Mathematical And Analogical Reasoning Of Young Learners

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Mathematical and Analogical Reasoning of Young Learners

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1135638691
Total Pages : 154 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Mathematical and Analogical Reasoning of Young Learners by : Lyn D. English

Download or read book Mathematical and Analogical Reasoning of Young Learners written by Lyn D. English and published by Routledge. This book was released on 2004-07-19 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.

Mathematical Reasoning

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1136491147
Total Pages : 407 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Mathematical Reasoning by : Lyn D. English

Download or read book Mathematical Reasoning written by Lyn D. English and published by Routledge. This book was released on 2013-04-03 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analogical Reasoning in Children

Author : Usha Goswami
Publisher : Psychology Press
ISBN 13 : 1317775392
Total Pages : 172 pages
Book Rating : 4.3/5 (177 download)

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Book Synopsis Analogical Reasoning in Children by : Usha Goswami

Download or read book Analogical Reasoning in Children written by Usha Goswami and published by Psychology Press. This book was released on 2013-10-23 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analogical reasoning is a fundamental cognitive skill, involved in classification, learning, problem-solving and creative thinking, and should be a basic building block of cognitive development. However, for a long time researchers have believed that children are incapable of reasoning by analogy. This book argues that this is far from the case, and that analogical reasoning may be available very early in development. Recent research has shown that even 3-year-olds can solve analogies, and that infants can reason about relational similarity, which is the hallmark of analogy. The book traces the roots of the popular misconceptions about children's analogical abilities and argues that when children fail to use analogies, it is because they do not understand the relations underlying the analogy rather than because they are incapable of analogical reasoning. The author argues that young children spontaneously use analogies in learning, and that their analogies can sometimes lead them into misconceptions. In the "real worlds" of their classrooms, children use analogies when learning basic skills like reading, and even babies seem to use analogies to learn about the world around them.

The SAGE Encyclopedia of Lifespan Human Development

Author : Marc H. Bornstein
Publisher : SAGE Publications
ISBN 13 : 1506353312
Total Pages : 2616 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis The SAGE Encyclopedia of Lifespan Human Development by : Marc H. Bornstein

Download or read book The SAGE Encyclopedia of Lifespan Human Development written by Marc H. Bornstein and published by SAGE Publications. This book was released on 2018-01-15 with total page 2616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lifespan human development is the study of all aspects of biological, physical, cognitive, socioemotional, and contextual development from conception to the end of life. In approximately 800 signed articles by experts from a wide diversity of fields, The SAGE Encyclopedia of Lifespan Human Development explores all individual and situational factors related to human development across the lifespan. Some of the broad thematic areas will include: Adolescence and Emerging Adulthood Aging Behavioral and Developmental Disorders Cognitive Development Community and Culture Early and Middle Childhood Education through the Lifespan Genetics and Biology Gender and Sexuality Life Events Mental Health through the Lifespan Research Methods in Lifespan Development Speech and Language Across the Lifespan Theories and Models of Development. This five-volume encyclopedia promises to be an authoritative, discipline-defining work for students and researchers seeking to become familiar with various approaches, theories, and empirical findings about human development broadly construed, as well as past and current research.

Math Analogies Level 1

Author : Linda Brumbaugh
Publisher :
ISBN 13 : 9781601441973
Total Pages : 48 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Math Analogies Level 1 by : Linda Brumbaugh

Download or read book Math Analogies Level 1 written by Linda Brumbaugh and published by . This book was released on 2013-12-11 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reasoning of Children and Adults

Author : Alina Galvão Spinillo
Publisher : Springer Nature
ISBN 13 : 303069657X
Total Pages : 324 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematical Reasoning of Children and Adults by : Alina Galvão Spinillo

Download or read book Mathematical Reasoning of Children and Adults written by Alina Galvão Spinillo and published by Springer Nature. This book was released on 2021-05-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner’s cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.

