Alfred S. Posamentier

"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"--

Magnificent mistakes in mathematics

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.

A Treasure Trove of Unexpected Entertainments

Mathematical Curiosities

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.

Challenging Problems in Geometry

Edward S. Wall

The authors present dynamic learning activities with research-based strategies and sources for further reading to increase students' confidence in math while effectively addressing NCTM standards.

47 Research-Based Strategies for the Standards-Based Classroom

What Successful Math Teachers Do, Grades PreK-5

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.

A Mathematical Journey

The Secrets of Triangles

The Fabulous Fibonacci Numbers

Stimulating collection of unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and many other topics. Challenges are arranged in order of difficulty and detailed solutions are included for all. An invaluable supplement to a basic geometry textbook.

A Biography of the World's Most Mysterious Number

Stimulating collection of over 300 unusual problems involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms and more. Problems range from easy to difficult. Detailed solutions, as well as brief answers, for all problems are provided.

Challenging Problems in Algebra

Herbert A. Hauptman

Tantalizing Tidbits for the Mind

Math Charmers

the story of its power and beauty

The Pythagorean theorem

The Glorious Golden Ratio

PI-this seemingly mundane numer-holds a world of mystery, which has fascinated mathematicians from ancient times to the present. What is PI? What is the real value of PI? How to mathematicians determine the value of PI? In what ways is PI used? How was it calculated in ancient times? Its elusive nature has led investigators over the years to ever-closer approximations.

: A Biography Of The World's Most Mysterious Number

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)

Student Activities and Teacher Notes

Making Pre-Algebra Come Alive

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.

A Resource for Secondary School Teachers

101+ Great Ideas for Introducing Key Concepts in Mathematics

Beverly S. Smith

Jay Stepelman

For courses in Secondary Mathematics Methods. Teaching Secondary Mathematics: Techniques and Enrichment Units, 7th edition has been thoroughly revised to discuss current methods of teaching mathematics, considering all aspects and responsibilities of the job, beginning with a brief overview of the history of mathematics education and how it has evolved over time to include standards for teaching and assessment. The authors address how to craft rich and effective daily lesson plans, and how to use a variety of instructional tools and strategies to reach all students in a classroom. Problem solving is a key focus from its instructional underpinnings to its recreational and motivational aspects. The second part of the text provides mathematics teachers with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum.

Techniques and Enrichment Units

Teaching Secondary Mathematics

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.

Afterword by Dr. Herbert A. Hauptman, Nobel LaureateThis delightful book reveals an incredibly interesting history of the development of our knowledge of this ubiquitous number in mathematics. . . . I recommend this book to anyone who remembers ever hearing about Pi!-Stanley H. Kaplan, Founder of the Kaplan Test Preparation and Admission Programs. . . Read this book and enjoy the journey through the mysteries of pi. Give it to your students and you will have aroused their appreciation of the many wonders of mathematics.-Alice F. Artzt, Professor of Mathematics Education; Director of Undergraduate and Graduate Secondary Mathematics Education, Queens College of the City University of New York. . . The history of pi and the attempts to fully understand what it represents makes for amusing, interesting and enjoyable reading.-Dr. Stephen Krulik, Professor of Mathematics Education, Temple UniversityWe all learned that the ratio of the circumference of a circle to its diameter is called p and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present.Mathematicians call it a transcendental number because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction. This elusive nature has led intrepid investigators over the years to attempt ever-closer approximations. In 2002, a Japanese professor using a supercomputer calculated the value to 1.24 trillion decimal places! Nonetheless, in this huge string of decimals there is no periodic repetition.In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review p's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating ? over the centuries, quirky examples of obsessing about p (including an attempt to legislate its exact value), and useful applications of p in everyday life, including statistics.This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.Alfred S. Posamentier, Ph.D. (New York, NY), is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published more than 40 books in the area of mathematics and mathematics education, including The Fabulous Fibonacci Numbers, Pi: A Biography of the World's Most Mysterious Number, and Math Charmers: Tantalizing Tidbits for the Mind..Ingmar Lehmann, Ph.D. (Berlin, Germany), is a mathematics educator at Humboldt University in Berlin and is the coauthor of The Fabulous Fibonacci Numbers and Pi: A Biography of the World's Most Mysterious Number.

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.

Magnificent Mistakes in Mathematics

Christian Spreitzer

An entertaining history of mathematics as chronicled through fifty short biographies. Mathematics today is the fruit of centuries of brilliant insights by men and women whose personalities and life experiences were often as extraordinary as their mathematical achievements. This entertaining history of mathematics chronicles those achievements through fifty short biographies that bring these great thinkers to life while making their contributions understandable to readers with little math background. Among the fascinating characters profiled are Isaac Newton (1642-1727), the founder of classical physics and infinitesimal calculus—he frequently quarreled with fellow scientists and was obsessed by alchemy and arcane Bible interpretation; Sophie Germain (1776 - 1831), who studied secretly at the Ecole Polytechnique in Paris, using the name of a previously enrolled male student—she is remembered for her work on Fermat's Last Theorem and on elasticity theory; Emmy Noether (1882 - 1935), whom Albert Einstein described as the most important woman in the history of mathematics—she made important contributions to abstract algebra and in physics she clarified the connection between conservation laws and symmetry; and Srinivasa Ramanujan (1887-1920), who came from humble origins in India and had almost no formal training, yet made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions.The unusual behavior and life circumstances of these and many other intriguing personalities make for fascinating reading and a highly enjoyable introduction to mathematics.

Alfred S. Posamentier

About

Books

Join the club