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Approximate Number System And Mathematics
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Book Synopsis Approximate Number System and Mathematics by : Jingguang Li
Download or read book Approximate Number System and Mathematics written by Jingguang Li and published by Frontiers Media SA. This book was released on 2019-11-25 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cognitive Foundations for Improving Mathematical Learning by : David C. Geary
Download or read book Cognitive Foundations for Improving Mathematical Learning written by David C. Geary and published by Academic Press. This book was released on 2019-01-03 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Space, Time and Number in the Brain by : Elizabeth Brannon
Download or read book Space, Time and Number in the Brain written by Elizabeth Brannon and published by Academic Press. This book was released on 2011-05-31 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Origin of Concepts by : Susan Carey
Download or read book The Origin of Concepts written by Susan Carey and published by . This book was released on 2011 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New in paperback-- A transformative book on the way we think about the nature of concepts and the relations between language and thought.
Book Synopsis Development of Mathematical Cognition by : Daniel B. Berch
Download or read book Development of Mathematical Cognition written by Daniel B. Berch and published by Academic Press. This book was released on 2015-10-03 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Mathematical Mindsets by : Jo Boaler
Download or read book Mathematical Mindsets written by Jo Boaler and published by John Wiley & Sons. This book was released on 2015-10-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.
Book Synopsis The Number Sense by : Stanislas Dehaene
Download or read book The Number Sense written by Stanislas Dehaene and published by OUP USA. This book was released on 2011-04-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Child's Conception of Number by : Jean Piaget
Download or read book Child's Conception of Number written by Jean Piaget and published by Routledge. This book was released on 2013-07-04 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1997. Routledge is an imprint of Taylor & Francis, an informa company.
Book Synopsis Constructing Number by : Anderson Norton
Download or read book Constructing Number written by Anderson Norton and published by Springer. This book was released on 2018-12-17 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.
Book Synopsis Exact and Approximate Modeling of Linear Systems by : Ivan Markovsky
Download or read book Exact and Approximate Modeling of Linear Systems written by Ivan Markovsky and published by SIAM. This book was released on 2006-01-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors discuss exact and approximate fitting of data by linear, bilinear, and quadratic static models and linear dynamic models, a formulation that enables readers to select the most suitable representation for a particular purpose. This book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. Readers will find an exposition of a wide variety of modeling problems starting from observed data. The presented theory leads to algorithms that are implemented in C language and in MATLAB.
Book Synopsis Quantitative Psychology by : Marie Wiberg
Download or read book Quantitative Psychology written by Marie Wiberg and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume highlights the latest research and developments in psychometrics and statistics. It represents selected and peer-reviewed presentations given at the 85th Annual International Meeting of the Psychometric Society (IMPS), held virtually on July 13-17, 2020. The IMPS is one of the largest international meetings on quantitative measurement in education, psychology and the social sciences. It draws approximately 500 participants from around the world, featuring paper and poster presentations, symposiums, workshops, keynotes, and invited presentations. Leading experts and promising young researchers have written the included chapters. The chapters address a wide variety of topics including but not limited to item response theory, adaptive testing, Bayesian estimation, propensity scores, and cognitive diagnostic models. This volume is the 9th in a series of recent works to cover research presented at the IMPS.
Book Synopsis Perceptual Learning by : Barbara Dosher
Download or read book Perceptual Learning written by Barbara Dosher and published by MIT Press. This book was released on 2020-10-13 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and integrated introduction to the phenomena and theories of perceptual learning, focusing on the visual domain. Practice or training in perceptual tasks improves the quality of perceptual performance, often by a substantial amount. This improvement is called perceptual learning (in contrast to learning in the cognitive or motor domains), and it has become an active area of research of both theoretical and practical significance. This book offers a comprehensive introduction to the phenomena and theories of perceptual learning, focusing on the visual domain. Perceptual Learning explores the tradeoff between the competing goals of system stability and system adaptability, signal and noise, retuning and reweighting, and top-down versus bottom-down processes. It examines and evaluates existing research and potential future directions, including evidence from behavior, physiology, and brain imaging, and existing perceptual learning applications, with a focus on important theories and computational models. It also compares visual learning to learning in other perceptual domains, and considers the application of visual training methods in the development of perceptual expertise and education as well as in remediation for limiting visual conditions. It provides an integrated treatment of the subject for students and researchers and for practitioners who want to incorporate perceptual learning into their practice.Practice or training in perceptual tasks improves the quality of perceptual performance, often by a substantial amount. This improvement is called perceptual learning, in contrast with learning in the cognitive or motor domains. Perceptual learning has been a very active area of research of both theoretical and practical interest. Research on perceptual learning is of theoretical significance in illuminating plasticity in adult perceptual systems, and in understanding the limitations of human information processing and how to improve them. It is of practical significance as a potential method for the development of perceptual expertise in the normal population, for its potential in advancing development and supporting healthy aging, and for noninvasive amelioration of deficits in challenged populations by training. Perceptual learning has become an increasingly important topic in biomedical research. Practitioners in