Approximate Number System And Mathematics

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Approximate Number System And Mathematics

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Author : Jingguang Li
language : en
Publisher: Frontiers Media SA
Release Date : 2019-11-25

Approximate Number System And Mathematics written by Jingguang Li and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-25 with categories.

Humans process quantity information without the aid of language or symbols to guide a variety of everyday life decisions. The cognitive system that supports this intuitive skill is often referred to as the approximate number system (ANS). It has been argued that the ANS serves as the foundation of the formal symbolic number system—mathematics. Abundant empirical evidence is supportive of this view: acuity of the ANS is positively correlated with symbolic math performance, training of the ANS may cause improvements in symbolic math performance, and the ANS and symbolic number processing may share a common neural underpinning. However, recently several theories and empirical data cast doubt on the role of the ANS in symbolic math processing. This e-book aims to advance our understanding of the underlying mechanisms of the overlap between the ANS and mathematics.

Space Time And Number In The Brain

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Author : Elizabeth Brannon
language : en
Publisher: Academic Press
Release Date : 2011-05-31

Space Time And Number In The Brain written by Elizabeth Brannon and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-31 with Mathematics categories.

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

The Origin Of Concepts

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Author : Susan Carey
language : en
Publisher: Oxford University Press
Release Date : 2009-05-06

The Origin Of Concepts written by Susan Carey 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 2009-05-06 with Psychology categories.

Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition are the output of dedicated input analyzers, as with perceptual representations, but these core representations differ from perceptual representations in having more abstract contents and richer functional roles. Carey argues that the key to understanding cognitive development lies in recognizing conceptual discontinuities in which new representational systems emerge that have more expressive power than core cognition and are also incommensurate with core cognition and other earlier representational systems. Finally, Carey fleshes out Quinian bootstrapping, a learning mechanism that has been repeatedly sketched in the literature on the history and philosophy of science. She demonstrates that Quinian bootstrapping is a major mechanism in the construction of new representational resources over the course of childrens cognitive development. Carey shows how developmental cognitive science resolves aspects of long-standing philosophical debates about the existence, nature, content, and format of innate knowledge. She also shows that understanding the processes of conceptual development in children illuminates the historical process by which concepts are constructed, and transforms the way we think about philosophical problems about the nature of concepts and the relations between language and thought.

The Number Sense

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Author : Stanislas Dehaene
language : en
Publisher: OUP USA
Release Date : 2011-04-29

The Number Sense written by Stanislas Dehaene and has been published by OUP USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-29 with Mathematics categories.

"Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind"-- Provided by publisher.

Understanding Trajectories And Promoting Change From Early To Complex Skills In Typical And Atypical Development A Cross Population Approach

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Author : Alessandra Sansavini
language : en
Publisher: Frontiers Media SA
Release Date : 2021-03-30

Understanding Trajectories And Promoting Change From Early To Complex Skills In Typical And Atypical Development A Cross Population Approach written by Alessandra Sansavini and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-30 with Science categories.

Numerical Mathematics

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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2017-01-26

Numerical Mathematics written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.

Child S Conception Of Number

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Author : Jean Piaget
language : en
Publisher: Routledge
Release Date : 2013-07-04

Child S Conception Of Number written by Jean Piaget and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-04 with Medical categories.

First published in 1997. This is Volume II of selected works of Jean Piaget which looks at his thinking on children and how their interaction and perception of number, touching on the areas of development in thinking on conversation of quantities and invariance of wholes; cardinal and ordinal one-one correspondence; as well as additive and multicatitive compositions. These explorations look into tracing the development of the operations which give rise to number and continuous quantities, to space, time, speed, etc., operations which, in these essential fields, lead from intuitive and egocentric pre-logic to rational co-ordination that is both deductive and inductive.

Numerical Development From Cognitive Functions To Neural Underpinnings

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Author : Korbinian Moeller
language : en
Publisher: Frontiers Media SA
Release Date : 2015-02-24

Numerical Development From Cognitive Functions To Neural Underpinnings written by Korbinian Moeller and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-24 with Functions categories.