Mathematics Education in the Early Years

Author : Tamsin Meaney
Publisher : Springer
ISBN 13 : 331923935X
Total Pages : 443 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Mathematics Education in the Early Years by : Tamsin Meaney

Download or read book Mathematics Education in the Early Years written by Tamsin Meaney and published by Springer. This book was released on 2016-01-22 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents chapters based on papers presented at the second POEM conference on early mathematics learning. These chapters broaden the discussion about mathematics education in early childhood, by exploring the debate about construction versus instruction. Specific sections investigate the teaching and learning of mathematical processes and mathematical content, early childhood teacher development, transitions for young children between home and preschool, between home and school and between preschool and school. The chapters use a range of innovative theoretical and methodological approaches which will form an interesting basis for future research in this area.

Cognitive Foundations for Improving Mathematical Learning

Author : David C. Geary
Publisher : Academic Press
ISBN 13 : 0128159537
Total Pages : 377 pages
Book Rating : 4.1/5 (281 download)

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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 377 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

Mathematical Learning and Cognition in Early Childhood

Author : Katherine M. Robinson
Publisher : Springer
ISBN 13 : 3030128954
Total Pages : 274 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Mathematical Learning and Cognition in Early Childhood by : Katherine M. Robinson

Download or read book Mathematical Learning and Cognition in Early Childhood written by Katherine M. Robinson and published by Springer. This book was released on 2019-05-07 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores mathematical learning and cognition in early childhood from interdisciplinary perspectives, including developmental psychology, neuroscience, cognitive psychology, and education. It examines how infants and young children develop numerical and mathematical skills, why some children struggle to acquire basic abilities, and how parents, caregivers, and early childhood educators can promote early mathematical development. The first section of the book focuses on infancy and toddlerhood with a particular emphasis on the home environment and how parents can foster early mathematical skills to prepare their children for formal schooling. The second section examines topics in preschool and kindergarten, such as the development of counting procedures and principles, the use of mathematics manipulatives in instruction, and the impacts of early intervention. The final part of the book focuses on particular instructional approaches in the elementary school years, such as different additive concepts, schema-based instruction, and methods of division. Chapters analyze the ways children learn to think about, work with, and master the language of mathematical concepts, as well as provide effective approaches to screening and intervention. Included among the topics: The relationship between early gender differences and future mathematical learning and participation. The connection between mathematical and computational thinking. Patterning abilities in young children. Supporting children with learning difficulties and intellectual disabilities. The effectiveness of tablets as elementary mathematics education tools. Mathematical Learning and Cognition in Early Childhood is an essential resource for researchers, graduate students, and professionals in infancy and early childhood development, child and school psychology, neuroscience, mathematics education, educational psychology, and social work.

Handbook of Research on the Psychology of Mathematics Education

Author :
Publisher : BRILL
ISBN 13 : 9087901127
Total Pages : 533 pages
Book Rating : 4.0/5 (879 download)

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Book Synopsis Handbook of Research on the Psychology of Mathematics Education by :

Download or read book Handbook of Research on the Psychology of Mathematics Education written by and published by BRILL. This book was released on 2006-01-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for Mathematics Education research in the coming years.

Mathematical Reasoning

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1136491074
Total Pages : 393 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Mathematical Reasoning by : Lyn D. English

Download or read book Mathematical Reasoning written by Lyn D. English and published by Routledge. This book was released on 2013-04-03 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analogical Reasoning in Children

Author : Usha Goswami
Publisher : Psychology Press
ISBN 13 : 1317775406
Total Pages : 167 pages
Book Rating : 4.3/5 (177 download)

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Book Synopsis Analogical Reasoning in Children by : Usha Goswami

Download or read book Analogical Reasoning in Children written by Usha Goswami and published by Psychology Press. This book was released on 2013-10-23 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analogical reasoning is a fundamental cognitive skill, involved in classification, learning, problem-solving and creative thinking, and should be a basic building block of cognitive development. However, for a long time researchers have believed that children are incapable of reasoning by analogy. This book argues that this is far from the case, and that analogical reasoning may be available very early in development. Recent research has shown that even 3-year-olds can solve analogies, and that infants can reason about relational similarity, which is the hallmark of analogy. The book traces the roots of the popular misconceptions about children's analogical abilities and argues that when children fail to use analogies, it is because they do not understand the relations underlying the analogy rather than because they are incapable of analogical reasoning. The author argues that young children spontaneously use analogies in learning, and that their analogies can sometimes lead them into misconceptions. In the "real worlds" of their classrooms, children use analogies when learning basic skills like reading, and even babies seem to use analogies to learn about the world around them.

