Essentials Of Mathematical Thinking

Author : Steven G. Krantz
Publisher : CRC Press
Page : 323 pages
File Size : 49,8 Mb
Release : 2017-10-06
Category : Mathematics
ISBN : 9781351642941

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Essentials of Mathematical Thinking by Steven G. Krantz Pdf

Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies. The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world. The book explains: What goes behind a Google search algorithm How to calculate the odds in a lottery The value of Big Data How the nefarious Ponzi scheme operates Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.

Author : John K. Lannin,Amy B. Ellis,Rebekah Elliott
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 54,7 Mb
Release : 2011
Category : Effective teaching
ISBN : 0873536665

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Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8 by John K. Lannin,Amy B. Ellis,Rebekah Elliott Pdf

How do your students determine whether a mathematical statement is true? Do they rely on a teacher, a textbook or various examples? How can you encourage them to connect examples, extend their ideas to new situations that they have not yet considered and reason more generally? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of mathematical reasoning requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about mathematical reasoning. It is organised around one big idea, supported by multiple smaller, interconnected ideas - essential understandings.Taking you beyond a simple introduction to mathematical reasoning, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Author : Keith J. Devlin
Publisher : Unknown
Page : 0 pages
File Size : 54,8 Mb
Release : 2012
Category : Mathematics
ISBN : 0615653634

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Introduction to Mathematical Thinking by Keith J. Devlin Pdf

"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 : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 48,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821813980

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How to Teach Mathematics, Second Edition by Steven George Krantz Pdf

This expanded edition of the original bestseller, How to Teach Mathematics, offers hands-on guidance for teaching mathematics in the modern classroom setting. Twelve appendices have been added that are written by experts who have a wide range of opinions and viewpoints on the major teaching issues. Eschewing generalities, the award-winning author and teacher, Steven Krantz, addresses issues such as preparation, presentation, discipline, and grading. He also emphasizes specifics--from how to deal with students who beg for extra points on an exam to mastering blackboard technique to how to use applications effectively. No other contemporary book addresses the principles of good teaching in such a comprehensive and cogent manner. The broad appeal of this text makes it accessible to areas other than mathematics. The principles presented can apply to a variety of disciplines--from music to English to business. Lively and humorous, yet serious and sensible, this volume offers readers incisive information and practical applications.

Author : John P. D'Angelo,Douglas Brent West
Publisher : Unknown
Page : 0 pages
File Size : 49,8 Mb
Release : 2018
Category : Mathematics
ISBN : 0134689577

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Mathematical Thinking by John P. D'Angelo,Douglas Brent West Pdf

For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.

Author : David Tall
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 45,9 Mb
Release : 2006-04-11
Category : Education
ISBN : 9780306472039

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Advanced Mathematical Thinking by David Tall Pdf

This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.

Author : Grace Kelemanik,Amy Lucenta
Publisher : Unknown
Page : 184 pages
File Size : 52,5 Mb
Release : 2022-01-24
Category : Electronic
ISBN : 0325120072

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Teaching for Thinking by Grace Kelemanik,Amy Lucenta Pdf

Teaching our children to think and reason mathematically is a challenge, not because students can't learn to think mathematically, but because we must change our own often deeply-rooted teaching habits. This is where instructional routines come in. Their predictable design and repeatable nature support both teachers and students to develop new habits. In Teaching for Thinking, Grace Kelemanik and Amy Lucenta pick up where their first book, Routines for Reasoning, left off. They draw on their years of experience in the classroom and as instructional coaches to examine how educators can make use of routines to make three fundamental shifts in teaching practice: Focus on thinking: Shift attention away from students' answers and toward their thinking and reasoning Step out of the middle: Shift the balance from teacher-student interactions toward student-student interactions Support productive struggle: Help students do the hard thinking work that leads to real learning With three complete new routines, support for designing your own routine, and ideas for using routines in your professional learning as well as in your classroom teaching, Teaching for Thinking will help you build new teaching habits that will support all your students to become and see themselves as capable mathematicians.

Author : Margie Pearse,K. M. Walton
Publisher : Corwin Press
Page : 241 pages
File Size : 50,8 Mb
Release : 2011-03-23
Category : Education
ISBN : 9781452224404

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Teaching Numeracy by Margie Pearse,K. M. Walton Pdf

Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.

Author : Friedrich Waismann
Publisher : Courier Corporation
Page : 272 pages
File Size : 52,9 Mb
Release : 2012-08-07
Category : Mathematics
ISBN : 9780486167428

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Introduction to Mathematical Thinking by Friedrich Waismann Pdf

Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.

Author : David Hunter
Publisher : Jones & Bartlett Publishers
Page : 510 pages
File Size : 53,8 Mb
Release : 2010-12-29
Category : Computers
ISBN : 9781449604424

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Essentials of Discrete Mathematics by David Hunter Pdf

This is the ideal text for a one-term discrete mathematics course to serve computer scientists as well as other students. It introduces students to the mathematical way of thinking, and also to many important modern applications.

Author : James T. Kinard,Alex Kozulin
Publisher : Cambridge University Press
Page : 210 pages
File Size : 49,9 Mb
Release : 2008-06-02
Category : Psychology
ISBN : 9781139472395

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Rigorous Mathematical Thinking by James T. Kinard,Alex Kozulin Pdf

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Author : Herbert Ginsburg
Publisher : Unknown
Page : 414 pages
File Size : 49,9 Mb
Release : 1983
Category : Mathematics
ISBN : UOM:39015004171875

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The Development of Mathematical Thinking by Herbert Ginsburg Pdf

Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 366 pages
File Size : 48,7 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521597188

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An Introduction to Mathematical Reasoning by Peter J. Eccles Pdf

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Author : William Byers
Publisher : Princeton University Press
Page : 424 pages
File Size : 46,9 Mb
Release : 2010-05-02
Category : Mathematics
ISBN : 9780691145990

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How Mathematicians Think by William Byers Pdf

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 : John P. D'Angelo,Douglas Brent West
Publisher : Unknown
Page : 412 pages
File Size : 45,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0132449021

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Mathematical Thinking by John P. D'Angelo,Douglas Brent West Pdf

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity.