Author: Stewart Shapiro Publisher: OUP Oxford ISBN: 0192893068 Category : Philosophy Languages : en Pages : 323
Book Description
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.
Author: Peter Liljedahl Publisher: Corwin Press ISBN: 1544374844 Category : Education Languages : en Pages : 454
Book Description
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.
Author: Jordan Ellenberg Publisher: Penguin ISBN: 0143127535 Category : Mathematics Languages : en Pages : 482
Book Description
“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Author: Stewart Shapiro Publisher: OUP USA ISBN: 0195148770 Category : Mathematics Languages : en Pages : 850
Book Description
Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.
Author: Kevin Houston Publisher: Cambridge University Press ISBN: 1139477056 Category : Mathematics Languages : en Pages : 341
Book Description
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.
Author: Keith J. Devlin Publisher: ISBN: 9780615653631 Category : Mathematics Languages : en Pages : 0
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: William Byers Publisher: Princeton University Press ISBN: 0691145997 Category : Mathematics Languages : en Pages : 424
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: Ted H. Hull Publisher: Corwin Press ISBN: 1452269408 Category : Education Languages : en Pages : 185
Book Description
"This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have!" —Therese Gessler Rodammer, Math Coach Thomas W. Dixon Elementary School, Staunton, VA Seeing is believing with this interactive approach to math instruction Do you ever wish your students could read each other′s thoughts? Now they can—and so can you! Veteran mathematics educators Ted Hull, Don Balka, and Ruth Harbin Miles explain why making students′ thought processes visible is the key to effective mathematics instruction. Their newest book contains numerous grade-specific sample problems and instructional strategies for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are: Interactive student-to-student learning Increased class participation Development of metacognitive thinking and problem-solving skills Helpful features include vignettes, relevant word problems, classroom scenarios, sample problems, lesson adaptations, and easy-to-follow examples of each strategy in action. The authors also explain how students can demonstrate their thinking using calculators and online tools. The final chapter outlines steps math leaders can take to implement visible thinking and maximize mathematics comprehension for all students.
Author: Edward B. Burger Publisher: Springer Science & Business Media ISBN: 9781931914413 Category : Mathematics Languages : en Pages : 798
Book Description
Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.
Author: Jonathan D. Katz Publisher: Rowman & Littlefield ISBN: 147581058X Category : Education Languages : en Pages : 145
Book Description
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.
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Author: Stewart Shapiro
Author: Peter Liljedahl
Author: Jordan Ellenberg
Author: Stewart Shapiro
Author: Kevin Houston
Author: Keith J. Devlin
Author: William Byers
Author: Ted H. Hull
Author: Edward B. Burger
Author: Jonathan D. Katz