Teaching Secondary Mathematics: Techniques and Enrichment Units / Edition 8

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This thorough revision of Teaching Secondary Mathematics: Techniques and Enrichment Units includes the most practical, step-by-step techniques for teaching mathematics in today’s assessment and standards driven environment. Part One on methods discusses all aspects of being a math teacher, from an overview of the discipline, to challenges of teaching today, the role of problem-solving, the importance of planning, assessment strategies, teaching more effective lessons, enriching mathematics instruction, and extracurricular activities for mathematics. Part Two supplies 125 enrichment units that teachers can use right away in their own classrooms that are suitable for the entire secondary school curriculum spectrum. From methods to hands on activities, this highly successful book takes students through the whole process of what teaching mathematics in the secondary schools will be like.

New To This Edition:

NEW: Includes the latest information on changes to student assessment that have been made possible due to innovations in technology.

NEW! Features new content on data driven planning.

NEW! Completely revised technology chapter reflects the rapidly changing technology environment of today.

NEW! No chapters remain untouched!

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Product Details

  • ISBN-13: 9780135000038
  • Publisher: Pearson
  • Publication date: 1/30/2009
  • Edition description: Older Edition
  • Edition number: 8
  • Pages: 528
  • Sales rank: 1,299,787
  • Product dimensions: 8.40 (w) x 10.80 (h) x 0.80 (d)

Meet the Author

Alfred S. Posamentier is Professor of Mathematics Education and Dean of the School of Education of The City College of the City University of New York. He is the author and co-author of many mathematics books for teachers and secondary school students.

After completing his A.B. degree in mathematics at Hunter College of the City University of New York, he took a position as a teacher of mathematics at Theodore Roosevelt High School in the Bronx (New York), where he focused his attention on the teaching process in general and the improvement of students' problem-solving skills in particular. He developed the school's first mathematics teams and established a special class whose primary focus was enrichment topics in mathematics and problem solving. After six years as a high school teacher, Dr. Posamentier joined the faculty of The City College where he also received his master’s degree. He began to develop in-service courses for secondary school mathematics teachers, focusing on practical classroom applications of educational research. These courses addressed such topics as the uses of new technology in mathematics instruction, efficient ways to teach weaker students, problem-solving strategies, and the enrichment of mathematics through a variety of ways including, but not limited to, recreational mathematics.

Dr. Posamentier received his Ph.D. from Fordham University (New York) in mathematics education. He is an Honorary Fellow at the South Bank University (London, England). He has been visiting professor at the Technical University of Vienna and the Humboldt University at Berlin, and a Fulbright Professor at the University of Vienna. Dr. Posamentier is often cited for his outstanding teaching. The City College Alumni Association named him Educator of the Year (1993) and he also on May 1, 1993 had a "Day" named in his honor by the City Council President of New York City. He was awarded the Grand Medal of Honor from the Federal Republic of Austria and the Medal of Distinction from the city of Vienna. In 1999 he was awarded the title of University Professor for Austrian Universities.

Now, after more than 35 years on the faculty of CCNY, he still exudes an ever-increasing energy and enthusiasm for mathematics and mathematics education. With his penchant for mathematics instruction, he has been especially concerned that during the recent years of mathematics teacher shortages, those who enter the classroom are as well prepared as possible. He enthusiastically believes that providing mathematics teachers with an appropriate repertoire of teaching strategies enables them to fulfill an essential role in society: empowering our nation's youngsters to engage in the critical study of mathematics.

Dr. Beverly Smith Beverly Smith holds a, MA and Ed.D. in mathematics education from Teachers College — Columbia University and an M.S. degree in computer science from Union College. Prior to becoming a mathematics-teacher-educator, Dr. Smith taught mathematics and computer science at the secondary school and college level in New York State and Massachusetts. She is currently an Associate Professor in the Secondary Education Department at The City College of New York.

Dr. Smith’s research interests are in the area of teacher professional development. As part of her responsibilities as a faculty member of MetroMath: The Center for Mathematics in America’s Cities, she is studying the development of alternatively certified mathematics teachers who are participating in the New York City Teaching Fellows Program. In addition, Dr. Smith is working with mathematics teachers to better understand how technology can support formative assessment in urban mathematics classrooms.

