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Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving

Author : George Pólya

Publisher :

Page : 236 pages

File Size : 50,80 MB

Release : 2009

Category : Mathematics

ISBN : 9784871878319

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Book Description

George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.



Proofs and Refutations

Author : Imre Lakatos

Publisher : Cambridge University Press

Page : 190 pages

File Size : 28,95 MB

Release : 1976

Category : Mathematics

ISBN : 9780521290388

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Book Description

Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.



Experimentation in Mathematics

Author : Jonathan M. Borwein

Publisher : CRC Press

Page : 372 pages

File Size : 48,49 MB

Release : 2004-04-12

Category : Mathematics

ISBN : 1439864195

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Book Description

New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of



The Young Child and Mathematics, Third Edition

Author : Angela Chan Turrou

Publisher :

Page : 128 pages

File Size : 17,85 MB

Release : 2021-10

Category : Education

ISBN : 9781938113932

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Book Description

Tap into the Power of Child-Led Math Teaching and Learning Everything a child does has mathematical value--these words are at the heart of this completely revised and updated third edition of The Young Child and Mathematics. Grounded in current research, this classic book focuses on how teachers working with children ages 3 to 6 can find and build on the math inherent in children's ideas in ways that are playful and intentional. This resource - Illustrates through detailed vignettes how math concepts can be explored in planned learning experiences as well as informal spaces - Highlights in-the-moment instructional decision-making and child-teacher interactions that meaningfully and dynamically support children in making math connections - Provides an overview of what children know about counting and operations, spatial relations, measurement and data, and patterns and algebra - Offers examples of informal documentation and assessment approaches that are embedded within classroom practice Deepen your understanding of how math is an integral part of your classroom all day, every day. Includes online video!



Learning and Teaching Early Math

Author : Douglas H. Clements

Publisher : Routledge

Page : 741 pages

File Size : 41,2 MB

Release : 2014-05-23

Category : Education

ISBN : 1134080786

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Book Description

In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child’s level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying levels of knowledge exhibited by individual students, which in turn allows them to better meet the learning needs of all children. Using straightforward, no-nonsense language, this book summarizes the current research about how children learn mathematics, and how to build on what children already know to realize more effective teaching. This second edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become quintessential professionals. Updates to the new edition include: • Explicit connections between Learning Trajectories and the new Common Core State Standards. • New coverage of patterns and patterning. • Incorporation of hundreds of recent research studies.



The Math Book

Author : DK

Publisher : Penguin

Page : 711 pages

File Size : 22,37 MB

Release : 2019-09-03

Category : Mathematics

ISBN : 1465494200

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Book Description

See how math's infinite mysteries and beauty unfold in this captivating educational book! Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised with this beautifully illustrated book. Get to know the great minds whose revolutionary discoveries changed our world today. You don't have to be a math genius to follow along with this book! This brilliant book is packed with short, easy-to-grasp explanations, step-by-step diagrams, and witty illustrations that play with our ideas about numbers. What is an imaginary number? Can two parallel lines ever meet? How can math help us predict the future? All will be revealed and explained in this encyclopedia of mathematics. It's as easy as 1-2-3! The Math Book tells the exciting story of how mathematical thought advanced through history. This diverse and inclusive account will have something for everybody, including the math behind world economies and espionage. This book charts the development of math around the world, from ancient mathematical ideas and inventions like prehistoric tally bones through developments in medieval and Renaissance Europe. Fast forward to today and gain insight into the recent rise of game and group theory. Delve in deeper into the history of math: - Ancient and Classical Periods 6000 BCE - 500 CE - The Middle Ages 500 - 1500 - The Renaissance 1500 - 1680 - The Enlightenment 1680 - 1800 - The 19th Century 1800 - 1900 - Modern Mathematics 1900 - Present The Series Simply Explained With over 7 million copies sold worldwide to date, The Math Book is part of the award-winning Big Ideas Simply Explained series from DK Books. It uses innovative graphics along with engaging writing to make complex subjects easier to understand.



