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Methods of Teaching Secondary Mathematics | |

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The Challenge of Teaching | |

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Today's Students, Mathematics, and Society's Need | |

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Crisis in Math Education | |

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The Teacher Shortage | |

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Goals and Challenges for Secondary Math Teachers Today | |

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The Standards: Twelve Years of Growth | |

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Professional Development: A Teacher's Resource | |

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Resources for Teachers | |

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A Mathematics Debate | |

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Long-Range and Short-Range Planning | |

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Long-Range Planning | |

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Short-Range Planning | |

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The Daily Lesson Plan | |

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Examining Lesson Components More Closely | |

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Performance Objectives | |

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What Is Cooperative Learning? | |

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How to Structure Small Learning Groups | |

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The Teacher's Role in Managing Small-Group Learning | |

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How to Incorporate Small-Group Learning Into Mathematics Class | |

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Sample Lessons | |

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Sample Standards Lessons | |

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Teaching More Effective Lessons | |

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Motivational Techniques | |

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What Is Motivation? | |

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Motivating Students: Eight Techniques | |

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Classroom Questioning | |

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Classroom Questioning Features to Develop | |

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Some Precautionary Considerations for Improving Classroom Questioning | |

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Ten Types of Questions to Avoid | |

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Classroom Questioning as a Means to Generate Higher-Order Thinking | |

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Strategies for Teaching More Effective Lessons | |

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Using Tree Diagrams, or Branching | |

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Using Paper Folding or Cutting | |

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A Picture Is Worth a Thousand Words | |

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Recognizing Patterns | |

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Using Mathematical Models and Manipulatives | |

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Extending Familiar Concepts | |

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Using a Graphing Calculator | |

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Writing in the Mathematics Classroom | |

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Student Logs | |

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Student Journals | |

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Exposition | |

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Criteria for Evaluating Student Writing Samples | |

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Benefits of Writing Activities in the Mathematics Classroom | |

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The Role of Problem Solving | |

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A Psychological View of Problem Solving | |

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Problem-Solving Preliminaries | |

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An Introduction to Problem-Solving Strategies | |

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The Ten Problem-Solving Strategies | |

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Creating Mathematical Problems | |

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Creativity in Problem Solving | |

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Using Technology to Enhance Mathematics Instruction | |

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Calculators | |

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Calculators as an Aid to Problem Solving | |

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Examples of Calculator Activities | |

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Solving Equations Using Matrices | |

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Calculus Applications | |

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Computers | |

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Using The Geometer's Sketchpad | |

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The Geometer's Sketchpad and Enrichment Units | |

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Multiple Assessment and Grading Strategies | |

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Using Performance Assessment Tasks | |

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Using Rubrics to Evaluate Student Work | |

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Constructing a Class Test | |

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Administering a Test | |

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Grading a Test | |

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Interpreting Test Results | |

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Multiple Choice Tests | |

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Student Responsibilities | |

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Parental Responsibilities | |

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Determining the Course Grade | |

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Other Grading Schemes | |

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Enriching Mathematics Instruction | |

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Enriching Mathematics Instruction with a Historical Approach | |

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Enrichment Techniques for All Levels | |

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The Gifted Student | |

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Using Calculators to Enrich Instruction | |

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Models and Manipulatives That Enrich Instruction | |

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Extracurricular Activities in Mathematics | |

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The Mathematics Club | |

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Mathematics Teams | |

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Mathematics Contests | |

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Mathematics Projects | |

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The Mathematics Fair | |

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Cooperation With a University | |

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The School Mathematics Magazine | |

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The Mathematics Assembly Program | |

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Guest Speakers Program | |

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Class Trips of Mathematical Significance | |

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Peer Teaching Program | |

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The Computer | |

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The Bulletin Board | |

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Enrichment Units for the Secondary School Classroom | |

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Cross-Catalogue of Enrichment Units | |

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Constructing Odd-Order Magic Squares | |

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Constructing Even-Order Magic Squares | |

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Introduction to Alphametics | |

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A Checkerboard Calculator | |

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The Game of Nim | |

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The Tower of Hanoi | |

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What Day of the Week Was It? | |

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Palindromic Numbers | |

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The Fascinating Number Nine | |

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Unusual Number Properties | |

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Enrichment with a Hand-Held Calculator | |

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Symmetric Multiplication | |

