Beginning Mathematical Reasoning
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Mathematical Reasoning
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Author : Raymond Nickerson
language : en
Publisher: Taylor & Francis
Release Date : 2011-02-25
Mathematical Reasoning written by Raymond Nickerson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Psychology categories.
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.
Enriching Early Mathematical Learning
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Author : Cook, Grace
language : en
Publisher: McGraw-Hill Education (UK)
Release Date : 1997-08-01
Enriching Early Mathematical Learning written by Cook, Grace and has been published by McGraw-Hill Education (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-01 with Education categories.
Accidents and the possibility of fraud in Max and Hadley's chemistry lab become the catalyst of their lives, throwing Hadley, Max, and Shelby into physically and emotionally dangerous proximity, forcing them to make hard choices about morality, futures, friendship, and marriage.
Supporting Early Mathematical Development
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Author : Caroline McGrath
language : en
Publisher: Routledge
Release Date : 2010-07-12
Supporting Early Mathematical Development written by Caroline McGrath and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-12 with Education categories.
Supporting Early Mathematical Development is an essential text for current Early Years practitioners and students, offering an excellent blend of theory and practice that will enable you to provide successful mathematical education for children from birth to eight years old. Charting the delivery of mathematical development in Playgroups, Children's Centres, Nurseries and Primary Schools, it forges links between current practice and fundamental Early Years principles and makes suggestions for creating effective pedagogies in maths teaching. Promoting mathematical development through play-based learning, this book presents: a wealth of practical multi-sensory teaching strategies instructional methodologies activity ideas incorporating play, books, songs, cookery and the outdoors examples of children's work advice on translating theory into practice questions for reflective practice. Throughout the book, Caroline McGrath breaks down the complexity of teaching and learning mathematics into simple steps and guides readers through possible gaps in their knowledge, bringing fresh enthusiasm to teaching mathematics. This is an invaluable resource for practitioners and trainee teachers wishing to strengthen their mathematical teaching and professional practice, or for students on a wide range of Early Years courses.
Reconceptualizing Early Mathematics Learning
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Author : Lyn D. English
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-09
Reconceptualizing Early Mathematics Learning written by Lyn D. English and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 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.
Mathematical Reasoning
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Author : Linda Brumbaugh
language : en
Publisher: Critical Thinking Company
Release Date : 2006
Mathematical Reasoning written by Linda Brumbaugh and has been published by Critical Thinking Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Education categories.
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.
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.
Understanding Children S Mathematical Graphics Beginnings In Play
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Author : Elizabeth Carruthers
language : en
Publisher: McGraw-Hill Education (UK)
Release Date : 2011-04-16
Understanding Children S Mathematical Graphics Beginnings In Play written by Elizabeth Carruthers and has been published by McGraw-Hill Education (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-16 with Education categories.
This book challenges traditional beliefs and practices of teaching 'written' mathematics in early childhood. It gives theoretical underpinnings and offers exciting insights and context to children's early mathematical thinking and in particular into children's mathematical graphics, showing how this supports their understanding of the abstract symbolic language of mathematics. Drawing on a wide range of examples, it illustrates and explains how children explore and communicate their mathematical thinking through their mathematical graphics, and how this begins in play. The book looks at the power of children's own marks, symbols and other graphical representations to convey meanings, exploring how they support complex thinking. The authors explore the relationship between children's play and meaning making. Rather than viewing mathematics as a separate subject or as a set of basic 'skills' to be transmitted, they demonstrate that in supportive learning cultures children develop their own mathematical thinking to solve problems. Key features include: Numerous new examples and case studies of children from birth to 8 years,highlighting the complexity and richness of children's thinking Explanation of pedagogical issues - showing how they can support rich play and mathematics Draws on the authors' latest research This book is valuable reading for students, teachers, primary mathematics coordinators' and all early years' professionals working in the Early Years Foundation Stage and Key Stage One.
Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Advanced Mathematical Thinking written by David Tall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking – what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students – has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: • the nature of advanced mathematical thinking, • cognitive theory, and • reviews of the progress of cognitive research into different areas of advanced mathematics.
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. The chapters offer summaries and synthesis of the research produced by the PME Group, presented to let the readers grasp the evolution of paradigms, questions, methodologies and most relevant research results during the last 30 years. They also include extensive lists of references. Beyond this, the chapters raise the main current research questions and suggest directions for future research. The handbook is divided into five sections devoted to the main research domains of interest to the PME Group. The first three sections summarize cognitively oriented research on learning and teaching specific content areas, transversal areas, and based on technology rich environments. The fourth section is devoted to the research on social, affective, cultural and cognitive aspects of Mathematics Education. Finally, the fifth section includes two chapters summarizing the PME research on teacher training and professional life of mathematics teachers. The volume is the result of the effort of 30 authors and 26 reviewers. Most of them are recognized leading PME researchers with great expertise on the topic of their chapter. This handbook shall be of interest to both experienced researchers and doctoral students needing detailed synthesis of the advances and future directions of research in Mathematics Education, and also to mathematics teacher trainers who need to have a comprehensive reference as background for their courses on Mathematics Education.
Spatial Reasoning In The Early Years
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Author : Brent Davis
language : en
Publisher: Routledge
Release Date : 2015-04-17
Spatial Reasoning In The Early Years written by Brent Davis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-17 with Education categories.
Over the past several years, "spatial reasoning" has gained renewed prominence among mathematics educators, as spatial skills are proving to be not just essential to mathematical understanding but also strong predictors of future success beyond the classroom in fields such as science, technology, and engineering. By exploring both primary and emergent dimensions, Spatial Reasoning in the Early Years helps define the concept of spatial reasoning and provides compelling evidence of the need for a clear focus within early education specifically. The authors review the research, look across current theories, and investigate implications for contemporary school mathematics pedagogy as they identify areas of inquiry necessary to bring a stronger spatial reasoning emphasis into the classroom. The book contains many classroom- or workshop-based vignettes, highlighting the complexity of spatial reasoning in educational practice, providing an in-depth analysis of spatial reasoning as it applies to classroom practice, and offering new ways of framing lessons to help young students hone their spatial reasoning abilities. The book concludes with a forward-looking agenda that contributes to developing a greater understanding of the role spatial reasoning plays in educational contexts and beyond. Supported by plentiful visual representations, Spatial Reasoning in the Early Years skillfully integrates the conceptual and the concrete, making this text a dynamic and accessible resource.