Mathematical Reasoning Of Children And Adults

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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.

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.

Math on the Move

Author : Malke Rosenfeld
Publisher : Heinemann Educational Books
ISBN 13 : 9780325074702
Total Pages : 0 pages
Book Rating : 4.0/5 (747 download)

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Book Synopsis Math on the Move by : Malke Rosenfeld

Download or read book Math on the Move written by Malke Rosenfeld and published by Heinemann Educational Books. This book was released on 2016-10-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ..."--Publisher description.

Transforming the Workforce for Children Birth Through Age 8

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309324882
Total Pages : 587 pages
Book Rating : 4.3/5 (93 download)

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Book Synopsis Transforming the Workforce for Children Birth Through Age 8 by : National Research Council

Download or read book Transforming the Workforce for Children Birth Through Age 8 written by National Research Council and published by National Academies Press. This book was released on 2015-07-23 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Reasoning Level B (B/W)

Author : Doug Brumbaugh
Publisher :
ISBN 13 : 9781601441829
Total Pages : 264 pages
Book Rating : 4.4/5 (418 download)

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Book Synopsis Mathematical Reasoning Level B (B/W) by : Doug Brumbaugh

Download or read book Mathematical Reasoning Level B (B/W) written by Doug Brumbaugh and published by . This book was released on 2008-03-11 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Young Children Reinvent Arithmetic

Author : Constance Kamii
Publisher : Teachers College Press
ISBN 13 : 0807776246
Total Pages : 394 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis Young Children Reinvent Arithmetic by : Constance Kamii

Download or read book Young Children Reinvent Arithmetic written by Constance Kamii and published by Teachers College Press. This book was released on 1999 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this fully revised second edition of the classic Young Children Reinvent Arithmetic, Constance Kamii describes and develops an innovative program of teaching arithmetic in the early elementary grades. Kamii bases her educational strategies on renowned constructivist Jean Piaget's scientific ideas of how children develop logico-mathematical thinking. Written in collaboration with a classroom teacher, and premised upon the conviction that children are capable of much more than teachers and parents generally realize, the book provides a rich theoretical foundation and a compelling explanation of educational goals and objectives. Kamii calls attention to the ways in which traditional textbook-based teaching can be harmful to children’s development of numerical reasoning, and uses extensive research and classroom-tested studies to illuminate the efficacy of the approach. This book is full of practical suggestions and developmentally appropriate activities that can be used to stimulate numerical thinking among students of varying abilities and learning styles, both within and outside of the classroom. “In this new edition of her important book, Connie Kamii demonstrates scholarship not just in what she has written, but in her willingness to incorporate new ideas and findings. Many people update their books; few assiduously revise them, confronting what they believe to be past errors or gaps in their thinking. Such intellectual honesty, along with consistent connections between theory and practice, make this book a solid contribution to mathematics education of young children.” —Douglas Clements, State University of New York at Buffalo “The development of young children’s logico-mathematical knowledge is at the heart of this text. Similar to the first edition, this revision provides a rich theoretical foundation as well as child-centered activities and principles of teaching that support problem solving, communicating, reasoning, making connections, and representing mathematical ideas. In this great resource for preservice and in-service elementary teachers, Professor Kamii continues to help us understand the implications of Piagetian theory.” —Frances R. Curcio, New York University

Problemoids

Author : Bill McCandliss
Publisher :
ISBN 13 : 9780898240337
Total Pages : 98 pages
Book Rating : 4.2/5 (43 download)

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Book Synopsis Problemoids by : Bill McCandliss

Download or read book Problemoids written by Bill McCandliss and published by . This book was released on 1982 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Resoning Beginning 2

Author : Douglas K. Brumbaugh
Publisher :
ISBN 13 : 9780894559037
Total Pages : 288 pages
Book Rating : 4.5/5 (59 download)

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Book Synopsis Mathematical Resoning Beginning 2 by : Douglas K. Brumbaugh

Download or read book Mathematical Resoning Beginning 2 written by Douglas K. Brumbaugh and published by . This book was released on 2012-03-08 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Children's Mathematics

Author : Thomas P. Carpenter
Publisher : Heinemann Educational Books
ISBN 13 : 9780325052878
Total Pages : 0 pages
Book Rating : 4.0/5 (528 download)

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Book Synopsis Children's Mathematics by : Thomas P. Carpenter

Download or read book Children's Mathematics written by Thomas P. Carpenter and published by Heinemann Educational Books. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.

