Mathematical And Analogical Reasoning Of Young Learners
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Mathematical And Analogical Reasoning Of Young Learners
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Author : Lyn D. English
language : en
Publisher: Routledge
Release Date : 2004-07-19
Mathematical And Analogical Reasoning Of Young Learners written by Lyn D. English and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-19 with Education categories.
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
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Author : Lyn D. English
language : en
Publisher: Routledge
Release Date : 2013-04-03
Mathematical Reasoning written by Lyn D. English and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-03 with Education categories.
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
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Author : Usha Goswami
language : en
Publisher: Psychology Press
Release Date : 2013-10-23
Analogical Reasoning In Children written by Usha Goswami and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Psychology categories.
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.
Mathematics Education In The Early Years
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Author : Tamsin Meaney
language : en
Publisher: Springer
Release Date : 2016-01-22
Mathematics Education In The Early Years written by Tamsin Meaney and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-22 with Education categories.
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
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Author : David C. Geary
language : en
Publisher: Academic Press
Release Date : 2019-01-03
Cognitive Foundations For Improving Mathematical Learning written by David C. Geary and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-03 with Psychology categories.
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 Reasoning Of Children And Adults
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Author : Alina Galvão Spinillo
language : en
Publisher: Springer Nature
Release Date : 2021-05-24
Mathematical Reasoning Of Children And Adults written by Alina Galvão Spinillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Education categories.
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.
Mathematical Learning And Cognition In Early Childhood
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Author : Katherine M. Robinson
language : en
Publisher: Springer
Release Date : 2019-05-07
Mathematical Learning And Cognition In Early Childhood written by Katherine M. Robinson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Psychology categories.
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
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Author :
language : en
Publisher: BRILL
Release Date : 2006-01-01
Handbook Of Research On The Psychology Of Mathematics Education written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Education categories.
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.
International Perspectives On Teaching And Learning Mathematics With Virtual Manipulatives
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Author : Patricia S. Moyer-Packenham
language : en
Publisher: Springer
Release Date : 2016-06-21
International Perspectives On Teaching And Learning Mathematics With Virtual Manipulatives written by Patricia S. Moyer-Packenham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-21 with Education categories.
This book explores terminology, frameworks, and research being conducted worldwide on virtual manipulatives. It brings together international authors who provide their perspectives on virtual manipulatives in research and teaching. By defining terminology, explaining conceptual and theoretical frameworks, and reporting research, the authors provide a comprehensive foundation on the study and use of virtual manipulatives for mathematics teaching and learning. This foundation provides a common way for researchers to communicate about virtual manipulatives and build on the major works that have been conducted on this topic. By discussing these big ideas, the book advances knowledge for future research on virtual manipulatives as these dynamic tools move from computer platforms to hand-held, touch-screen, and augmented platforms.
Reconceptualizing Early Mathematics Learning
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Author : Lyn D. English
language : en
Publisher: Springer
Release Date : 2013-05-23
Reconceptualizing Early Mathematics Learning written by Lyn D. English and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-23 with Education categories.
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.