Thinking About Mathematics
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Thinking About Mathematics
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Author : Stewart Shapiro
language : en
Publisher: OUP Oxford
Release Date : 2000-07-13
Thinking About Mathematics written by Stewart Shapiro and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-13 with Philosophy categories.
Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
Building Thinking Classrooms In Mathematics Grades K 12
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Author : Peter Liljedahl
language : en
Publisher: Corwin Press
Release Date : 2020-09-28
Building Thinking Classrooms In Mathematics Grades K 12 written by Peter Liljedahl and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Education categories.
A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.
How Mathematicians Think
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Author : William Byers
language : en
Publisher: Princeton University Press
Release Date : 2010-05-02
How Mathematicians Think written by William Byers and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-02 with Mathematics categories.
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.
Uncovering Student Thinking In Mathematics
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Author : Cheryl M. Rose
language : en
Publisher: Corwin Press
Release Date : 2006-12-20
Uncovering Student Thinking In Mathematics written by Cheryl M. Rose and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-20 with Education categories.
"Uncovering Student Thinking in Mathematics shows us ways to listen and observe children and their mathematical understandings so we can find better ways to help them take their next learning steps. This book is a gift to educators who ′seek to understand before being understood.′" —From the Foreword by Anne Davies "A fresh and unique resource for mathematics teachers who recognize the importance of carefully establishing the starting points of instruction in terms of what students already know. The collection of assessment probes is inventive, engaging for students, and invaluable for teachers." —Richard H. Audet, Associate Professor, Roger Williams University Use formative assessment probes to take the guesswork out of mathematics instruction and improve learning! Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student′s progress. To identify fallacies in students′ preconceived ideas, Uncovering Student Thinking in Mathematics offers educators a powerful diagnostic technique in the form of field-tested assessment probes—brief, easily administered activities to determine students′ thinking on core mathematical concepts. Designed to question students′ conceptual knowledge and reveal common understandings and misunderstandings, the probes generate targeted information for modifying mathematics instruction, allowing teachers to build on students′ existing knowledge and individually address their identified difficulties. Linked to National Council of Teachers of Mathematics standards, this invaluable handbook assists educators with: 25 ready-to-use mathematical probes Teacher guides for implementing each probe at any grade level Examples of typical obstacles and faulty thinking demonstrated by students This rich resource combines standards, educational research findings, and practical craft knowledge to help teachers deliver informed instruction that strengthens all students′ learning and achievement in mathematics.
Introduction To Mathematical Thinking
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Author : Keith J. Devlin
language : en
Publisher:
Release Date : 2012
Introduction To Mathematical Thinking written by Keith J. Devlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
"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.
How To Think Like A Mathematician
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Author : Kevin Houston
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-12
How To Think Like A Mathematician written by Kevin Houston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-12 with Mathematics categories.
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
Thinking In Numbers
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Author : Daniel Tammet
language : en
Publisher: Hachette UK
Release Date : 2013-07-30
Thinking In Numbers written by Daniel Tammet and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-30 with Mathematics categories.
The irresistibly engaging book that "enlarges one's wonder at Tammet's mind and his all-embracing vision of the world as grounded in numbers" (Oliver Sacks, MD). Thinking in Numbers is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired variously by the complexity of snowflakes, Anne Boleyn's eleven fingers, and his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. His provocative and inspiring new book will change the way you think about math and fire your imagination to view the world with fresh eyes.
Developing Mathematical Thinking
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Author : Jonathan D. Katz
language : en
Publisher: Bloomsbury Publishing PLC
Release Date : 2014-07-07
Developing Mathematical Thinking written by Jonathan D. Katz and has been published by Bloomsbury Publishing PLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-07 with Education categories.
In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.
The Oxford Handbook Of Philosophy Of Mathematics And Logic
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 2005-02-10
The Oxford Handbook Of Philosophy Of Mathematics And Logic written by Stewart Shapiro and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-10 with Mathematics categories.
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
Ways To Think About Mathematics
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Author : Steve Benson
language : en
Publisher: Corwin Press
Release Date : 2005
Ways To Think About Mathematics written by Steve Benson and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Education categories.
Funded by the National Science Foundation and successfully field-tested in a variety of settings, the materials presented give teachers the opportunity to grow as learners for the classes they teach.