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.

Mathematical Reasoning

Author : Raymond Nickerson
Publisher : Psychology Press
ISBN 13 : 1136945385
Total Pages : 628 pages
Book Rating : 4.1/5 (369 download)

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Book Synopsis Mathematical Reasoning by : Raymond Nickerson

Download or read book Mathematical Reasoning written by Raymond Nickerson and published by Psychology Press. This book was released on 2011-02-25 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Adventures of Mind and Mathematics

Author : Wolff-Michael Roth
Publisher : Springer Nature
ISBN 13 : 3030518094
Total Pages : 265 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Adventures of Mind and Mathematics by : Wolff-Michael Roth

Download or read book Adventures of Mind and Mathematics written by Wolff-Michael Roth and published by Springer Nature. This book was released on 2020-08-24 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph uses the concept and category of “event” in the study of mathematics as it emerges from an interaction between levels of cognition, from the bodily experiences to symbolism. It is subdivided into three parts.The first moves from a general characterization of the classical approach to mathematical cognition and mind toward laying the foundations for a view on the mathematical mind that differs from going approaches in placing primacy on events.The second articulates some common phenomena–mathematical thought, mathematical sign, mathematical form, mathematical reason and its development, and affect in mathematics–in new ways that are based on the previously developed ontology of events. The final part has more encompassing phenomena as its content, most prominently the thinking body of mathematics, the experience in and of mathematics, and the relationship between experience and mind. The volume is well-suited for anyone with a broad interest in educational theory and/or social development, or with a broad background in psychology.

Bringing Math Home

Author : Suzanne L. Churchman
Publisher : Chicago Review Press
ISBN 13 : 1569766886
Total Pages : 241 pages
Book Rating : 4.5/5 (697 download)

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Book Synopsis Bringing Math Home by : Suzanne L. Churchman

Download or read book Bringing Math Home written by Suzanne L. Churchman and published by Chicago Review Press. This book was released on 2006-05-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ultimate parents' guide to elementary school math features projects, games, and activities children and parents can do together to increase their understanding of basic math concepts. Fun activities such as mapping a child's bedroom for practice in measurements or keeping a diary of numeric items like vacation mileage and expenses reinforce the math skills outlined in each lesson. Using the standards issued by the National Council of Teachers of Mathematics as a foundation, this book covers both content and process standards for areas such as algebra, geometry, measurement, problem solving, and reasoning/proofs. It also includes a glossary of math terms and dozens of suggestions for additional children's reading to further math understanding.

Early Education and Development

Author : Susanne A. Denham
Publisher : Routledge
ISBN 13 : 1134573189
Total Pages : 127 pages
Book Rating : 4.1/5 (345 download)

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Book Synopsis Early Education and Development by : Susanne A. Denham

Download or read book Early Education and Development written by Susanne A. Denham and published by Routledge. This book was released on 2013-10-15 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Volume 16, number 3 of Early education and Development, published in July 2005. This edition includes articles on Family-school communication, African American involvement, the development of logico-mathematical and perceptions of math-mediated language and social skills in kindergarten and preschool.

Creativity Across the Primary Curriculum

Author : Anna Craft
Publisher : Psychology Press
ISBN 13 : 9780415200943
Total Pages : 200 pages
Book Rating : 4.2/5 (9 download)

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Book Synopsis Creativity Across the Primary Curriculum by : Anna Craft

Download or read book Creativity Across the Primary Curriculum written by Anna Craft and published by Psychology Press. This book was released on 2000 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inspirational look at how to foster children's creativity whilst following the National Curriculum. A practical book it will ring bells with educators who want to teach with originality and scope.

Adult Learning and Development

Author : M. Cecil Smith
Publisher : Routledge
ISBN 13 : 1135686378
Total Pages : 294 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Adult Learning and Development by : M. Cecil Smith

Download or read book Adult Learning and Development written by M. Cecil Smith and published by Routledge. This book was released on 2013-06-17 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bridge between educational psychology and the fields of adult learning and development. For researchers, teachers, and graduate students in these fields.

Rigorous Mathematical Thinking

Author : James T. Kinard
Publisher : Cambridge University Press
ISBN 13 : 1139472399
Total Pages : 210 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Rigorous Mathematical Thinking by : James T. Kinard

Download or read book Rigorous Mathematical Thinking written by James T. Kinard and published by Cambridge University Press. This book was released on 2008-06-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.