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Mathematical and Analogical Reasoning of Young Learners

Mathematical and Analogical Reasoning of Young Learners
Author: Lyn D. English
Publisher: Routledge
Total Pages: 154
Release: 2004-07-19
Genre: Education
ISBN: 1135638691
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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 and Analogical Reasoning of Young Learners

Mathematical and Analogical Reasoning of Young Learners
Author: Lyn D. English
Publisher: Routledge
Total Pages: 237
Release: 2004-07-19
Genre: Education
ISBN: 1135638705
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This book draws upon studies of the development of young children's mathematical and analogical reasoning in the United States and Australia to address a number of significant issues in the mathematical development of young children.

Analogical Reasoning in Children

Analogical Reasoning in Children
Author: Usha Goswami
Publisher: Psychology Press
Total Pages: 172
Release: 2013-10-23
Genre: Psychology
ISBN: 1317775392
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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.

Mathematical Reasoning

Mathematical Reasoning
Author: Lyn D. English
Publisher: Routledge
Total Pages: 407
Release: 2013-04-03
Genre: Education
ISBN: 1136491147
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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.

Mathematical Reasoning of Children and Adults

Mathematical Reasoning of Children and Adults
Author: Alina Galvão Spinillo
Publisher: Springer Nature
Total Pages: 324
Release: 2021-05-24
Genre: Education
ISBN: 303069657X
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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.

The SAGE Encyclopedia of Lifespan Human Development

The SAGE Encyclopedia of Lifespan Human Development
Author: Marc H. Bornstein
Publisher: SAGE Publications
Total Pages: 2616
Release: 2018-01-15
Genre: Psychology
ISBN: 1506353312
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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.

Mathematics Education in the Early Years

Mathematics Education in the Early Years
Author: Tamsin Meaney
Publisher: Springer
Total Pages: 443
Release: 2016-01-22
Genre: Education
ISBN: 331923935X
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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

Cognitive Foundations for Improving Mathematical Learning
Author: David C. Geary
Publisher: Academic Press
Total Pages: 377
Release: 2019-01-03
Genre: Psychology
ISBN: 0128159537
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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

Mathematical Cognition

Mathematical Cognition
Author: Lyn D. English
Publisher:
Total Pages:
Release: 1999
Genre:
ISBN: 9780863776038
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Mathematical Learning and Cognition in Early Childhood

Mathematical Learning and Cognition in Early Childhood
Author: Katherine M. Robinson
Publisher: Springer
Total Pages: 274
Release: 2019-05-07
Genre: Psychology
ISBN: 3030128954
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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.