Mathematics As The Science Of Patterns
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Mathematics
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Author : Keith Devlin
language : en
Publisher: Macmillan
Release Date : 1996-12-15
Mathematics written by Keith Devlin and has been published by Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-15 with Mathematics categories.
To most people, mathematics means working with numbers. But as Keith Devlin shows in Mathematics: The Science of Patterns, this definition has been out of date for nearly 2,500 years. Mathematicians now see their work as the study of patterns—real or imagined, visual or mental, arising from the natural world or from within the human mind. Using this basic definition as his central theme, Devlin explores the patterns of counting, measuring, reasoning, motion, shape, position, and prediction, revealing the powerful influence mathematics has over our perception of reality. Interweaving historical highlights and current developments, and using a minimum of formulas, Devlin celebrates the precision, purity, and elegance of mathematics.
Mathematics As The Science Of Patterns
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Author : Patrick M. Jenlink
language : en
Publisher: IAP
Release Date : 2022-02-01
Mathematics As The Science Of Patterns written by Patrick M. Jenlink and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-01 with Education categories.
Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.
Mathematics As A Science Of Patterns
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Author : Michael D. Resnik
language : en
Publisher: Clarendon Press
Release Date : 1997-07-31
Mathematics As A Science Of Patterns written by Michael D. Resnik and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-31 with Philosophy categories.
Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.
Mathematics The Science Of Patterns
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Author : Keith J. Devlin
language : en
Publisher: Times Books
Release Date : 1994
Mathematics The Science Of Patterns written by Keith J. Devlin and has been published by Times Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
With this fascinating volume, Keith Devlin proves that the guiding principles of some of the most mysterious mathematical topics can be made comprehensible. Writing with an elegant lucidity, Devlin shows just why the definition of mathematics as "working with numbers" has been out of date for nearly 2,500 years. And he demonstrates that far from being too abstract to matter, mathematics is instead an essential and uniquely human endeavor, one that helps us understand the universe and ourselves. In this century alone, there has been a veritable explosion of mathematical activity. A body of knowledge that in 1900 might have filled 80 volumes now would require nearly 100,000. Fields such as algebra and topology have grown tremendously, while complexity theory, dynamical systems theory, and other new areas have developed. And in the last two decades, a common thread running through the many facets of mathematics has been recognized: mathematicians of all kinds now see their work as the study of patterns - real or imagined, visual or mental, arising from the natural world or from within the human mind. Devlin uses this basic definition as his central theme, revealing the search for patterns that drives the mathematics of counting (natural numbers), reasoning (language and logic), motion (calculus), shape (geometry, tilings), and position (topology, knots, symmetry). Interweaving historical highlights and current developments, and using a minimum of formulas, he lets readers see into the kind of reasoning that allows mathematicians to create and explore arcane subjects. And he makes clear the many ways mathematics informs our perceptions of reality - both the physical, biological, and social worlds without, and the realm of ideas and thoughts within. "Mathematics, rightly viewed, possesses not only truth, but supreme beauty," the noted philosopher and mathematician Bertrand Russell once wrote. In Mathematics: The Science of Patterns, Keith Devlin makes such a vision accessible, entertaining, and meaningful. It is an insightful, richly illustrated celebration of the simplicity, the precision, the purity, and the elegance of mathematics.
Mathematics As A Science Of Patterns
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Author : Michael D. Resnik
language : en
Publisher:
Release Date : 1997
Mathematics As A Science Of Patterns written by Michael D. Resnik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Resnik expresses his commitment to a structuralist philosophy of mathematics and links this to a defence of realism about the metaphysics of mathematics - the view that mathematics is about things that really exist.
The Fabric Of Civilization
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Author : Virginia Postrel
language : en
Publisher: Hachette UK
Release Date : 2020-11-10
The Fabric Of Civilization written by Virginia Postrel and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-10 with History categories.
From Neanderthal string to 3D knitting, an “expansive” global history that highlights “how textiles truly changed the world” (Wall Street Journal) The story of humanity is the story of textiles—as old as civilization itself. Since the first thread was spun, the need for textiles has driven technology, business, politics, and culture. In The Fabric of Civilization, Virginia Postrel synthesizes groundbreaking research from archaeology, economics, and science to reveal a surprising history. From Minoans exporting wool colored with precious purple dye to Egypt, to Romans arrayed in costly Chinese silk, the cloth trade paved the crossroads of the ancient world. Textiles funded the Renaissance and the Mughal Empire; they gave us banks and bookkeeping, Michelangelo’s David and the Taj Mahal. The cloth business spread the alphabet and arithmetic, propelled chemical research, and taught people to think in binary code. Assiduously researched and deftly narrated, The Fabric of Civilization tells the story of the world’s most influential commodity.
New Physical Ideas Are Here Needed Revolutionizing Education
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Author : Art Bardige
language : en
Publisher: Lulu.com
Release Date : 2007-04-23
New Physical Ideas Are Here Needed Revolutionizing Education written by Art Bardige and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-23 with Education categories.
