Posamentier Alfred S's Books

The Circle

A Mathematical Exploration beyond the Line

By: Alfred S. Posamentier,Robert Geretschläger

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The Circle

A Mathematical Exploration beyond the Line

By: Alfred S. Posamentier,Robert Geretschläger

The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson’s terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry—leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves – many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle’s place on the sphere bring "full circle" this presentation of a key element of geometry.

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352

Publisher

Prometheus Books

Published Date

ISBN 10

1633881687

ISBN 13

9781633881686

Mathematics Entertainment for the Millions

By: Alfred S. Posamentier

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Mathematics Entertainment for the Millions

By: Alfred S. Posamentier

About the author -- Introduction -- Arithmetic entertainments -- The fun of logical reasoning -- Geometric surprises -- A potpourri of mathematical entertainments -- Final thoughts.

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100

Published Date

ISBN 10

981121929X

ISBN 13

9789811219290

Math Charmers

Tantalizing Tidbits for the Mind

By: Alfred S. Posamentier

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Math Charmers

Tantalizing Tidbits for the Mind

By: Alfred S. Posamentier

Readers are invited to have fun with math in this reader-friendly volume--theideal book for adults looking for a way to turn their kids on to an importantsubject. Illustrations throughout.

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301

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Prometheus Books

Published Date

ISBN 10

1615921729

ISBN 13

9781615921720

Making Pre-Algebra Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

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Making Pre-Algebra Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in pre-algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for curriculum goals and classroom management. Each activity is connected to the Principles and Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM). This link to the NCTM 2000 standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. The activities are meant to be motivational first and foremost. As much as possible, the goal is to be attractive to people who thought they didn't like mathematics. To accomplish this, it is necessary for the activities to be quite different from what students encounter in their basal texts, different in both substance and form. Activities on number theory and arithmetic operations, geometry and topology, binary and exponential arithmetic, problem solving, and recreational mathematics are included. (ASK)

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164

Publisher

Corwin Press

Published Date

ISBN 10

0761975950

ISBN 13

9780761975953

The Pythagorean Theorem

The Story of Its Power and Beauty

By: Alfred S. Posamentier

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The Pythagorean Theorem

The Story of Its Power and Beauty

By: Alfred S. Posamentier

The Pythagorean theorem may be the best-known equation in mathematics. Its origins reach back to the beginnings of civilization, and today every student continues to study it. What most nonmathematicians don''t understand or appreciate is why this simply stated theorem has fascinated countless generations. In this entertaining and informative book, a veteran math educator makes the importance of the Pythagorean theorem delightfully clear.He begins with a brief history of Pythagoras and the early use of his theorem by the ancient Egyptians, Babylonians, Indians, and Chinese, who used it intuitively long before Pythagoras''s name was attached to it. He then shows the many ingenious ways in which the theorem has been proved visually using highly imaginative diagrams. Some of these go back to ancient mathematicians; others are comparatively recent proofs, including one by the twentieth president of the United States, James A. Garfield. After demonstrating some curious applications of the theorem, the author then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of the right triangle (e.g, 3, 4, 5 and 5, 12, 13). And many will truly amaze the reader. He then turns to the "Pythagorean means" (the arithmetic, geometric, and harmonic means). By comparing their magnitudes in a variety of ways, he gives the reader a true appreciation for these mathematical concepts. The final two chapters view the Pythagorean theorem from an artistic point of view - namely, how Pythagoras''s work manifests itself in music and how the Pythagorean theorem can influence fractals. The author''s lucid presentation and gift for conveying the significance of this key equation to those with little math background will inform, entertain, and inspire the reader, once again demonstrating the power and beauty of mathematics!

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320

Publisher

Prometheus Books

Published Date

ISBN 10

1616143215

ISBN 13

9781616143213

Pi

A Biography of the World's Most Mysterious Number

By: Alfred S. Posamentier,Ingmar Lehmann

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Pi

A Biography of the World's Most Mysterious Number

By: Alfred S. Posamentier,Ingmar Lehmann

The authors review Pi's history from prebiblical times to the twenty-first century and the many amusing and often mind-boggling attempts to estimate its precise value ...