Living at the beginning of the 21st century requires being numerate, because numerical abilities are not only essential for life prospects of individuals but also for economic interests of post-industrial knowledge societies. Thus, numerical development is at the core of both individual as well as societal interests. There is the notion that we are already born with a very basic ability to deal with small numerosities. Yet, this often called “number sense” seems to be very restricted, approximate, and driven by perceptual constraints. During our numerical development in formal (e.g., school) but also informal contexts (e.g., family, street) we acquire culturally developed abstract symbol systems to represent exact numerosities – in particular number words and Arabic digits – refining our numerical capabilities. In recent years, numerical development has gained increasing research interest documented in a growing number of behavioural, neuro-scientific, educational, cross-cultural, and neuropsychological studies addressing this issue. Additionally, our understanding of how numerical competencies develop has also benefitted considerably from the advent of different neuro-imaging techniques allowing for an evaluation of developmental changes in the human brain. In sum, we are now starting to put together a more and more coherent picture of how numerical competencies develop and how this development is associated with neural changes as well. In the end, this knowledge might also lead to a better understanding of the reasons for atypical numerical development which often has grieve consequences for those who suffer from developmental dyscalculia or mathematics learning disabilities. Therefore, this Research Topic deals with all aspects of numerical development: findings from behavioural performance to underlying neural substrates, from cross-sectional to longitudinal evaluations, from healthy to clinical populations. To this end, we included empirical contributions using different experimental methodologies, but also theoretical contributions, review articles, or opinion papers.

Effective Teaching Strategies For Dyscalculia And Learning Difficulties In Mathematics

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Author : Marie-Pascale Noël
language : en
Publisher: Taylor & Francis
Release Date : 2022-03-28

Effective Teaching Strategies For Dyscalculia And Learning Difficulties In Mathematics written by Marie-Pascale Noël and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-28 with Education categories.

Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics provides an essential bridge between scientific research and practical interventions with children. It unpacks what we know about the possible cognitive causation of mathematical difficulties in order to improve teaching and therefore learning. Each chapter considers a specific domain of children’s numerical development: counting and the understanding of numbers, understanding of the base-10 system, arithmetic, word problem solving, and understanding rational numbers. The accessible guidance includes a literature review on each topic, surveying how each process develops in children, the difficulties encountered at that level by some pupils, and the intervention studies that have been published. It guides the reader step-by-step through practical guidelines of how to assess these processes and how to build an intervention to help children master them. Illustrated throughout with examples of materials used in the effective interventions described, this essential guide offers deep understanding and effective strategies for developmental and educational psychologists, special educational needs and/or disabilities coordinators, and teachers working with children experiencing mathematical difficulties.

Encyclopedia Of Infant And Early Childhood Development

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Author :
language : en
Publisher: Elsevier
Release Date : 2020-03-13

Encyclopedia Of Infant And Early Childhood Development written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-13 with Psychology categories.

Encyclopedia of Infant and Early Childhood Development, Second Edition, provides a comprehensive entry point into the existing literature on child development in the fields of psychology, genetics, neuroscience and sociology. Featuring 171 chapters, across 3 volumes, this work helps readers understand these developmental changes, when they occur, why they occur, how they occur, and the factors that influence development. Although some medical information is included, the emphasis lies mainly in normal growth, primarily from a psychological perspective. Comprehensive and in-depth scholarly articles cover theoretical, applied and basic science topics, providing an interdisciplinary approach. All articles have been completely updated, making this resource ideal for a wide range of readers, including advanced undergraduate and graduate students, researchers and clinicians in developmental psychology, medicine, nursing, social science and early childhood education. Cutting-edge content that cover the period of neonates to age three Organized alphabetically by topic for ease of reference Provides in-depth scholarly articles, covering theoretical, applied and basic science Includes suggested readings at the end of each article