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.

The Roles Of The Approximate Number System And Number Numerosity Mapping On The Mathematics Achievement In Normally And Low Achieving Children And Children With Mathematics Learning Disability

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Author : Tin-Yau Wong
language : en
Publisher:
Release Date : 2017-01-27

The Roles Of The Approximate Number System And Number Numerosity Mapping On The Mathematics Achievement In Normally And Low Achieving Children And Children With Mathematics Learning Disability written by Tin-Yau Wong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with categories.

This dissertation, "The Roles of the Approximate Number System and Number-numerosity Mapping on the Mathematics Achievement in Normally- and Low-achieving Children and Children With Mathematics Learning Disability" by Tin-yau, Wong, 王天佑, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Humans are born with a basic sense of number. This number sense, which is now called the Approximate Number System (ANS), allows us to represent numerosity without the use of symbols. There has been a debate on whether this nonsymbolic ANS contributes to our symbolic mathematics skills, and the recent findings are inclined to support the link between the two. However, what remains unclear is the mechanism underlying the relationship between the ANS and our mathematics skills, and whether children with Mathematics Learning Disabilities (MLD) suffer from a defective ANS. The present thesis aimed at addressing the above issues in two studies. Study 1 aimed at identifying the mechanism of how the ANS contributes to children's mathematics skills. A group of 210 kindergarteners were tested on their ANS acuity, number-numerosity mapping skills (measured by counting and estimation tasks), and their arithmetic skills. They were then re-tested twice when they were in Grade 1.Using Structural Equation Modeling, it was found that children's ANS acuity in kindergarten predicted their arithmetic skills one year later, and the relationship was mediated by their number-numerosity mapping skills. This suggested that ANS may contribute to mathematics learning by enabling more precise mapping between number symbols and the corresponding numerosity representation, hence making numbers meaningful. Studies 2A and 2B aimed at verifying whether children with MLD suffered from deficits in their ANS as well as their number-numerosity mapping skills. The same group of participants was followed one more time in Grade 2. Using the standard low-achievement method (Study 2A) and a more data-driven method known as the latent class growth analysis(Study 2B), two groups of children with MLD were identified. Both groups of children had deficits in both the ANS and their number-numerosity mapping skills as compared with their normally-achieving peers. Other groups of low-achieving children were also identified, and their difficulties seemed to be contributed by factors other than their ANS. While one of the low-achieving groups seemed to have deficit lying mainly on the number-numerosity mapping skills, the other low-achieving group did not show any cognitive deficits but had much lower SES compared to other groups. The relationship between the ANS and children's mathematics achievement was supported and elaborated in the present study. The findings not only articulated a potential mechanism of how children learned about mathematics, but they also allowed educators to have better understanding of the cognitive profiles of children with MLD, thus facilitating early identification and intervention. The different profiles of the low-achieving groups also highlighted the need for differential intervention for different groups of low-achieving children. DOI: 10.5353/th_b5334868 Subjects: Mathematics - Study and teaching - Psychological aspects Number concept Mathematical ability

Cognitive Foundations For Improving Mathematical Learning

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Author : David C. Geary
language : en
Publisher: Academic Press
Release Date : 2019-01-03

Cognitive Foundations For Improving Mathematical Learning written by David C. Geary and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-03 with Psychology categories.

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

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

An Introduction To Mathematical Cognition

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Author : Camilla Gilmore
language : en
Publisher: Routledge
Release Date : 2018-06-13

An Introduction To Mathematical Cognition written by Camilla Gilmore and has been published by Routledge 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.

The Roles Of The Approximate Number System And Number Numerosity Mapping On The Mathematics Achievement In Normally And Low Achieving Children And Children With Mathematics Learning Disability

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Author : 王天佑
language : en
Publisher:
Release Date : 2014

The Roles Of The Approximate Number System And Number Numerosity Mapping On The Mathematics Achievement In Normally And Low Achieving Children And Children With Mathematics Learning Disability written by 王天佑 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematical ability categories.

The Origin Of Concepts

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Author : Susan Carey
language : en
Publisher: Oxford Series in Cognitive Dev
Release Date : 2011

The Origin Of Concepts written by Susan Carey and has been published by Oxford Series in Cognitive Dev this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Medical categories.

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 children's cognitive development.

Development Of Mathematical Cognition

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Author : Daniel B. Berch
language : en
Publisher: Academic Press
Release Date : 2015-10-03

Development Of Mathematical Cognition written by Daniel B. Berch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-03 with Psychology categories.

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

The Cognitive Neuroscience Of Mathematics

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Author : Robert Emerson
language : en
Publisher:
Release Date : 2014

The Cognitive Neuroscience Of Mathematics written by Robert Emerson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematical ability categories.

"Living in today's society demands a functional control of math. Recent research suggests that adult mathematical skill is founded on an ontogenetically early emerging number sense, or ability to approximately estimate quantities. This ability is shared with many species, suggesting it represents a core and primitive approximate number system (ANS). Neuroimaging research in both monkeys and humans has linked the ANS to the to the neural responses of the intraparietal sulcus (IPS). As children mature, learn to count and calculate, the BOLD responses of the IPS bear the ratio-dependent signature of the approximate number system. These neural responses show longitudinal profiles that suggest the ANS is relatively stable and sharpens its numerical representations across development in a way that predict their behavioral performance (Emerson & Cantlon, 2014). Children also show math-specific functional connections between the IPS and areas of frontal cortex (Emerson & Cantlon, 2012). This suggests that the IPS plays a role in fine-tuning number and math skills during development. In adults, we have observed a segregation of number-related processes vs other quantitative processes (size/brightness) in the IPS. Regions of the IPS that show a selective response to number overlap with regions that show a ratio-dependent response profile, defining the right IPS as an area of the brain that supports non-verbal numerical skill. Furthermore, we find that cortical thickness correlates with scores on standardized math assessments (SAT) in an area of the right IPS, overlapping regions that are functionally related to number skill. In other words, anatomical and functional variability in the IPS is related to both the ANS and math skill in typical adults. When we tested this region in people with advanced math training, we observed both a heightened neural response to numerical ratio as well as significantly thinner cortex in the depth of the IPS. Compared to typical adults, experts are showing a stronger response of the ANS as well as thinner cortex in a region that correlates with math skills in non-experts (Emerson, Vo, Lussier, Kurtz, & Cantlon, submitted). Taken together, these data converge on the conclusion that our uniquely human ability to use symbolic arithmetic is critically linked to our primitive approximate number skill through a shared neural substrate in the intraparietal sulcus"--Pages v-vi.

Cognitive Foundations For Improving Mathematical Learning

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Author : David C. Geary
language : en
Publisher: Academic Press
Release Date : 2019-01-30

Cognitive Foundations For Improving Mathematical Learning written by David C. Geary and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Psychology categories.

Cognitive Foundations for Improving Mathematical Learning, Volume 5, the latest release 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. Chapters cover the use of numerical play and games for improving foundational number knowledge, 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. In addition, the book examines 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 more. 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