Cognitive Foundations For Improving Mathematical Learning

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Cognitive Foundations for Improving Mathematical Learning

David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Cognitive Foundations for Improving Mathematical Learning Book PDF

Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Page : 377 pages
File Size : 41,6 Mb
Release : 2019-01-03
Category : Psychology
ISBN : 9780128159538

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Cognitive Foundations for Improving Mathematical Learning by David C. Geary,Daniel B. Berch,Kathleen Mann Koepke Pdf

The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. Identifies the relative influence of school and family on math learning Discusses the efficacy of numerical play for improvement in math Features learning trajectories in math Examines the role of math language in numeracy skills Includes assessments of math skills Explores the role of cognition in treating math-based learning difficulties

Mathematical Cognition

James M. Royer
Mathematical Cognition Book PDF

Author : James M. Royer
Publisher : Information Age Pub Incorporated
Page : 259 pages
File Size : 43,9 Mb
Release : 2003
Category : Education
ISBN : 1930608349

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Mathematical Cognition by James M. Royer Pdf

This book deals addresses how the development of the human capacity for mathematical cognition occurs through educational experience. Chapters include: (1) "The Development of Math Competence in the Preschool and Early School Years: Cognitive Foundations and Instructional Strategies " (Sharon Griffin); (2) "Perspectives on Mathematics Strategy Development" (Martha Carr and Hillary Hettinger); (3) "Mathematical Problem Solving" (Richard E. Mayer); (4) "Learning Disabilities in Basic Mathematics: Deficits in Memory and Cognition" (David C. Geary and Mary K. Hoard); (5) "Relationships among Basic Computational Automaticity, Working Memory and Complex Mathematical Problem Solving: What We Know and What We Need to Know" (Loel T. Tronsky and James M. Royer); (6) "Mathematics Instruction: Cognitive, Affective and Existential Perspectives" (Allan Feldman); (7) "A Brief History of American K-12 Mathematics Education in the 20th Century" (David Klein); and (8) "Assessment in Mathematics: A Developmental Approach" (John Pegg). (Author/KHR).

Mathematics Learning in Early Childhood

National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Mathematics Learning in Early Childhood Book PDF

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Publisher : National Academies Press
Page : 399 pages
File Size : 46,8 Mb
Release : 2009-11-13
Category : Education
ISBN : 9780309147439

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Mathematics Learning in Early Childhood by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics Pdf

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.

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts

David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke
Acquisition of Complex Arithmetic Skills and Higher Order Mathematics Concepts Book PDF

Author : David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke
Publisher : Academic Press
Page : 360 pages
File Size : 48,8 Mb
Release : 2017-02-08
Category : Psychology
ISBN : 9780128133682

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Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts by David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke Pdf

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public

Mathematical Cognition and Understanding

Katherine M. Robinson,Adam K. Dubé,Donna Kotsopoulos
Mathematical Cognition and Understanding Book PDF

Author : Katherine M. Robinson,Adam K. Dubé,Donna Kotsopoulos
Publisher : Springer Nature
Page : 285 pages
File Size : 40,5 Mb
Release : 2023-05-31
Category : Education
ISBN : 9783031291951

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Mathematical Cognition and Understanding by Katherine M. Robinson,Adam K. Dubé,Donna Kotsopoulos Pdf

This book focuses on elementary and middle school children’s understanding of mathematics as well as the cognitive aspects involved in the development of mathematical knowledge, skills, and understanding. Children’s success in and understanding of mathematics stem from factors beyond the mathematics curriculum. Researchers are increasingly becoming aware of the necessity to consider a complex set of variables when accounting for large individual differences in mathematics achievement. These chapters contribute to how both researchers and educators can consider the multidimensionality of skills involved in developing mathematical knowledge in the middle school years as well as to how this knowledge can be used to enhance practices in the mathematics classroom. Topics include the cognitive and spatial skills involved in mathematics knowledge, the role of motivation in mathematics learning, the neurological processes and development of children’s mathematics skills, the development of understanding of arithmetic and fraction concepts, the factors relating to children’s word problem success, and techniques to promote mathematics understanding. This book and its companion, Mathematical Teaching and Learning, take an interdisciplinary perspective to mathematical learning and development in the elementary and middle school years. The authors and perspectives in this book draw from education, neuroscience, developmental psychology, and cognitive psychology. The book will be relevant to scholars/educators in the field of mathematics education and also those in childhood development and cognition. Each chapter also includes practical tips and implications for parents as well as for educators and researchers.