this area include science disciplines such as psychology, neuroscience, computer sciences, and optometry, and developers in applied areas of learning game design, cognitive development and aging, and military and biomedical applications. Commercial development of training products, protocols, and games is a multi-billion dollar industry. Perceptual learning provides the basis for many of the developments in these areas. This book is written for anyone who wants to understand the phenomena and theories of perceptual learning or to apply the technology of perceptual learning to the development of training methods and products. Our aim is to provide an introduction to those researchers and students just entering this exciting field, to provide a comprehensive and integrated treatment of the phenomena and the theories of perceptual learning for active perceptual learning researchers, and to describe and develop the basic techniques and principles for readers who want to successfully incorporate perceptual learning into applied developments. The book considers the special challenges of perceptual learning that balance the competing goals of system stability and system adaptability. It provides a systematic treatment of the major phenomena and models in perceptual learning, the determinants of successful learning and of specificity and transfer. The book provides a cohesive consideration of the broad range of perceptual learning through the theoretical framework of incremental learning of reweighting evidence that supports successful task performance. It provides a detailed analysis of the mechanisms by which perceptual learning improves perceptual limitations, the relationship of perceptual learning and the critical period of development, and the semi-supervised modes of learning that dominate perceptual learning. It considers limitations and constraints on learning multiple tasks and stimuli simultaneously, the implications of training at high or low levels of performance accuracy, and the importance of feedback to perceptual learning. The basis of perceptual learning in physiology is discussed along with the relationship of visual perceptual learning to learning in other sensory domains. The book considers the applications of perceptual learning in the development of expertise, in education and gaming, in training during development and aging, and applications to remediation of mental health and vision disorders. Finally, it applies the phenomena and models of perceptual learning to considerations of optimizing training.
Book Synopsis How Not to Be Wrong by : Jordan Ellenberg
Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin Press. This book was released on 2014-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.
Book Synopsis Continuous Issues in Numerical Cognition by : Avishai Henik
Download or read book Continuous Issues in Numerical Cognition written by Avishai Henik and published by Academic Press. This book was released on 2016-05-18 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous Issues in Numerical Cognition: How Many or How Much re-examines the widely accepted view that there exists a core numerical system within human beings and an innate ability to perceive and count discrete quantities. This core knowledge involves the brain's intraparietal sulcus, and a deficiency in this region has traditionally been thought to be the basis for arithmetic disability. However, new research findings suggest this wide agreement needs to be examined carefully and that perception of sizes and other non-countable amounts may be the true precursors of numerical ability. This cutting-edge book examines the possibility that perception and evaluation of non-countable dimensions may be involved in the development of numerical cognition. Discussions of the above and related issues are important for the achievement of a comprehensive understanding of numerical cognition, its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. - Serves as an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse topic - Features chapters from leading researchers in the field - Includes an overview of the multiple disciplines that comprise numerical cognition and discusses the measures that can be used in analysis - Introduces novel ideas that connect non-countable continuous variables to numerical cognition
Book Synopsis The Mathematical Brain Across the Lifespan by :
Download or read book The Mathematical Brain Across the Lifespan written by and published by Elsevier. This book was released on 2016-06-20 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Brain Across the Lifespan is the latest volume in the Progress in Brain Research series that focuses on new trends and developments. This established international series examines major areas of basic and clinical research within the neurosciences, as well as popular and emerging subfields. Provides a comprehensive review of the most recent progress in the mathematical brain across the lifespan Explores new trends and developments in the field Enhances the literature of neuroscience by further expanding the established, ongoing international series Progress in Brain Research
Book Synopsis Conceptual Spaces: Elaborations and Applications by : Mauri Kaipainen
Download or read book Conceptual Spaces: Elaborations and Applications written by Mauri Kaipainen and published by Springer. This book was released on 2019-06-25 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book focuses on concepts and their applications using the theory of conceptual spaces, one of today’s most central tracks of cognitive science discourse. It features 15 papers based on topics presented at the Conceptual Spaces @ Work 2016 conference. The contributors interweave both theory and applications in their papers. Among the first mentioned are studies on metatheories, logical and systemic implications of the theory, as well as relations between concepts and language. Examples of the latter include explanatory models of paradigm shifts and evolution in science as well as dilemmas and issues of health, ethics, and education. The theory of conceptual spaces overcomes many translational issues between academic theoretization and practical applications. The paradigm is mainly associated with structural explanations, such as categorization and meronomy. However, the community has also been relating it to relations, functions, and systems. The book presents work that provides a geometric model for the representation of human conceptual knowledge that bridges the symbolic and the sub-conceptual levels of representation. The model has already proven to have a broad range of applicability beyond cognitive science and even across a number of disciplines related to concepts and representation.
Book Synopsis An Introduction to the Approximation of Functions by : Theodore J. Rivlin
Download or read book An Introduction to the Approximation of Functions written by Theodore J. Rivlin and published by Courier Corporation. This book was released on 1981-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