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373

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Prometheus Books

Published Date

ISBN 10

1615920811

ISBN 13

9781615920815

Problem Solving in Mathematics, Grades 3-6

Powerful Strategies to Deepen Understanding

By: Alfred S. Posamentier,Stephen Krulik

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Problem Solving in Mathematics, Grades 3-6

Powerful Strategies to Deepen Understanding

By: Alfred S. Posamentier,Stephen Krulik

Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level." —Janice L. Richardson, Associate Professor and Education Coordinator, Department of Mathematics Elon University Help students succeed as problem solvers in and out of the classroom! Problem solving skills are critical to students′ success in mathematics, but the techniques can′t be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process. Problem Solving in Mathematics, Grades 3–6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can: Apply the strategies to problems at different grade levels Incorporate these strategies into a mathematics program Understand how each strategy can be applied to real-life situations Make each strategy an integral part of students′ thinking processes With helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!

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153

Publisher

Corwin Press

Published Date

ISBN 10

1452272611

ISBN 13

9781452272610

Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12

A Resource for the Mathematics Teacher

By: Alfred S. Posamentier,Stephen Krulik

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Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12

A Resource for the Mathematics Teacher

By: Alfred S. Posamentier,Stephen Krulik

The authors have provided a unique, strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving." —Howard W. Smith, Superintendent Public Schools of the Tarrytowns, Sleepy Hollow, NY "Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers." —Daniel Jaye, Principal Bergen County Academies, Hackensack, NJ Help students become skilled and confident problem solvers! Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods—including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation—make problem solving easier, neater, and more understandable for students as well as teachers. Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes: A variety of new problems that show how to use the strategies References to current NCTM standards Solutions to the problems in each chapter Extensive discussions of the empowering strategies used to solve sample problems The second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6–12 helps teachers develop students′ creative problem-solving skills for success in and out of school.

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281

Publisher

Corwin Press

Published Date

ISBN 10

1452295573

ISBN 13

9781452295572

Making Algebra Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

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Making Algebra Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

Activities in Algebra is a set of versatile enrichment exercises that covers a very broad range of mathematical topics and applications-from the Moebius strip to the googol. Several criteria have been used in developing the activities and in selecting the topics that are included. All of them bear heavily, and equally, on our concerns for curriculum goals and classroom management. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for the teacher. Each activity is keyed to the National Council of Teachers of Mathematics (NCTM) Standards, Revised. This link to the NCTM standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to people who thought they didn't like mathematics. To accomplish this, it is necessary for the activities to be quite different from what students encounter in their basal texts-different in both substance and form. This seems especially critical; no matter how excellent a basal text is being used, nearly every class experiences the "blahs." Unfortunately, this sort of boredom is often well entrenched long before the teacher and perhaps even the students are aware of it. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any subject.

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176

Publisher

Corwin Press

Published Date

ISBN 10

0761975977

ISBN 13

9780761975977

Making Geometry Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

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Making Geometry Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

Please update SAGE UK and SAGE INDIA addresses on imprint page.

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178

Publisher

Corwin Press

Published Date

ISBN 10

0761975993

ISBN 13

9780761975991

Geometric Gems: An Appreciation For Geometric Curiosities - Volume I: The Wonders Of Triangles

By: Alfred S Posamentier,Robert Geretschlager

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Geometric Gems: An Appreciation For Geometric Curiosities - Volume I: The Wonders Of Triangles

By: Alfred S Posamentier,Robert Geretschlager

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties.

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Page Count

397

Publisher

World Scientific

Published Date

ISBN 10

9811279608

ISBN 13

9789811279607

Strategy Games To Enhance Problem-solving Ability In Mathematics

By: Alfred S Posamentier,Stephen Krulik

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Strategy Games To Enhance Problem-solving Ability In Mathematics

By: Alfred S Posamentier,Stephen Krulik

Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.

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Page Count

136

Publisher

World Scientific

Published Date

ISBN 10

9813146362

ISBN 13

9789813146365

The Mathematics Coach Handbook

By: Alfred S Posamentier,Stephen Krulik

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The Mathematics Coach Handbook

By: Alfred S Posamentier,Stephen Krulik

Many schools throughout the United States are now employing coaches to support teachers in the teaching of mathematics. Very often, these are professionals selected from the current teaching ranks who did not receive any special training to serve as a coach. This book provides the skills, knowledge, and lessons from experience that lead such a mentor to function effectively. Aside from describing the basic duties of an effective math coach, we also provide a plethora of resources to enrich instruction, improve problem-solving direction, and provide teachers with a wide variety of techniques to enhance their teaching effectiveness.