Math Analogies Level 3

Author : Darin Beigie
Publisher :
ISBN 13 : 9781601447012
Total Pages : 48 pages
Book Rating : 4.4/5 (47 download)

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Book Synopsis Math Analogies Level 3 by : Darin Beigie

Download or read book Math Analogies Level 3 written by Darin Beigie and published by . This book was released on 2015-03-01 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Engaging Young Children in Mathematics

Author : Douglas H. Clements
Publisher : Routledge
ISBN 13 : 0805842101
Total Pages : 474 pages
Book Rating : 4.8/5 (58 download)

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Book Synopsis Engaging Young Children in Mathematics by : Douglas H. Clements

Download or read book Engaging Young Children in Mathematics written by Douglas H. Clements and published by Routledge. This book was released on 2004 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's mathematics; federal government officials; mathematicians; mathematics educators; researchers from mathematics education, early childhood education, and psychology; curriculum developers; teachers; policymakers; and professionals from organizations such as the National Conference of Teachers of Mathematics and the National Association for the Education of Young Children. The main goal of the Conference was to work collectively to help those responsible for framing and implementing early childhood mathematics standards. Although it has its roots in the Conference, the expanded scope of the standards and recommendations covered in this book includes the full range of kindergarten to grade 2. The volume is organized into two main parts and an online appendix (http://www.gse.buffalo.edu/org/conference/). Part One, Major Themes and Recommendations, offers a framework for thinking about pre-kindergarten - grade 2 mathematics education and specific recommendations. Part Two, Elaboration of Major Themes and Recommendations, provides substantive detail regarding young students' understandings of mathematical ideas. Each Part includes five parallel subsections: "Standards in Early Childhood Education"; "Math Standards and Guidelines"; "Curriculum, Learning, Teaching, and Assessment"; "Professional Development"; and "Toward the Future: Implementation and Policy." As a whole the book: * presents comprehensive summaries of research that provide specific guidelines for standards, curriculum, and teaching; * takes the recent reports and recommendations for early childhood mathematics education to the next level; * integrates practical details and research throughout; and * provides a succinct, but thorough review of research on the topics, sequences, and learning trajectories that children can and should learn at each of their first years of life, with specific developmental guidelines that suggest appropriate content for each topic for each year from 2-year-olds to 7-year-olds. This is an indispensable volume for mathematics educators, researchers, curriculum developers, teachers and policymakers, including those who create standards, scope and sequences, and curricula for young children and professional teacher development materials, and students in mathematics education, early childhood trainers, teacher educators, and faculty in mathematics education.

Journal for Research in Mathematics Education

Author :
Publisher :
ISBN 13 :
Total Pages : 564 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Journal for Research in Mathematics Education by :

Download or read book Journal for Research in Mathematics Education written by and published by . This book was released on 2011 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reconceptualizing Early Mathematics Learning

Author : Lyn D. English
Publisher : Springer
ISBN 13 : 9789400764392
Total Pages : 0 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Reconceptualizing Early Mathematics Learning by : Lyn D. English

Download or read book Reconceptualizing Early Mathematics Learning written by Lyn D. English and published by Springer. This book was released on 2013-05-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and early school settings indicate that young learners do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe characteristics of structural development in young students’ mathematics. Collectively, the chapters highlight the importance of providing more exciting, relevant, and challenging 21st century mathematics learning for our young students. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualising the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed.

Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators

Author : Berinderjeet Kaur
Publisher : World Scientific
ISBN 13 : 9814405442
Total Pages : 336 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators by : Berinderjeet Kaur

Download or read book Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators written by Berinderjeet Kaur and published by World Scientific. This book was released on 2012-04-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Reasoning, Communication and Connections in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reasoning, communication and connections in mathematics classrooms.Several renowned international researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three major themes: mathematical tasks, classroom discourse, and connectivity within and beyond mathematics, shape the ideas underpinning reasoning, communication and connections in these chapters. The book makes a significant contribution towards mathematical processes essential for learners of mathematics. It is a good resource for mathematics educators and research students.