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Table of Contents


Chapter 1 The Challenge of Teaching

Chapter 2 Planning for Instruction

Chapter 3 Teaching More Effective Lessons

Chapter 4 The Role of Problem-Solving

Chapter 5 Using Technology to Enhance Mathematics Instruction

Chapter 6 Assessment

Chapter 7 Enriching Mathematics Instruction

Chapter 8 Extracurricular Activities in Mathematics


Cross-Catalogue of Enrichment Units

Constructing Odd-Order Magic Squares

Constructing Even-Order Magic Squares

Introduction to Alphametics

A Checkerboard Calculator

The Game of Nim

The Tower of Hanoi

What Day of the Week Was It?

Palindromic Numbers

The Fascinating Number Nine

Unusual Number Properties

Enrichment with a Handheld Calculator

Symmetric Multiplication

Variations on a Theme–Multiplication

Ancient Egyptian Arithmetic

Napier's Rods

Unit Pricing

Successive Discounts and Increases

Prime and Composite Factors of a Whole Number

Prime Numeration System

Repeating Decimal Expansions

Peculiarities of Perfect Repeating Decimals

Patterns in Mathematics

Googol and Googolplex

Mathematics of Life Insurance

Geometric Dissections

The Klein Bottle

The Four-Color Map Problem

Mathematics on a Bicycle

Mathematics and Music

Mathematics in Nature

The Birthday Problem

The Structure of the Number System

Excursions in Number Bases

Raising Interest

Reflexive, Symmetric, and Transitive Relations

Bypassing an Inaccessible Region

The Inaccessible Angle

Triangle Constructions

The Criterion of Constructibility

Constructing Radical Lengths

Constructing a Pentagon

Investigating the Isosceles Triangle Fallacy

The Equiangular Point

The Minimum-Distance Point of a Triangle

The Isosceles Triangle Revisited

Reflective Properties of the Plane

Finding the Length of a Cevian of a Triangle

A Surprising Challenge

Making Discoveries in Mathematics


Introducing the Pythagorean Theorem

Trisection Revisited

Proving Lines Concurrent


Proving Points Collinear

Angle Measurement with a Circle

Trisecting a Circle

Ptolemy's Theorem

Constructing π

The Arbelos

The Nine-Point Circle

The Euler Line

The Simson Line

The Butterfly Problem


The Inscribed Circle and the Right Triangle

The Golden Rectangle

The Golden Triangle

Geometric Fallacies

Regular Polyhedra

An Introduction to Topology

Angles on a Clock

Averaging Rates–The Harmonic Mean


Digit Problems Revisited

Algebraic Identities

A Method for Factoring Trinomials of the Form: ax 2 + bx + c

Solving Quadratic Equations

The Euclidean Algorithm

Prime Numbers

Algebraic Fallacies

Sum Derivations With Arrays

Pythagorean Triples


Fibonacci Sequence

Diophantine Equations

Continued Fractions and Diophantine Equations

Simplifying Expressions Involving Infinity

Continued Fraction Expansion of Irrational Numbers

The Farey Sequence

The Parabolic Envelope

Application of Congruence to Divisibility

Problem Solving–A Reverse Strategy

Decimals and Fractions in Other Bases

Polygonal Numbers


Angle Trisection–Possible or Impossible?

Comparing Means

Pascal's Pyramid

The Multinomial Theorem

Algebraic Solution of Cubic Equations

Solving Cubic Equations

Calculating Sums of Finite Series

A General Formula for the Sum of Series of the Form ∑ tr

A Parabolic Calculator

Constructing Ellipses

Constructing the Parabola

Using Higher Plane Curves to Trisect an Angle

Constructing Hypocycloid and Epicycloid Circular Envelopes

The Harmonic Sequence

Transformations and Matrices

The Method of Differences

Probability Applied to Baseball

Introduction to Geometric Transformations

The Circle and the Cardioid

Complex-Number Applications

Hindu Arithmetic

Proving Numbers Irrational

How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems

The Three Worlds of Geometry

πie Mix

Graphical Iteration

The Feigenbaum Plot

The Sierpinski Triangle



Additional Exercises


About the Authors

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