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184

Publisher

World Scientific

Published Date

ISBN 10

9813271728

ISBN 13

9789813271722

Psychology Of Problem Solving, The: The Background To Successful Mathematics Thinking

By: Alfred S Posamentier,Gary Kose,Danielle Sauro Virgadamo,Kathleen Keefe-cooperman

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Psychology Of Problem Solving, The: The Background To Successful Mathematics Thinking

By: Alfred S Posamentier,Gary Kose,Danielle Sauro Virgadamo,Kathleen Keefe-cooperman

The art or skill of problem solving in mathematics is mostly relegated to the strategies one can use to solve problems in the field. Although this book addresses that issue, it delves deeply into the psychological aspects that affect successful problem-solving. Such topics as decision-making, judgment, and reasoning as well as using memory effectively and a discussion of the thought processes that could help address certain problem-solving situations.Most books that address problem-solving and mathematics focus on the various skills. This book goes beyond that and investigates the psychological aspects to solving problems in mathematics.

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Page Count

168

Publisher

World Scientific

Published Date

ISBN 10

9811205728

ISBN 13

9789811205729

Problem-solving Strategies In Mathematics: From Common Approaches To Exemplary Strategies

By: Alfred S Posamentier,Stephen Krulik

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Problem-solving Strategies In Mathematics: From Common Approaches To Exemplary Strategies

By: Alfred S Posamentier,Stephen Krulik

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

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Page Count

188

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9814651656

ISBN 13

9789814651653

Innovative Teaching: Best Practices From Business And Beyond For Mathematics Teachers

By: Denise H Sutton,Alfred S Posamentier

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Innovative Teaching: Best Practices From Business And Beyond For Mathematics Teachers

By: Denise H Sutton,Alfred S Posamentier

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.

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222

Publisher

World Scientific

Published Date

ISBN 10

9811231680

ISBN 13

9789811231681

Teaching Secondary School Mathematics: Techniques And Enrichment

By: Alfred S Posamentier,Beverly Smith

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Teaching Secondary School Mathematics: Techniques And Enrichment

By: Alfred S Posamentier,Beverly Smith

The primary aim of this book is to provide teachers of mathematics with all the tools they would need to conduct most effective mathematics instruction. The book guides teachers through the all-important planning process, which includes short and long-term planning as well as constructing most effective lessons, with an emphasis on motivation, classroom management, emphasizing problem-solving techniques, assessment, enriching instruction for students at all levels, and introducing relevant extracurricular mathematics activities. Technology applications are woven throughout the text.A unique feature of this book is the second half, which provides 125 highly motivating enrichment units for all levels of secondary school mathematics. Many years of proven success makes this book essential for both pre-service and in-service mathematics teachers.

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1042

Publisher

World Scientific

Published Date

ISBN 10

9811211434

ISBN 13

9789811211430

The Secret Lives of Numbers

Numerals and Their Peculiarities in Mathematics and Beyond

By: Alfred S. Posamentier

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The Secret Lives of Numbers

Numerals and Their Peculiarities in Mathematics and Beyond

By: Alfred S. Posamentier

We see numbers on automobile license plates, addresses, weather reports, and, of course, on our smartphones. Yet we look at these numbers for their role as descriptors, not as an entity in and unto themselves. Each number has its own history of meaning, usage, and connotation in the larger world. The Secret Lives of Numbers takes readers on a journey through integers, considering their numerological assignments as well as their significance beyond mathematics and in the realm of popular culture. Of course we all know that the number 13 carries a certain value of unluckiness with it. The phobia of the number is called Triskaidekaphobia; Franklin Delano Roosevelt was known to invite and disinvite guests to parties to avoid having 13 people in attendance; high-rise buildings often skip the 13th floor out of superstition. There are many explanations as to how the number 13 received this negative honor, but from a mathematical point of view, the number 13 is also the smallest prime number that when its digits are reversed is also a prime number. It is honored with a place among the Fibonacci numbers and integral Pythagorean triples, as well as many other interesting and lesser-known occurrences. In The Secret Lives of Numbers, popular mathematician Alfred S. Posamentier provides short and engaging mini-biographies of more than 100 numbers, starting with 1 and featuring some especially interesting numbers –like 6,174, a number with most unusual properties –to provide readers with a more comprehensive picture of the lives of numbers both mathematically and socially. ,

