265 pages
File Size : 44,9 Mb
Release : 2018-06-13
Category : Psychology
ISBN : 9781317410119

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An Introduction to Mathematical Cognition by Camilla Gilmore,Silke M. Göbel,Matthew Inglis Pdf

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.

Author : Jamie I.D. Campbell
Publisher : Psychology Press
Page : 527 pages
File Size : 54,6 Mb
Release : 2005-08-15
Category : Psychology
ISBN : 9781135423667

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The Handbook of Mathematical Cognition by Jamie I.D. Campbell Pdf

How does the brain represent number and make mathematical calculations? What underlies the development of numerical and mathematical abilities? What factors affect the learning of numerical concepts and skills? What are the biological bases of number knowledge? Do humans and other animals share similar numerical representations and processes? What underlies numerical and mathematical disabilities and disorders, and what is the prognosis for rehabilitation? These questions are the domain of mathematical cognition, the field of research concerned with the cognitive and neurological processes that underlie numerical and mathematical abilities. TheHandbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field.

Author : Pearla Nesher,Jeremy Kilpatrick
Publisher : CUP Archive
Page : 234 pages
File Size : 48,5 Mb
Release : 1990-02-23
Category : Education
ISBN : 0521367875

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Mathematics and Cognition by Pearla Nesher,Jeremy Kilpatrick Pdf

This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.

Author : Marcel Danesi
Publisher : Springer Nature
Page : 344 pages
File Size : 44,5 Mb
Release : 2019-09-14
Category : Mathematics
ISBN : 9783030225377

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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.

Author : James M. Royer
Publisher : IAP
Page : 273 pages
File Size : 46,6 Mb
Release : 2003-01-01
Category : Education
ISBN : 9781607527961

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Mathematical Cognition by James M. Royer Pdf

Author : Daniel B. Berch,David C. Geary,Kathleen Mann Koepke
Publisher : Academic Press
Page : 366 pages
File Size : 51,8 Mb
Release : 2018-07-27
Category : Psychology
ISBN : 9780128125755

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Language and Culture in Mathematical Cognition by Daniel B. Berch,David C. Geary,Kathleen Mann Koepke Pdf

Language and Culture in Mathematical Cognition, First Edition focuses on the role of linguistic and cultural factors in math cognition and development. It covers a wide range of topics, including analogical mapping in numerical development, arithmetic fact retrieval in the bilingual brain, cross-cultural comparisons of mathematics achievement, the shaping of numerical processing by number word construction, the influence of Head Start programs, the mathematical skills of children with specific language impairments, the role of culture and language in creating associations between number and space, and electrophysiological studies of linguistic traces in core knowledge at the neural level. Includes cutting-edge findings, innovative measures, recent methodological advances and groundbreaking theoretical developments Synthesizes research from various subdomains of math cognition research Covers the full complement of research in mathematical thinking and learning Informs researchers, scholars, educators, students and policymakers

Author : Daniel B. Berch,David C. Geary,Kathleen Mann Koepke
Publisher : Academic Press
Page : 414 pages
File Size : 45,5 Mb
Release : 2015-10-03
Category : Psychology
ISBN : 9780128019092

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Development of Mathematical Cognition by Daniel B. Berch,David C. Geary,Kathleen Mann Koepke Pdf

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

Author : Jean Lave
Publisher : Cambridge University Press
Page : 236 pages
File Size : 54,6 Mb
Release : 1988-07-29
Category : Mathematics
ISBN : 0521357349

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Cognition in Practice by Jean Lave Pdf

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.

Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Page : 377 pages
File Size : 44,7 Mb
Release : 2019-01-03
Category : Psychology
ISBN : 9780128159538

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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

Author : Katherine M. Robinson,Helena P. Osana,Donna Kotsopoulos
Publisher : Springer
Page : 274 pages
File Size : 51,5 Mb
Release : 2019-05-07
Category : Psychology
ISBN : 9783030128951

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Mathematical Learning and Cognition in Early Childhood by Katherine M. Robinson,Helena P. Osana,Donna Kotsopoulos Pdf

This book explores mathematical learning and cognition in early childhood from interdisciplinary perspectives, including developmental psychology, neuroscience, cognitive psychology, and education. It examines how infants and young children develop numerical and mathematical skills, why some children struggle to acquire basic abilities, and how parents, caregivers, and early childhood educators can promote early mathematical development. The first section of the book focuses on infancy and toddlerhood with a particular emphasis on the home environment and how parents can foster early mathematical skills to prepare their children for formal schooling. The second section examines topics in preschool and kindergarten, such as the development of counting procedures and principles, the use of mathematics manipulatives in instruction, and the impacts of early intervention. The final part of the book focuses on particular instructional approaches in the elementary school years, such as different additive concepts, schema-based instruction, and methods of division. Chapters analyze the ways children learn to think about, work with, and master the language of mathematical concepts, as well as provide effective approaches to screening and intervention. Included among the topics: The relationship between early gender differences and future mathematical learning and participation. The connection between mathematical and computational thinking. Patterning abilities in young children. Supporting children with learning difficulties and intellectual disabilities. The effectiveness of tablets as elementary mathematics education tools. Mathematical Learning and Cognition in Early Childhood is an essential resource for researchers, graduate students, and professionals in infancy and early childhood development, child and school psychology, neuroscience, mathematics education, educational psychology, and social work.

Author : Mateusz Hohol
Publisher : Routledge
Page : 315 pages
File Size : 48,5 Mb
Release : 2019-09-12
Category : Psychology
ISBN : 9780429509216

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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.

Author : Joseph W. Houpt,Leslie M. Blaha
Publisher : Routledge
Page : 288 pages
File Size : 55,6 Mb
Release : 2016-05-20
Category : Psychology
ISBN : 9781317297482

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Mathematical Models of Perception and Cognition Volume II by Joseph W. Houpt,Leslie M. Blaha Pdf

In this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend’s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.

Author : George Lakoff,Rafael E. Nunez
Publisher : Unknown
Page : 520 pages
File Size : 53,8 Mb
Release : 2000-11-02
Category : Mathematics
ISBN : UOM:39015049551552

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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.

Author : Brian Butterworth,Lisa Cipolotti
Publisher : Psychology Press
Page : 272 pages
File Size : 46,7 Mb
Release : 1996
Category : Cognition
ISBN : 0863774180

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Mathematical Cognition by Brian Butterworth,Lisa Cipolotti Pdf

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.

Author : Andre Knops
Publisher : Routledge
Page : 206 pages
File Size : 53,6 Mb
Release : 2019-12-10
Category : Psychology
ISBN : 9781000766455

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Numerical Cognition by Andre Knops Pdf

Numerical Cognition: The Basics provides an understanding of the neural and cognitive mechanisms that enable us to perceive, process, and memorize numerical information. Starting from basic numerical competencies that humans share with other species, the book explores the mental coding of numbers and their neural representation. It explains the strategies of mental calculation, their pitfalls and their development, as well as the developmental steps children make while learning about numbers. The book gradually builds our understanding of the underlying mental processes of numeracy and concludes with an insightful examination of the diagnosis, etiology and treatment of dyscalculia. Written in an accessible manner, the book summarizes and critically evaluates the major psychological explanations for various empirical phenomena in numerical cognition. Containing a wealth of student-friendly features including end of chapter summaries, informative figures, further reading lists, and links to relevant websites, Numerical Cognition: The Basics is an essential starting point for anybody new to the field.