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Abstract: --PART I METHODS OF TEACHING SECONDARY MATHEMATICS Chapter 1 The Challenge of Teaching *Today's Students, Mathematics, and Society's Need Chapter 2 Planning for Instruction *Long-Range Planning of the Curriculum *Unit Plans *Short-Range Planning *Differentiated Instruction *Cooperative Learning *Mathematical Tasks *Final Thoughts on Lesson Planning Chapter 3 Teaching More Effective Lessons *Motivational Techniques *Classroom Questioning *Strategies for Teaching More Effective Lessons *Literacy in Mathematics *Writing Chapter 4 The Role of Problem-Solving *A Psychnological View of Problem Solving *Problem-Solving Preliminaries *An Introduction to Problem Solving *The Ten Problem-Solving Strategies *Creating Mathematical Problems *Creativity in Problem Solving Chapter 5 Using Technology to Enhance Mathematics Instruction *Calculators *Computers Chapter 6 Assessment *Assessment for Monitoring Student Progress *Assessment for Making Instructional Decisions *Evaluating Student Achievement Chapter 7 Enriching Mathematics Instruction *Enriching Mathematics Instruction with a Historical Approach *Enrichment Techniques for All Levels *The Gifted Student *Using Calculators to Enrich Instruction *Models and Manipulatives That Enrich Instruction Chapter 8 Extracurricular Activities in Mathematics *The Mathematics Club *Mathematics Teams *Mathematics Contests *Mathematics Projects *The Mathematics Fair *Cooperation with a University *The School Mathematics Magazine *The Mathematics Assembly Program *Guest Speakers Program *Class Trips of Mathematical Significance *Peer Teaching Program *The Computer *The Bulletin Board PART II ENRICHMENT UNITS FOR THE SECONDARY SCHOOL CLASSROOM 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 *Tessellations *Introducing the Pythagorean Theorem *Trisection Revisited *Proving Lines Concurrent *Squares *Proving Points Collinear *Angle Measurement with a Circle *Trisecting a Circle *Ptolemy's Theorem *Constructing pi *The Arbelos *The Nine-Point Circle *The Euler Line *The Simson Line *The Butterfly Problem *Equicircles *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 *Howlers *Digit Problems Revisited *Algebraic Identities *A Method for Factoring Trinomials of the Form: ax2 + bx + c *Solving Quadratic Equations *The Euclidean Algorithm *Prime Numbers *Algebraic Fallacies *Sum Derivations With Arrays *Pythagorean Triples *Divisibility *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 *Networks *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 *piie Mix *Graphical Iteration *The Feigenbaum Plot *The Sierpinski Triangle *Fractals Appendix Additional Exercises Index About the Authors