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Page Count

249

Publisher

Rowman & Littlefield

Published Date

ISBN 10

1633887618

ISBN 13

9781633887619

Challenging Problems in Algebra

By: Alfred S. Posamentier,Charles T. Salkind

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Challenging Problems in Algebra

By: Alfred S. Posamentier,Charles T. Salkind

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

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296

Publisher

Courier Corporation

Published Date

ISBN 10

0486131548

ISBN 13

9780486131542

What Successful Math Teachers Do, Grades PreK-5

47 Research-Based Strategies for the Standards-Based Classroom

By: Edward S. Wall,Alfred S. Posamentier

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What Successful Math Teachers Do, Grades PreK-5

47 Research-Based Strategies for the Standards-Based Classroom

By: Edward S. Wall,Alfred S. Posamentier

The book is very easy to follow, with practical, research-based strategies for the teacher to use. It also provides insight to better remediate students who are struggling." -Allen Stevens, Math/Science Teacher Mooresville Middle School, NC "The ′Precautions and Pitfalls′ section is such a welcome feature! This is a powerful book for beginning teachers or seasoned teachers who want to improve their practice to ensure student learning." -Rhonda Naylor, Math Teacher/Coordinator Campus Middle School, Englewood, CO "The research and vignettes that follow each strategy clearly support why the strategy is important and how it can be effective." -Trish Guinee, Mathematics Coordinator Peoria Public Schools, IL Facilitate learning in PreK-5 mathematics and maximize student achievement with research-based teaching strategies! This easy-to-navigate guide offers research-based teaching strategies for introducing prekindergarten and elementary school students to the content and skills recommended by the NCTM principles and standards for mathematics. Using the popular format of the What Successful Teachers Do books, the authors present 47 dynamic learning activities, each including: A concise statement of the teaching strategy Research-based validations for the strategy How the strategy aligns with NCTM standards Grade-specific classroom applications and vignettes Precautions and possible pitfalls Primary sources for further reading This insightful resource allows teachers to increase students′ confidence in math-and their enthusiasm-with practical and engaging activities, while responding effectively to NCTM standards.

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169

Publisher

Corwin Press

Published Date

ISBN 10

1483361519

ISBN 13

9781483361512

Math Charmers

Tantalizing Tidbits for the Mind

By: Alfred S. Posamentier

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Math Charmers

Tantalizing Tidbits for the Mind

By: Alfred S. Posamentier

Readers are invited to have fun with math in this reader-friendly volume--theideal book for adults looking for a way to turn their kids on to an importantsubject. Illustrations throughout.

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Page Count

301

Publisher

Prometheus Books

Published Date

ISBN 10

1615921729

ISBN 13

9781615921720

101+ Great Ideas for Introducing Key Concepts in Mathematics

A Resource for Secondary School Teachers

By: Alfred S. Posamentier,Herbert A. Hauptman

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101+ Great Ideas for Introducing Key Concepts in Mathematics

A Resource for Secondary School Teachers

By: Alfred S. Posamentier,Herbert A. Hauptman

Multiply math mastery and interest with these inspired teaching tactics! Invigorate instruction and engage students with this treasure trove of "Great Ideas" compiled by two of the greatest minds in mathematics. From commonly taught topics in algebra, geometry, trigonometry and statistics, to more advanced explorations into indirect proofs, binomial theorem, irrationality, relativity and more, this guide outlines actual equations and techniques that will inspire veteran and new educators alike. This updated second edition offers more proven practices for bringing math concepts to life in the classroom, including 114 innovative strategies organized by subject area User-friendly content identifying "objective," "materials," and "procedure" for each technique A range of teaching models, including hands-on and computer-based methods Specific and straightforward examples with step-by-step lessons Written by two distinguished leaders in the field-mathematician, author, professor, university dean and popular commentator Alfred S. Posamentier, along with mathematical pioneer and Nobel Prize recipient Herbert A. Hauptman-this guide brings a refreshing perspective to secondary math instruction to spark renewed interest and success among students and teachers.

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297

Publisher

Corwin Press

Published Date

ISBN 10

1412927064

ISBN 13

9781412927062

The Pythagorean Theorem

The Story of Its Power and Beauty

By: Alfred S. Posamentier

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The Pythagorean Theorem

The Story of Its Power and Beauty

By: Alfred S. Posamentier

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320

Publisher

Prometheus Books

Published Date

ISBN 10

1616143215

ISBN 13

9781616143213

Creative Secondary School Mathematics: 125 Enrichment Units For Grades 7 To 12

By: Alfred S Posamentier

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Creative Secondary School Mathematics: 125 Enrichment Units For Grades 7 To 12

By: Alfred S Posamentier

There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units — ranging from grades 7 through 12 — that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!