How can we meet the increasing demands on American education for more content, greater complexity, and much higher levels of student success? How can we make every student a more effective learner? How can we help every teacher support learning more productively? How can we create schools that enable each and every child to achieve the education to which he or she aspires? We can with a new technology of education - a technology focused on student practice and conceptual visualization. Fortunately, this new technology is now at hand, and it can enable us to revolutionize education. Please join me in an exploration of these new physical ideas that are here, so desperately, needed. Art Bardige
Pattern Theory
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Author : Rachel H. Ellaway
language : en
Publisher: Taylor & Francis
Release Date : 2024-12-30
Pattern Theory written by Rachel H. Ellaway and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Science categories.
Pattern Theory is a groundbreaking exploration of the concept of pattern across a range of disciplines, including science, neuroscience, psychology, and social sciences. This book examines the meaning and implications of pattern, presenting a comprehensive body of theory that unifies concepts of form, order, and regularity and connects them to memory and perception. By challenging existing orthodoxies and linking evidence from brain and mind function, it outlines a robust theoretical framework around pattern searching and matching, pattern activation, and the continuity of pattern nexuses. This in-depth study of pattern theory and pattern thinking delves into the cognitive basis of patterns, their impact on reasoning and learning, and the social and collaborative nature of pattern recognition, expression, and representation. It also addresses philosophical issues and implications surrounding shared pattern thinking and introduces a broad conceptual basis for "pattern inquiry", providing a range of questions and methodologies for applying pattern theory. The book culminates in a manifesto for pattern theory and its application in pattern inquiry, offering 50 key principles that can be applied across various settings. Researchers, scholars, and practitioners are encouraged to explore and critique this unified theory as a lens for examining social and cognitive phenomena. Ideal for academics and professionals seeking to challenge their understanding of the connections between mind and society, as well as for those looking to deepen their understanding of pattern as a cognitive phenomenon, as a theoretical lens, and as a meta-methodology for inquiry, this text provides a substantive foundation for ongoing development and application of pattern science across multiple fields.
A Passion For Patterns
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-04-22
A Passion For Patterns written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-22 with Nature categories.
A Passion for Patterns is a fascinating exploration of the patterns that surround us. From the natural world to the human world, patterns can be found everywhere. They can be beautiful, interesting, and even mysterious. They can also be used to understand the world around us and to create art, music, and literature. In this book, Pasquale De Marco takes readers on a journey through the world of patterns. They explore the patterns found in nature, such as the patterns of leaves on a tree or the patterns of waves in the ocean. They also explore the patterns found in art, music, and science. For example, they discuss how artists use patterns to create paintings, sculptures, and music, and how scientists use patterns to study the weather and the stars. Pasquale De Marco also explores the patterns found in human culture. They discuss the patterns of language, the patterns of religion, and the patterns of social behavior. They show how these patterns can be used to understand human culture and to create art, music, and literature. Pasquale De Marco believes that patterns are a fundamental part of the world around us. They are a source of beauty, fascination, and mystery. They can also be a source of understanding and creativity. In this book, they share their passion for patterns with readers, and they invite readers to explore the world of patterns for themselves. A Passion for Patterns is a must-read for anyone who is interested in the world around them. It is a book that will open your eyes to the beauty and mystery of patterns and will inspire you to see the world in a new way. If you like this book, write a review on google books!
A Guide To Teaching Elementary Science
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Author : Yvette F. Greenspan
language : en
Publisher: Springer
Release Date : 2015-12-21
A Guide To Teaching Elementary Science written by Yvette F. Greenspan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-21 with Education categories.
Nationally and internationally, educators now understand the critical importance of STEM subjects—science, technology, engineering, and mathematics. Today, the job of the classroom science teacher demands finding effective ways to meet current curricula standards and prepare students for a future in which a working knowledge of science and technology will dominate. But standards and goals don’t mean a thing unless we: • grab students’ attention; • capture and deepen children’s natural curiosity; • create an exciting learning environment that engages the learner; and • make science come alive inside and outside the classroom setting. A Guide to Teaching Elementary Science: Ten Easy Steps gives teachers, at all stages of classroom experience, exactly what the title implies. Written by lifelong educator Yvette Greenspan, this book is designed for busy classroom teachers who face tough conditions, from overcrowded classrooms to shrinking budgets, and too often end up anxious and overwhelmed by the challenges ahead and their desire for an excellent science program. This book: • helps teachers develop curricula compatible with the Next Generation Science Standards and the Common Core Standards; • provides easy-to-implement steps for setting up a science classroom, plus strategies for using all available resources to assemble needed teaching materials; • offers detailed sample lesson plans in each STEM subject, adaptable to age and ability and designed to embrace the needs of all learners; and • presents bonus information about organizing field trips and managing science fairs. Without question, effective science curricula can help students develop critical thinking skills and a lifelong passion for science. Yvette Greenspan received her doctorate degree in science education and has developed science curriculum at all levels. A career spent in teaching elementary students in an urban community, she now instructs college students, sharing her love for the teaching and learning of science. She considers it essential to encourage today’s students to be active learners and to concentrate on STEM topics that will help prepare them for the real world.