Concept-Rich Mathematics Instruction

Meir Ben-Hur
Concept Rich Mathematics Instruction Book PDF

Author : Meir Ben-Hur
Publisher : ASCD
Page : 162 pages
File Size : 52,9 Mb
Release : 2006-06-15
Category : Education
ISBN : 9781416617938

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Concept-Rich Mathematics Instruction by Meir Ben-Hur Pdf

Have you ever wondered why students too often have only a rudimentary understanding of mathematics, why even rich and exciting hands-on learning does not always result in "real" learning of new concepts? The answer lies in whether students have actually learned mathematical concepts, rather than merely memorizing facts and formulas. Concept-Rich Mathematics Instruction is based on the constructivist view that concepts are not simply facts to be memorized and later recalled, but rather knowledge that learners develop through an active process of adapting to new experiences. The teacher's role is critical in this process. When teachers prompt students to reflect on their experiences and report and answer questions verbally, students must re-examine and even revise their concepts of reality. Meir Ben-Hur offers expert guidance on all aspects of Concept-Rich Mathematics Instruction, including * Identifying the core concepts of the mathematics curriculum. * Planning instructional sequences that build upon concepts that students already understand. * Designing learning experiences that provoke thoughtful discussions about new concepts and prepare students to apply these concepts on their own. * Identifying student errors, particularly those caused by preconceptions, as important sources of information and as key instructional tools. * Conducting classroom dialogues that are rich in alternative representations. * Using a variety of formative assessment methods to reveal the state of students' learning. * Incorporating problem-solving activities that provoke cognitive dissonance and enhance students' cognitive competence. Concept-Rich Mathematics Instruction is grounded in the belief that all students can learn to think mathematically and solve challenging problems. If you're looking for a powerful way to improve students' performance in mathematics and move closer to fulfilling the NCTM standards, look no further: this approach provides the building blocks for constructing a first-class mathematics program. Note: This product listing is for the reflowable (ePub) version of the book.

Transforming the Workforce for Children Birth Through Age 8

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
Transforming the Workforce for Children Birth Through Age 8 Book PDF

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
Page : 706 pages
File Size : 45,9 Mb
Release : 2015-07-23
Category : Social Science
ISBN : 9780309324885

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Transforming the Workforce for Children Birth Through Age 8 by 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 Pdf

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.

Foundations for the Future in Mathematics Education

Richard A. Lesh,Eric Hamilton,James J. Kaput
Foundations for the Future in Mathematics Education Book PDF

Author : Richard A. Lesh,Eric Hamilton,James J. Kaput
Publisher : Routledge
Page : 476 pages
File Size : 46,9 Mb
Release : 2007
Category : Education
ISBN : 0805860576

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Foundations for the Future in Mathematics Education by Richard A. Lesh,Eric Hamilton,James J. Kaput Pdf

Foundations for the Future in Mathematics Education.

Heterogeneous Contributions to Numerical Cognition

Wim Fias,Avishai Henik
Heterogeneous Contributions to Numerical Cognition Book PDF

Author : Wim Fias,Avishai Henik
Publisher : Academic Press
Page : 422 pages
File Size : 53,5 Mb
Release : 2021-05-28
Category : Medical
ISBN : 9780128174159

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Heterogeneous Contributions to Numerical Cognition by Wim Fias,Avishai Henik Pdf

Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, neuropsychological, behavioral, and interactional levels. Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical Cognition examines research in mathematical education methods and their neurodevelopmental basis, focusing on the underlying neurodevelopmental features that must be taken into account when teaching and learning mathematics. Cognitive domains and functions such as executive functions, memory, attention, and language contribute to numerical cognition and are essential for its proper development. These lines of research and thinking in neuroscience are discussed in this book to further the understanding of the neurodevelopmental and cognitive basis of more complex forms of mathematics – and how to best teach them. By unravelling the basic building blocks of numerical thinking and the developmental basis of human capacity for arithmetic, this book and the discussions within 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. A novel innovative reference on the emerging field of numerical cognition and neurodevelopment underlying mathematical education Includes an overview of the multiple disciplines that comprise numerical cognition written by world-leading researchers in the numerical cognition and neurodevelopment fields Features an innovative organization with each section providing a general overview, developmental research, neurocognitive mechanisms, and discussion about relevant studies

The Development of Early Childhood Mathematics Education

Anonim
The Development of Early Childhood Mathematics Education Book PDF

Author : Anonim
Publisher : Academic Press
Page : 322 pages
File Size : 43,5 Mb
Release : 2017-08-24
Category : Psychology
ISBN : 9780128134498