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556

Publisher

World Scientific

Published Date

ISBN 10

9811240442

ISBN 13

9789811240447

Effective Techniques to Motivate Mathematics Instruction

By: Alfred S. Posamentier,Stephen Krulik

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Effective Techniques to Motivate Mathematics Instruction

By: Alfred S. Posamentier,Stephen Krulik

Effective Techniques to Motivate Mathematics Instruction offers pre-and in-service teachers best practices and techniques that can be used to motivate students in the first few minutes of any lesson in mathematics. Veteran teacher educators Posamentier and Krulik show how a bit of creativity and planning up front pays back by enabling a successful lesson on even the most challenging mathematics topic. Organized around nine different motivational techniques, each chapter includes a variety of illustrative examples of how the technique may be applied. Designed to complement any methods textbook, this practical, accessible guide helps future math teachers ease the transition from successful student to successful teacher by developing the tools needed to create motivational introductions in their classes.

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Page Count

183

Publisher

Routledge

Published Date

ISBN 10

1317248279

ISBN 13

9781317248279

The Secrets of Triangles

A Mathematical Journey

By: Alfred S. Posamentier,Ingmar Lehmann

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The Secrets of Triangles

A Mathematical Journey

By: Alfred S. Posamentier,Ingmar Lehmann

Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point-no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.

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300

Publisher

Prometheus Books

Published Date

ISBN 10

1616145889

ISBN 13

9781616145880

Advanced Euclidian Geometry

Excursions for Students and Teachers

By: Alfred S. Posamentier

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Advanced Euclidian Geometry

Excursions for Students and Teachers

By: Alfred S. Posamentier

Advanced Euclidean Geometry provides a thorough review of the essentials of high school geometry and then expands those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions. The text contains hundreds of illustrations created in The Geometer's Sketchpad Dynamic Geometry® software. It is packaged with a CD-ROM containing over 100 interactive sketches using SketchpadTM (assumes that the user has access to the program).

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Page Count

276

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1930190859

ISBN 13

9781930190856

Mathematics: Its Historical Aspects, Wonders And Beyond

By: Arthur D Kramer,Alfred S Posamentier

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Mathematics: Its Historical Aspects, Wonders And Beyond

By: Arthur D Kramer,Alfred S Posamentier

Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.

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Page Count

403

Publisher

World Scientific

Published Date

ISBN 10

9811248591

ISBN 13

9789811248597

Geometry, Its Elements and Structure

Second Edition

By: Alfred S. Posamentier,Robert L. Bannister

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Geometry, Its Elements and Structure

Second Edition

By: Alfred S. Posamentier,Robert L. Bannister

Geared toward high school students as well as for independent study, this text covers plane, solid, coordinate, vector, and non-Euclidean geometry. More than 2,000 illustrations. Electronic solutions manual available. 1977 edition.

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Page Count

627

Publisher

Courier Corporation

Published Date

ISBN 10

0486782166

ISBN 13

9780486782164

Pi

A Biography of the World's Most Mysterious Number

By: Alfred S. Posamentier,Ingmar Lehmann

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Pi

A Biography of the World's Most Mysterious Number

By: Alfred S. Posamentier,Ingmar Lehmann

The authors review Pi's history from prebiblical times to the twenty-first century and the many amusing and often mind-boggling attempts to estimate its precise value ...

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Page Count

373

Publisher

Prometheus Books

Published Date

ISBN 10

1615920811

ISBN 13

9781615920815

The Joy of Mathematics

Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Class

By: Alfred S. Posamentier,Robert Geretschläger,Charles Li,Christian Spreitzer

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The Joy of Mathematics

Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Class

By: Alfred S. Posamentier,Robert Geretschläger,Charles Li,Christian Spreitzer

Arithmetic novelties -- Algebraic explanations of accepted concepts -- Geometric curiosities -- Probability applied to everyday experiences -- Common sense from a mathematical perspective

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Page Count

322

Publisher

Prometheus Books

Published Date

ISBN 10

1633882977

ISBN 13

9781633882973

The Circle

A Mathematical Exploration Beyond the Line

By: Alfred S. Posamentier,Robert Geretschläger

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The Circle

A Mathematical Exploration Beyond the Line

By: Alfred S. Posamentier,Robert Geretschläger

The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson's terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry--leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves - many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle's place on the sphere bring "full circle" this presentation of a key element of geometry.

