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Cognitive Foundations For Improving Mathematical Learning

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Cognitive Foundations for Improving Mathematical Learning

Cognitive Foundations for Improving Mathematical Learning Book
Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Release : 2019-01-03
ISBN : 0128159537
Language : En, Es, Fr & De

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Book Description :

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

Cognitive Foundations for Improving Mathematical Learning

Cognitive Foundations for Improving Mathematical Learning Book
Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Release : 2019-01-30
ISBN : 0128159529
Language : En, Es, Fr & De

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Book Description :

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

Mathematics Learning in Early Childhood

Mathematics Learning in Early Childhood Book
Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Publisher : National Academies Press
Release : 2009-11-13
ISBN : 9780309147439
Language : En, Es, Fr & De

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Book Description :

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.

Cognitive Science and Mathematics Education

Cognitive Science and Mathematics Education Book
Author : Alan H. Schoenfeld
Publisher : Routledge
Release : 2013-04-03
ISBN : 1136461841
Language : En, Es, Fr & De

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Book Description :

This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.

Transforming the Workforce for Children Birth Through Age 8

Transforming the Workforce for Children Birth Through Age 8 Book
Author : National Research Council,Institute of Medicine,Board on Children, Youth, and Families,Committee on the Science of Children Birth to Age 8: Deepening and Broadening the Foundation for Success
Publisher : National Academies Press
Release : 2015-07-23
ISBN : 0309324882
Language : En, Es, Fr & De

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Book Description :

Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children.

The Cognitive Foundations of Reading and Its Acquisition

The Cognitive Foundations of Reading and Its Acquisition Book
Author : Wesley A. Hoover,William E. Tunmer
Publisher : Springer Nature
Release : 2020-06-09
ISBN : 3030441954
Language : En, Es, Fr & De

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Book Description :

This book serves as a succinct resource on the cognitive requirements of reading. It provides a coherent, overall view of reading and learning to read, and does so in a relatively sparse fashion that supports retention. The initial sections of the book describe the cognitive structure of reading and the cognitive foundation upon which that structure is built. This is followed by discussions of how an understanding of these cognitive requirements can be used in practice with standards, assessments, curriculum and instruction, to advance the teaching of reading and the delivery of interventions for students who encounter difficulties along the way. The book focuses on reading in English as its exemplar, but shows how its framework can be adapted to understand the broad cognitive requirements for reading and learning to read in any phonologically-based orthography. It provides a way for reading professionals to think about reading and its development and gives them mechanisms that, coupled with such understanding, will help them link what children must know to become strong readers to what teaching can best provide through the competent use of available tools. In this way, the book will help reading professionals be both efficient and effective in what they provide all their students and be much better equipped to support those students who struggle to learn to read.

Eager to Learn

Eager to Learn Book
Author : National Research Council,Division of Behavioral and Social Sciences and Education,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Early Childhood Pedagogy
Publisher : National Academies Press
Release : 2001-01-22
ISBN : 0309068363
Language : En, Es, Fr & De

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Book Description :

Clearly babies come into the world remarkably receptive to its wonders. Their alertness to sights, sounds, and even abstract concepts makes them inquisitive explorers--and learners--every waking minute. Well before formal schooling begins, children's early experiences lay the foundations for their later social behavior, emotional regulation, and literacy. Yet, for a variety of reasons, far too little attention is given to the quality of these crucial years. Outmoded theories, outdated facts, and undersized budgets all play a part in the uneven quality of early childhood programs throughout our country. What will it take to provide better early education and care for our children between the ages of two and five? Eager to Learn explores this crucial question, synthesizing the newest research findings on how young children learn and the impact of early learning. Key discoveries in how young children learn are reviewed in language accessible to parents as well as educators: findings about the interplay of biology and environment, variations in learning among individuals and children from different social and economic groups, and the importance of health, safety, nutrition and interpersonal warmth to early learning. Perhaps most significant, the book documents how very early in life learning really begins. Valuable conclusions and recommendations are presented in the areas of the teacher-child relationship, the organization and content of curriculum, meeting the needs of those children most at risk of school failure, teacher preparation, assessment of teaching and learning, and more. The book discusses: Evidence for competing theories, models, and approaches in the field and a hard look at some day-to-day practices and activities generally used in preschool. The role of the teacher, the importance of peer interactions, and other relationships in the child's life. Learning needs of minority children, children with disabilities, and other special groups. Approaches to assessing young children's learning for the purposes of policy decisions, diagnosis of educational difficulties, and instructional planning. Preparation and continuing development of teachers. Eager to Learn presents a comprehensive, coherent picture of early childhood learning, along with a clear path toward improving this important stage of life for all children.

Foundations of Geometric Cognition

Foundations of Geometric Cognition Book
Author : Mateusz Hohol
Publisher : Routledge
Release : 2019-09-12
ISBN : 0429509219
Language : En, Es, Fr & De

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Book Description :

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.

International Handbook of Mathematical Learning Difficulties

International Handbook of Mathematical Learning Difficulties Book
Author : Annemarie Fritz,Vitor Geraldi Haase,Pekka Räsänen
Publisher : Springer
Release : 2019-01-30
ISBN : 3319971484
Language : En, Es, Fr & De

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Book Description :

This comprehensive volume provides teachers, researchers and education professionals with cutting edge knowledge developed in the last decades by the educational, behavioural and neurosciences, integrating cognitive, developmental and socioeconomic approaches to deal with the problems children face in learning mathematics. The neurocognitive mechanisms and the cognitive processes underlying acquisition of arithmetic abilities and their significance for education have been the subject of intense research in the last few decades, but the most part of this research has been conducted in non-applied settings and there’s still a deep discrepancy between the level of scientific knowledge and its implementation into actual educational settings. Now it’s time to bring the results from the laboratory to the classroom. Apart from bringing the theoretical discussions to educational settings, the volume presents a wide range of methods for early detection of children with risks in mathematics learning and strategies to develop effective interventions based on innovative cognitive test instruments. It also provides insights to translate research knowledge into public policies in order to address socioeconomic issues. And it does so from an international perspective, dedicating a whole section to the cultural diversity of mathematics learning difficulties in different parts of the world. All of this makes the International Handbook of Mathematical Learning Difficulties an essential tool for those involved in the daily struggle to prepare the future generations to succeed in the global knowledge society.

The Handbook of Mathematical Cognition

The Handbook of Mathematical Cognition Book
Author : Jamie I.D. Campbell
Publisher : Psychology Press
Release : 2005-08-15
ISBN : 1135423652
Language : En, Es, Fr & De

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Book Description :

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. The Handbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field.

Development of Mathematical Cognition

Development of Mathematical Cognition Book
Author : Daniel B. Berch,David C. Geary,Kathleen Mann Koepke
Publisher : Academic Press
Release : 2015-10-03
ISBN : 0128019093
Language : En, Es, Fr & De

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Book Description :

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

How Learning Works

How Learning Works Book
Author : Susan A. Ambrose,Michael W. Bridges,Michele DiPietro,Marsha C. Lovett,Marie K. Norman
Publisher : John Wiley & Sons
Release : 2010-04-16
ISBN : 9780470617601
Language : En, Es, Fr & De

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Book Description :

Praise for How Learning Works "How Learning Works is the perfect title for this excellent book. Drawing upon new research in psychology, education, and cognitive science, the authors have demystified a complex topic into clear explanations of seven powerful learning principles. Full of great ideas and practical suggestions, all based on solid research evidence, this book is essential reading for instructors at all levels who wish to improve their students' learning." —Barbara Gross Davis, assistant vice chancellor for educational development, University of California, Berkeley, and author, Tools for Teaching "This book is a must-read for every instructor, new or experienced. Although I have been teaching for almost thirty years, as I read this book I found myself resonating with many of its ideas, and I discovered new ways of thinking about teaching." —Eugenia T. Paulus, professor of chemistry, North Hennepin Community College, and 2008 U.S. Community Colleges Professor of the Year from The Carnegie Foundation for the Advancement of Teaching and the Council for Advancement and Support of Education "Thank you Carnegie Mellon for making accessible what has previously been inaccessible to those of us who are not learning scientists. Your focus on the essence of learning combined with concrete examples of the daily challenges of teaching and clear tactical strategies for faculty to consider is a welcome work. I will recommend this book to all my colleagues." —Catherine M. Casserly, senior partner, The Carnegie Foundation for the Advancement of Teaching "As you read about each of the seven basic learning principles in this book, you will find advice that is grounded in learning theory, based on research evidence, relevant to college teaching, and easy to understand. The authors have extensive knowledge and experience in applying the science of learning to college teaching, and they graciously share it with you in this organized and readable book." —From the Foreword by Richard E. Mayer, professor of psychology, University of California, Santa Barbara; coauthor, e-Learning and the Science of Instruction; and author, Multimedia Learning

