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Author: David Tall
Publisher: Cambridge University Press
ISBN: 1107035708
Category : Education
Languages : en
Pages : 483
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Book Description
How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
Author: David Tall
Publisher: Cambridge University Press
ISBN: 1107035708
Category : Education
Languages : en
Pages : 483
Get Book Here
Book Description
How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
Author: Francis Su
Publisher: Yale University Press
ISBN: 0300248814
Category : Mathematics
Languages : en
Pages : 287
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Book Description
Winner of the Mathematics Association of America's 2021 Euler Book Prize, this is an inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish“This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math Project"A good book is an entertaining read. A great book holds up a mirror that allows us to more clearly see ourselves and the world we live in. Francis Su’s Mathematics for Human Flourishing is both a good book and a great book."—MAA Reviews For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity’s most beautiful ideas.In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award‑winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires—such as for play, beauty, freedom, justice, and love—and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother’s, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher’s letters to the author appear throughout the book and show how this intellectual pursuit can—and must—be open to all.
Author: Keith J. Devlin
Publisher:
ISBN: 9780615653631
Category : Mathematics
Languages : en
Pages : 0
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Book Description
"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
Author: ALAN H. SCHOENFELD
Publisher: Elsevier
ISBN: 1483295486
Category : Mathematics
Languages : en
Pages : 426
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Book Description
This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.
Author: Marcelo C. Borba
Publisher: Springer Science & Business Media
ISBN: 0387242643
Category : Education
Languages : en
Pages : 239
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Book Description
This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge is not constructed solely by humans, but by collectives of humans and technologies of intelligence.
Author: Bharath Sriraman
Publisher: Birkhäuser
ISBN: 331961231X
Category : Mathematics
Languages : en
Pages : 357
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Book Description
This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
Author: William Byers
Publisher: Princeton University Press
ISBN: 0691145997
Category : Mathematics
Languages : en
Pages : 424
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Book Description
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Author: Max Tegmark
Publisher: Vintage
ISBN: 0307744256
Category : Science
Languages : en
Pages : 434
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Book Description
Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Author: Barbara Oakley, PhD
Publisher: Penguin
ISBN: 052550446X
Category : Juvenile Nonfiction
Languages : en
Pages : 258
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Book Description
A surprisingly simple way for students to master any subject--based on one of the world's most popular online courses and the bestselling book A Mind for Numbers A Mind for Numbers and its wildly popular online companion course "Learning How to Learn" have empowered more than two million learners of all ages from around the world to master subjects that they once struggled with. Fans often wish they'd discovered these learning strategies earlier and ask how they can help their kids master these skills as well. Now in this new book for kids and teens, the authors reveal how to make the most of time spent studying. We all have the tools to learn what might not seem to come naturally to us at first--the secret is to understand how the brain works so we can unlock its power. This book explains: Why sometimes letting your mind wander is an important part of the learning process How to avoid "rut think" in order to think outside the box Why having a poor memory can be a good thing The value of metaphors in developing understanding A simple, yet powerful, way to stop procrastinating Filled with illustrations, application questions, and exercises, this book makes learning easy and fun.
Author: Alan Jacobs
Publisher: Crown Currency
ISBN: 0451499603
Category : Psychology
Languages : en
Pages : 162
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Book Description
"Absolutely splendid . . . essential for understanding why there is so much bad thinking in political life right now." —David Brooks, New York Times How to Think is a contrarian treatise on why we’re not as good at thinking as we assume—but how recovering this lost art can rescue our inner lives from the chaos of modern life. As a celebrated cultural critic and a writer for national publications like The Atlantic and Harper’s, Alan Jacobs has spent his adult life belonging to communities that often clash in America’s culture wars. And in his years of confronting the big issues that divide us—political, social, religious—Jacobs has learned that many of our fiercest disputes occur not because we’re doomed to be divided, but because the people involved simply aren’t thinking. Most of us don’t want to think. Thinking is trouble. Thinking can force us out of familiar, comforting habits, and it can complicate our relationships with like-minded friends. Finally, thinking is slow, and that’s a problem when our habits of consuming information (mostly online) leave us lost in the spin cycle of social media, partisan bickering, and confirmation bias. In this smart, endlessly entertaining book, Jacobs diagnoses the many forces that act on us to prevent thinking—forces that have only worsened in the age of Twitter, “alternative facts,” and information overload—and he also dispels the many myths we hold about what it means to think well. (For example: It’s impossible to “think for yourself.”) Drawing on sources as far-flung as novelist Marilynne Robinson, basketball legend Wilt Chamberlain, British philosopher John Stuart Mill, and Christian theologian C.S. Lewis, Jacobs digs into the nuts and bolts of the cognitive process, offering hope that each of us can reclaim our mental lives from the impediments that plague us all. Because if we can learn to think together, maybe we can learn to live together, too.