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Page Count

352

Publisher

Prometheus Books

Published Date

ISBN 10

1633881679

ISBN 13

9781633881679

100 Commonly Asked Questions in Math Class

Answers That Promote Mathematical Understanding, Grades 6-12

By: Alfred S. Posamentier,William Farber,Terri L. Germain-Williams,Elaine Paris,Bernd Thaller,Ingmar Lehmann

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100 Commonly Asked Questions in Math Class

Answers That Promote Mathematical Understanding, Grades 6-12

By: Alfred S. Posamentier,William Farber,Terri L. Germain-Williams,Elaine Paris,Bernd Thaller,Ingmar Lehmann

100 ways to get students hooked on math! That one question got you stumped? Or maybe you have the answer, but it’s not all that compelling. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students’100 most frequently asked math questions. Even if you already have the answers, Al’s explanations are certain to keep kids hooked. The big benefits? You’ll discover high-interest ways to Teach to the Common Core’s math content standards Promote inquiry and process in mathematical thinking Build procedural skills and conceptual understanding Encourage flexibility in problem solving Emphasize efficient test-taking strategies

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Page Count

233

Publisher

Corwin Press

Published Date

ISBN 10

1483332837

ISBN 13

9781483332833

Challenging Problems in Geometry

By: Alfred S. Posamentier,Charles T. Salkind

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Challenging Problems in Geometry

By: Alfred S. Posamentier,Charles T. Salkind

Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.

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Page Count

275

Publisher

Courier Corporation

Published Date

ISBN 10

0486134865

ISBN 13

9780486134864

Magnificent Mistakes in Mathematics

By: Alfred S. Posamentier,Ingmar Lehmann

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Magnificent Mistakes in Mathematics

By: Alfred S. Posamentier,Ingmar Lehmann

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

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Page Count

298

Publisher

Prometheus Books

Published Date

ISBN 10

1616147482

ISBN 13

9781616147488

Mathematical Curiosities

A Treasure Trove of Unexpected Entertainments

By: Alfred S. Posamentier,Ingmar Lehmann

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Mathematical Curiosities

A Treasure Trove of Unexpected Entertainments

By: Alfred S. Posamentier,Ingmar Lehmann

An innovative and appealing way for the layperson to develop math skills--while actually enjoying it Most people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun! As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill. The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum. The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions. If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.

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Page Count

384

Publisher

Prometheus Books

Published Date

ISBN 10

1616149329

ISBN 13

9781616149321

The Fabulous Fibonacci Numbers

By: Alfred S. Posamentier,Ingmar Lehmann

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The Fabulous Fibonacci Numbers

By: Alfred S. Posamentier,Ingmar Lehmann

The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few. Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

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Page Count

385

Publisher

Prometheus Books

Published Date

ISBN 10

1615920226

ISBN 13

9781615920228

Making Pre-Algebra Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

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Making Pre-Algebra Come Alive

Student Activities and Teacher Notes

By: Alfred S. Posamentier

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Page Count

164

Publisher

Corwin Press

Published Date

ISBN 10

0761975950

ISBN 13

9780761975953

Mathematical Amazements and Surprises

Fascinating Figures and Noteworthy Numbers

By: Alfred S. Posamentier,Ingmar Lehmann

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Mathematical Amazements and Surprises

Fascinating Figures and Noteworthy Numbers

By: Alfred S. Posamentier,Ingmar Lehmann

With many entertaining examples of mathematical curiosities, educators Posamentier and Lehmann have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject.

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Page Count

269

Publisher

Prometheus Books

Published Date

ISBN 10

1615922946

ISBN 13

9781615922949

Mathematics Entertainment For The Millions

By: Alfred S Posamentier

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Mathematics Entertainment For The Millions

By: Alfred S Posamentier

The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers.'CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics — to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics — something most general readers will not initially find possible, but we hope will be an end product of this book.

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Page Count

304

Publisher

World Scientific

Published Date

ISBN 10

9811219303

ISBN 13

9789811219306

Book's by Posamentier Alfred S

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