Meaning in Mathematics PDF Download

Author: John Polkinghorne
Publisher: OUP Oxford
ISBN: 0191621897
Category : Mathematics
Languages : en
Pages : 176

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Book Description
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.

Author: Jeremy Kilpatrick
Publisher: Springer Science & Business Media
ISBN: 0387240403
Category : Education
Languages : en
Pages : 260

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Book Description
What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.

Author: David Pimm
Publisher: Routledge
ISBN: 1134823665
Category : Education
Languages : en
Pages : 235

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Book Description
This timely book explores the various uses and aspects of symbols in school mathematics and the notion of mathematical meaning. In addition, the author addresses a number of key issues for the 1990's eg. changes within mathematical functioning.

Author: Gabriele Lolli
Publisher: MIT Press
ISBN: 0262371049
Category : Mathematics
Languages : en
Pages : 177

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Book Description
Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

Author: Graham Flegg
Publisher: Courier Corporation
ISBN: 0486166511
Category : Mathematics
Languages : en
Pages : 304

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Book Description
Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

Author: John Polkinghorne
Publisher: Oxford University Press
ISBN: 019960505X
Category : Mathematics
Languages : en
Pages : 172

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Book Description
Is mathematics invented or discovered? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? Famous mathematicians, mathematical physicists and philosophers of mathematics try to answer these questions in a series of accessible chapters that shed light on what mathematics really means.

Author: Matematicheskiĭ institut im. V.A. Steklova
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 384

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Book Description

Author: Ernest Davis
Publisher: Springer
ISBN: 331921473X
Category : Mathematics
Languages : en
Pages : 379

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Book Description
The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume: Jeremy Avigad Jody Azzouni David H. Bailey David Berlinski Jonathan M. Borwein Ernest Davis Philip J. Davis Donald Gillies Jeremy Gray Jesper Lützen Ursula Martin Kay O’Halloran Alison Pease Steven Piantadosi Lance Rips Micah T. Ross Nathalie Sinclair John Stillwell Hellen Verran

Author: James Heath
Publisher: Createspace Independent Publishing Platform
ISBN: 9781974214891
Category : Mathematical ability
Languages : en
Pages : 104

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Book Description
The Meaning of Math is a book intended to help teachers, parents, tutors, etc. teach basic math concepts to beginning students. Nearly 50 years ago the United States decided to abandon the teaching of conceptual math in favor of what was then called the "New Math". As a result, the math skills of our students have continually dropped until we are now among the most poorly educated mathematicians in the industrialized world. Recently, there has been a growing movement to return to teaching conceptual math. This book is just a beginning. It explains basic math concepts in simple, easy to understand language with examples drawn for everyday life. The hope is that students, and perhaps their teachers, will come to understand that math is a natural function of the human mind and that it can actually be fun to use. One of the more difficult subjects to teach is negative numbers. A great deal of time has been invested in creating a chapter about negative numbers using a more visual approach to the subject. The purpose is to help make the subject easier to relate to everyday experiences and, hopefully, easier to teach and learn. A good, solid understanding of the fundamental math concepts makes learning the more advanced areas of math much easier and enjoyable.

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN: 9780195105193
Category : Juvenile Nonfiction
Languages : en
Pages : 596

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Book Description
The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid . . . easily understandable".--Albert Einstein. 301 linecuts.