cognitive foundations for improving mathematical learning

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Cognitive Foundations for Improving Mathematical Learning
Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Release Date : 2019-01-03
ISBN 10 : 0128159537
Pages : 377 pages
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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

Development of Mathematical Cognition
Author : Daniel B. Berch,David C. Geary,Kathleen Mann Koepke
Publisher : Academic Press
Release Date : 2015-10-03
ISBN 10 : 0128019093
Pages : 414 pages
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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

Learning and Teaching Early Math
Author : Douglas H. Clements,Julie Sarama
Publisher : Routledge
Release Date : 2020-12-30
ISBN 10 : 1000288544
Pages : 468 pages
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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.

Foundations of Geometric Cognition
Author : Mateusz Hohol
Publisher : Routledge
Release Date : 2019-09-12
ISBN 10 : 042950859X
Pages : 188 pages
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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.

Mathematics Learning in Early Childhood
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 Date : 2009-12-13
ISBN 10 : 0309128064
Pages : 398 pages
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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 Foundations of Clinical Psychology (Psychology Revivals)
Author : Chris R. Brewin
Publisher : Psychology Press
Release Date : 2013-12-16
ISBN 10 : 1317932447
Pages : 214 pages
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Originally published in 1988, this was the first textbook to review and integrate the cognitive theories underlying the practice of modern clinical psychology. Written in a clear and readable way, it uses many clinical examples to relate the theories to what therapists actually do. It describes the strengths and weaknesses of the theories and develops a common framework drawn from research in social and cognitive psychology to explain the mechanisms of behavioural and cognitive therapy. Among the topics covered are the validity of self-reports; experimental investigations of nonconscious processes; cognitive theories of conditioning; the relation between cognition and emotional disorders such as anxiety and depression; self-esteem and the development of self-schema; self-efficacy; explanation and causal attribution; personal values and goals; self-regulation and the techniques of cognitive therapy. This textbook is designed for advanced undergraduate and postgraduate courses in clinical and abnormal psychology. Its practical focus will also make it of particular interest to practising clinical psychologists, psychiatrists and other mental health professionals.

The Mathematical Brain Across the Lifespan
Author : N.A
Publisher : Elsevier
Release Date : 2016-06-20
ISBN 10 : 0444637028
Pages : 416 pages
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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

The Cognitive Foundations of Reading and Its Acquisition
Author : Wesley A. Hoover,William E. Tunmer
Publisher : Springer Nature
Release Date : 2020-06-09
ISBN 10 : 3030441954
Pages : 263 pages
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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.

Cognitive Foundations of Natural History
Author : Scott Atran
Publisher : Cambridge University Press
Release Date : 1993-01-29
ISBN 10 : 9780521438711
Pages : 360 pages
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Inspired by a debate between Noam Chomsky and Jean Piaget, this work traces the development of natural history from Aristotle to Darwin, and demonstrates how the science of plants and animals has emerged from the common conceptions of folkbiology.

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts
Author : David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke
Publisher : Academic Press
Release Date : 2017-02-08
ISBN 10 : 0128133686
Pages : 360 pages
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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

Deaf Cognition
Author : Marc Marschark,Peter C Hauser
Publisher : Oxford University Press
Release Date : 2008-06-30
ISBN 10 : 9780199709397
Pages : 496 pages
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Deaf Cognition examines the cognitive underpinnings of deaf individuals' learning. Marschark and Hauser have brought together scientists from different disciplines, which rarely interact, to share their ideas and create this book. It contributes to the science of learning by describing and testing theories that might either over or underestimate the role that audition or vision plays in learning and memory, and by shedding light on multiple pathways for learning. International experts in cognitive psychology, brain sciences, cognitive development, and deaf children offer a unique, integrative examination of cognition and learning, with discussions on their implications for deaf education. Each chapter focuses primarily on the intersection of research in cognitive psychology, developmental psychology, and deaf education. The general theme of the book is that deaf and hearing individuals differ to some extent in early experience, brain development, cognitive functioning, memory organization, and problem solving. Identifying similarities and differences among these domains provides new insights into potential methods for enhancing achievement in this traditionally under-performing population.

Evolutionary Origins and Early Development of Number Processing
Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
Publisher : Academic Press
Release Date : 2014-11-04
ISBN 10 : 0128008881
Pages : 400 pages
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The first volume in this ground-breaking series focuses on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative concepts and skills along with evolutionary precursors and early developmental trajectories. Brings together and focuses the efforts and research of multiple disciplines working in math cognition. The contributors bring vast knowledge and experience to bear on resolving extant substantive and methodological challenges to help advance the field of basic number processing. Introductory sections and summaries will be included to provide background for non-specialist readers.

Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers
Author : Mareike Kunter,Jürgen Baumert,Werner Blum,Ute Klusmann,Stefan Krauss,Michael Neubrand
Publisher : Springer Science & Business Media
Release Date : 2013-03-29
ISBN 10 : 1461451493
Pages : 378 pages
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This work reports the findings of the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students ́ Mathematical Literacy project (COACTIV). COACTIV applies a broad, innovative conceptualization of teacher competence to examine how mathematics teachers’ knowledge, beliefs, motivational orientations, and self-regulation skills influence their instructional practice and teaching outcomes In this project data was collected on various aspects of teacher competence and classroom instruction from the perspective of both the teachers themselves and their students. Moreover, it gauges the effects of these teacher characteristics on student learning, as indexed by the progress students in each class. Questions addressed in the study which are reported in this volume include: What are the characteristics of successful teaching? What distinguishes teachers who succeed in their profession? How can the quality of instruction be improved?

Sociocognitive Foundations of Educational Measurement
Author : Robert J. Mislevy
Publisher : Routledge
Release Date : 2018-04-09
ISBN 10 : 1317976525
Pages : 438 pages
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Several key developments challenge the field of educational measurement today: demands for tests at larger scales with higher stakes, an improved understanding of how people develop capabilities, and new technologies for interactive digital assessments. Sociocognitive Foundations of Educational Measurement integrates new developments in educational measurement and educational psychology in order to provide researchers, testing professionals, and students with an innovative sociocognitive perspective on assessment. This comprehensive volume begins with a broad explanation of the sociocognitive perspective and the foundations of assessment, then provides a series of focused applications to major topics such as assessment arguments, validity, fairness, interactive assessment, and a conception of "measurement" in educational assessment. Classical test theory, item response theory, categorical models, mixture models, cognitive diagnosis models, and Bayesian networks are explored from the resulting perspective. Ideal for specialists in these areas, graduate students, developers, and scholars in both educational measurement and fields that contribute to a sociocognitive perspective, this book consolidates nearly a decade of research into a fresh perspective on educational measurement.

Growing Minds
Author : Carol Copple
Publisher : National Association of Education of Young Children
Release Date : 2012
ISBN 10 : 9781928896791
Pages : 148 pages
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From the beginning of life, young children's learning and activities depend on their cognitive capabilities and development. To cope with the environment they live in, children need to learn about their physical and social worlds; acquire language; regulate their bodies, emotions, and thoughts; and gain competence in literacy, mathematics, science, and other knowledge domains. This collection of readings from books and Young Children articles outlines important dimensions of their early cognitive development and describes approaches for promoting it.

Cognitive Foundations of Clinical Psychology (Psychology Revivals)
Author : Chris R. Brewin
Publisher : Psychology Press
Release Date : 2013-12-16
ISBN 10 : 1317932455
Pages : 214 pages
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Originally published in 1988, this was the first textbook to review and integrate the cognitive theories underlying the practice of modern clinical psychology. Written in a clear and readable way, it uses many clinical examples to relate the theories to what therapists actually do. It describes the strengths and weaknesses of the theories and develops a common framework drawn from research in social and cognitive psychology to explain the mechanisms of behavioural and cognitive therapy. Among the topics covered are the validity of self-reports; experimental investigations of nonconscious processes; cognitive theories of conditioning; the relation between cognition and emotional disorders such as anxiety and depression; self-esteem and the development of self-schema; self-efficacy; explanation and causal attribution; personal values and goals; self-regulation and the techniques of cognitive therapy. This textbook is designed for advanced undergraduate and postgraduate courses in clinical and abnormal psychology. Its practical focus will also make it of particular interest to practising clinical psychologists, psychiatrists and other mental health professionals.

Mathematical Reasoning
Author : Lyn D. English
Publisher : Routledge
Release Date : 2013-04-03
ISBN 10 : 1136491147
Pages : 392 pages
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How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

Foundations of Rule Learning
Author : Johannes Fürnkranz,Dragan Gamberger,Nada Lavrač
Publisher : Springer Science & Business Media
Release Date : 2012-11-06
ISBN 10 : 3540751971
Pages : 334 pages
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Rules – the clearest, most explored and best understood form of knowledge representation – are particularly important for data mining, as they offer the best tradeoff between human and machine understandability. This book presents the fundamentals of rule learning as investigated in classical machine learning and modern data mining. It introduces a feature-based view, as a unifying framework for propositional and relational rule learning, thus bridging the gap between attribute-value learning and inductive logic programming, and providing complete coverage of most important elements of rule learning. The book can be used as a textbook for teaching machine learning, as well as a comprehensive reference to research in the field of inductive rule learning. As such, it targets students, researchers and developers of rule learning algorithms, presenting the fundamental rule learning concepts in sufficient breadth and depth to enable the reader to understand, develop and apply rule learning techniques to real-world data.

International Handbook of Mathematical Learning Difficulties
Author : Annemarie Fritz,Vitor Geraldi Haase,Pekka Räsänen
Publisher : Springer
Release Date : 2019-01-30
ISBN 10 : 3319971484
Pages : 843 pages
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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.

Continuous Issues in Numerical Cognition
Author : Avishai Henik
Publisher : Academic Press
Release Date : 2016-05-18
ISBN 10 : 0128017937
Pages : 456 pages
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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