Early Investigations of Ceres and the Discovery of Pallas

Author : Clifford Cunningham

Publisher : Springer

Page : 426 pages

File Size : 33,48 MB

Release : 2016-08-22

Category : Science

ISBN : 3319288156

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Book Description

An asteroid scholar, Cunningham in this book picks up where his Discovery of the First Asteroid, Ceres left off in telling the story of the impact created by the discovery of this new class of object in the early 1800s. The best and brightest minds of mathematics, science, and philosophy were fascinated by Ceres, and figures as diverse as Gauss, Herschel, Brougham, Kant, and Laplace all contributed something to the conversation. The first few chapters deal with the mathematical and philosophical aspects of the discovery, and the rivalry between Germany and France that so affected science and astronomy of that era. The jockeying for glory over the discovery of Ceres by both Piazzi and Bode is examined in detail, as is the reception given to Herschel’s use of the word 'asteroid.' Archival research that reveals the creator of the word 'asteroid' is presented in this book. Astronomy was a truly cosmopolitan field at the time, spanning across various disciplines, and the discovery of Pallas, a story completely told in these pages, exemplifies the excitement and drama of early 1800s astronomy. All the private correspondence about the study of Ceres and Pallas in 1802 is given here, which helps to contextualize and personalize the discovery.



Finding Zero

Author : Amir D. Aczel

Publisher : Macmillan

Page : 258 pages

File Size : 14,95 MB

Release : 2015-01-06

Category : Mathematics

ISBN : 1137279842

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Book Description

The invention of numbers is perhaps the greatest achievement of the human mind-- virtually everything in our lives is digital, numerical, quantified. However, the origins of these numbers has until now been unknown. Amir Aczel crisscrosses the world, scouring dusty, moldy texts, cross-examining self-proclaimed experts with wildly differing theories, to discover where the so-called Hindu-Arabic numerals come from. It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero-- the keystone of our entire system of numbers-- on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves-- who finally reveal where our numbers come from. Aczel takes the reader on a fascinating ride-- Front book jacket flap.



The Collected Works of John Dewey

Author : John Dewey

Publisher : Good Press

Page : 2308 pages

File Size : 28,69 MB

Release : 2023-12-04

Category : Philosophy

ISBN :

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Book Description

In 'The Collected Works of John Dewey', the reader is presented with a comprehensive collection of the philosophical writings of the influential American thinker. Known for his pragmatic approach to philosophy, Dewey's works explore themes of education, democracy, and the nature of experience. His writing style is clear and accessible, making complex ideas understandable to a wide audience. Dewey's work is situated within the context of the Progressive Era in American history, a time of social and political reform, which influenced his ideas on social change and the role of the individual in society. This collection showcases the evolution of Dewey's thought over his long and illustrious career, making it an essential read for anyone interested in the development of American philosophy. The depth and breadth of Dewey's writings offer valuable insights into the challenges and possibilities of the modern world, making 'The Collected Works of John Dewey' a must-read for scholars and students of philosophy alike.



JOHN DEWEY Premium Collection – 40+ Books in One Single Volume: Works on Psychology, Education, Philosophy & Politics

Author : John Dewey

Publisher : Good Press

Page : 2307 pages

File Size : 32,74 MB

Release : 2024-01-12

Category : Education

ISBN :

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Book Description

John Dewey's 'Premium Collection' is a comprehensive compilation of over 40 of his most influential works in one single volume, covering a wide range of subjects including psychology, education, philosophy, and politics. Known for his pragmatic approach to philosophy, Dewey's writings in this collection are characterized by their clarity, logic, and relevance to contemporary issues. His exploration of the relationship between individual experience and societal progress is highlighted throughout the diverse range of topics covered in this profound collection. By delving into the complexities of human thought and behavior, Dewey provides readers with a deeper understanding of the underlying principles that shape our world. It is a must-read for anyone interested in the intersection of philosophy, psychology, education, and politics. John Dewey, a renowned American philosopher, psychologist, and educational reformer, draws on his extensive knowledge and experience to offer readers a thought-provoking and insightful collection that continues to resonate with modern audiences. Dewey's innovative ideas and forward-thinking philosophies continue to influence scholarly discussions in various fields, making this collection a valuable resource for academics, students, and anyone seeking intellectual stimulation and enlightenment.