Children s Errors in Mathematics

Children s Errors in Mathematics Book
Author : Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees
Publisher : Learning Matters
Release : 2014-06-23
ISBN : 1473905532
Language : En, Es, Fr & De

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Book Description :

This practical guide to children’s common errors and misconceptions in mathematics is a popular planning tool for primary trainees. It supports a deeper understanding of the difficulties encountered in mathematical development. This third edition has been updated to link to the new National Curriculum. New for this edition is a chapter on addressing errors misconceptions which explores how errors can best be identified and countered. The text examines misconceptions individually and in each case provides a description of the error alongside an explanation of why the error happens. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions.

How People Learn

How People Learn Book
Author : National Research Council,Division of Behavioral and Social Sciences and Education,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice
Publisher : National Academies Press
Release : 2000-08-11
ISBN : 0309131979
Language : En, Es, Fr & De

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Book Description :

First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.

Knowing What Students Know

Knowing What Students Know Book
Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Board on Testing and Assessment,Committee on the Foundations of Assessment
Publisher : National Academies Press
Release : 2001-10-27
ISBN : 0309072727
Language : En, Es, Fr & De

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Book Description :

Education is a hot topic. From the stage of presidential debates to tonight's dinner table, it is an issue that most Americans are deeply concerned about. While there are many strategies for improving the educational process, we need a way to find out what works and what doesn't work as well. Educational assessment seeks to determine just how well students are learning and is an integral part of our quest for improved education. The nation is pinning greater expectations on educational assessment than ever before. We look to these assessment tools when documenting whether students and institutions are truly meeting education goals. But we must stop and ask a crucial question: What kind of assessment is most effective? At a time when traditional testing is subject to increasing criticism, research suggests that new, exciting approaches to assessment may be on the horizon. Advances in the sciences of how people learn and how to measure such learning offer the hope of developing new kinds of assessments-assessments that help students succeed in school by making as clear as possible the nature of their accomplishments and the progress of their learning. Knowing What Students Know essentially explains how expanding knowledge in the scientific fields of human learning and educational measurement can form the foundations of an improved approach to assessment. These advances suggest ways that the targets of assessment-what students know and how well they know it-as well as the methods used to make inferences about student learning can be made more valid and instructionally useful. Principles for designing and using these new kinds of assessments are presented, and examples are used to illustrate the principles. Implications for policy, practice, and research are also explored. With the promise of a productive research-based approach to assessment of student learning, Knowing What Students Know will be important to education administrators, assessment designers, teachers and teacher educators, and education advocates.

The Oxford Handbook of Numerical Cognition

The Oxford Handbook of Numerical Cognition Book
Author : Roi Kadosh,Ann Dowker
Publisher : OUP Oxford
Release : 2015-07-30
ISBN : 0191036005
Language : En, Es, Fr & De

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Book Description :

How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.

Helping Children Learn Mathematics

Helping Children Learn Mathematics Book
Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Publisher : National Academies Press
Release : 2002-07-31
ISBN : 0309131987
Language : En, Es, Fr & De

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Book Description :

Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we’re teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre--kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

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

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being Book
Author : George Lakoff,Rafael E. Nunez
Publisher : Unknown
Release : 2000-11-02
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.

Exploring Math Science in Preschool

Exploring Math   Science in Preschool Book
Author : Teaching Young Children
Publisher : Unknown
Release : 2015
ISBN : 9781938113093
Language : En, Es, Fr & De

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Book Description :

"Much of the content in this book is adapted from Teaching Young Children (TYC), NAEYC's award-winning magazine ..."--Page [104]

Children s Mathematical Development

Children s Mathematical Development Book
Author : David C. Geary
Publisher : Amer Psychological Assn
Release : 1994-01-01
ISBN : 9781557982582
Language : En, Es, Fr & De

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Book Description :

"Children's Mathematical Development" [offers] the 1st comprehensive treatment of number-skills development from infancy through adolescence. [The author] presents basic research in early number development, arithmetic, and mathematical problem solving; explores theoretical perspectives; and discusses implications for educators, offering his own thought-provoking conclusions. /// [He also] identifies 3 different forms of disability and describes specific math-related cognitive deficits. Using hard data, he critiques current philosophical approaches to education reform, offers suggestions for how to improve the teaching of math procedures and concepts, and examines how to address math anxiety and remediate math disability.