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Variations on a Theme--Multiplication | |

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Ancient Egyptian Arithmetic | |

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Napier's Rods | |

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Unit Pricing | |

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Successive Discounts and Increases | |

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Prime and Composite Factors of a Whole Number | |

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Prime Numeration System | |

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Repeating Decimal Expansions | |

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Peculiarities of Perfect Repeating Decimals | |

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Patterns in Mathematics | |

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Googol and Googolplex | |

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Mathematics of Life Insurance | |

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Geometric Dissections | |

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The Klein Bottle | |

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The Four Color Map Problem | |

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Mathematics on a Bicycle | |

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Mathematics and Music | |

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Mathematics in Nature | |

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The Birthday Problem | |

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The Structure of the Number System | |

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Excursions in Number Bases | |

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Raising Interest | |

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Reflexive, Symmetric, and Transitive Relations | |

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Bypassing an Inaccessible Region | |

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The Inaccessible Angle | |

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Triangle Constructions | |

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The Criterion of Constructibility | |

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Constructing Radical Lengths | |

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Constructing a Pentagon | |

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Investigating the Isosceles Triangle Fallacy | |

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The Equiangular Point | |

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The Minimum Distance Point of a Triangle | |

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The Isosceles Triangle Revisited | |

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Reflective Properties of the Plane | |

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Finding the Length of a Cevian of a Triangle | |

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A Surprising Challenge | |

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Making Discoveries in Mathematics | |

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Tessellations | |

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Introducing the Pythagorean Theorem | |

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Trisection Revisited | |

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Proving Lines Concurrent | |

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Squares | |

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Proving Points Collinear | |

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Angle Measurement with a Circle | |

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Trisecting a Circle | |

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Ptolemy's Theorem | |

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Constructing [pi] | |

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The Arbelos | |

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The Nine-Point Circle | |

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The Euler Line | |

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The Simson Line | |

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The Butterfly Problem | |

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Equicircles | |

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The Inscribed Circle and the Right Triangle | |

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The Golden Rectangle | |

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The Golden Triangle | |

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Geometric Fallacies | |

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Regular Polyhedra | |

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An Introduction to Topology | |

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Angles on a Clock | |

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Averaging Rates--The Harmonic Mean | |

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Howlers | |

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Digit Problems Revisited | |

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Algebraic Identities | |

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A Method for Factoring Trinomials of the Form: ax[superscript 2] + bx + c | |

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Solving Quadratic Equations | |

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The Euclidean Algorithm | |

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Prime Numbers | |

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Algebraic Fallacies | |

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Sum Derivations with Arrays | |

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Pythagorean Triples | |

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Divisibility | |

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Fibonacci Sequence | |

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Diophantine Equations | |

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Continued Fractions and Diophantine Equations | |

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Simplifying Expressions Involving Infinity | |

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Continued Fraction Expansions of Irrational Numbers | |

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The Farey Sequence | |

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The Parabolic Envelope | |

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Application of Congruence to Divisibility | |

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Problem Solving--A Reverse Strategy | |

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Decimals and Fractions in Other Bases | |

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Polygonal Numbers | |

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Networks | |

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Angle Trisection--Possible or Impossible? | |

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Comparing Means | |

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Pascal's Pyramid | |

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The Multinomial Theorem | |

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Algebraic Solution of Cubic Equations | |

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Solving Cubic Equations | |

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Calculating Sums of Finite Series | |

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A General Formula for the Sum of a Series of the Form [characters not reproducible] | |

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A Parabolic Calculator | |

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Constructing Ellipses | |

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Constructing the Parabola | |

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Using Higher Plane Curves to Trisect an Angle | |

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Constructing Hypocycloid and Epicycloid Circular Envelopes | |

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The Harmonic Sequence | |

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Transformations and Matrices | |

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The Method of Differences | |

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Probability Applied to Baseball | |

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Introduction to Geometric Transformations | |

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The Circle and the Cardioid | |

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Complex Number Applications | |

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Hindu Arithmetic | |

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Proving Numbers Irrational | |

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

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The Three Worlds of Geometry | |

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[pi]ie Mix | |

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Graphical Iteration | |

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The Feigenbaum Plot | |

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The Sierpinski Triangle | |

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Fractals | |

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Additional Exercises | |

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Assigning Homework | |

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Index | |

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About the Authors | |