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The Development of Early Childhood Mathematics Education by Anonim Pdf

The Development of Early Childhood Mathematics Education, Volume 53 in the Advances in Child Development and Behavior series, includes chapters that highlight some of the most recent research in the field of developmental psychology. Users will find updated chapters on a variety of topics, including sections on The DREME Network: Research and Interventions in Early Childhood Mathematics, The Use of Concrete Experiences in Early Childhood Mathematics Instruction, Interventions in Early Mathematics: Avoiding Pollution and Dilution, Coaching in Early Mathematics, and Designing Studies to Test Causal Questions About Early Math: The Development of Making Pre-K Count. Each chapter provides in-depth discussions, with this volume serving as an invaluable resource for developmental or educational psychology researchers, scholars and students. Contains chapters that highlight some of the most recent research in the area of child development and behavior Presents a wide array of topics that are discussed in detail

Learning and Teaching Early Math

Douglas H. Clements,Julie Sarama
Learning and Teaching Early Math Book PDF

Author : Douglas H. Clements,Julie Sarama
Publisher : Routledge
Page : 549 pages
File Size : 45,7 Mb
Release : 2020-12-29
Category : Education
ISBN : 9781000288544

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Learning and Teaching Early Math by Douglas H. Clements,Julie Sarama Pdf

The third edition of this significant and groundbreaking book summarizes current research into how young children learn mathematics and how best to develop foundational knowledge to realize more effective teaching. Using straightforward, practical language, early math experts Douglas Clements and Julie Sarama show how learning trajectories help teachers understand children’s level of mathematical understanding and lead to better teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous: helping teachers understand the varying levels of knowledge exhibited by individual students, it allows them to better meet the learning needs of all children. This thoroughly revised and contemporary third edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become confident, credible professionals. The new edition draws on numerous new research studies, offers expanded international examples, and includes updated illustrations throughout. This new edition is closely linked with Learning and Teaching with Learning Trajectories–[LT]2–an open-access, web-based tool for early childhood educators to learn about how children think and learn about mathematics. Head to LearningTrajectories.org for ongoing updates, interactive games, and practical tools that support classroom learning.

Rigorous Mathematical Thinking

James T. Kinard,Alex Kozulin
Rigorous Mathematical Thinking Book PDF

Author : James T. Kinard,Alex Kozulin
Publisher : Cambridge University Press
Page : 210 pages
File Size : 46,6 Mb
Release : 2008-06-02
Category : Psychology
ISBN : 9781139472395

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Rigorous Mathematical Thinking by James T. Kinard,Alex Kozulin Pdf

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Foundations of Geometric Cognition

Mateusz Hohol
Foundations of Geometric Cognition Book PDF

Author : Mateusz Hohol
Publisher : Routledge
Page : 315 pages
File Size : 46,9 Mb
Release : 2019-09-12
Category : Psychology
ISBN : 9780429509216

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Foundations of Geometric Cognition by Mateusz Hohol Pdf

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.

The Development of Arithmetic Concepts and Skills

Arthur J. Baroody,Ann Dowker
The Development of Arithmetic Concepts and Skills Book PDF

Author : Arthur J. Baroody,Ann Dowker
Publisher : Routledge
Page : 513 pages
File Size : 45,9 Mb
Release : 2013-06-17
Category : Education
ISBN : 9781135672232

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The Development of Arithmetic Concepts and Skills by Arthur J. Baroody,Ann Dowker Pdf

This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars, past and present, have suggested. The results of psychological, educational, and clinical studies using a wide range of arithmetic tasks and populations (including "normally" and atypically developing children, non-injured and brain-injured adults, and savants) all point to the same conclusion: The heart of arithmetic fluency, in general, and the flexible and creative use of strategies, in particular, is what is termed "adaptive expertise" (meaningful or conceptually based knowledge). The construction of adaptive expertise in mathematics is, for the first time, examined across various arithmetic topics and age groups. This book will be an invaluable resource for researchers and graduate students interested in mathematical cognition and learning (including mathematics educators, developmental and educational psychologists, and neuropsychologists), educators (including teachers, curriculum supervisors, and school administrators), and others interested in improving arithmetic instruction (including officials in national and local education departments, the media, and parents).

Adding It Up

National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Adding It Up Book PDF

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Publisher : National Academies Press
Page : 460 pages
File Size : 52,9 Mb
Release : 2001-11-13
Category : Education
ISBN : 0309132843

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Adding It Up by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee Pdf

Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.