METHODS OF TEACHING SECONDARY MATHEMATICS 

1  (232) 

The Challenge of Teaching 


2  (16) 

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


3  (1) 


3  (1) 


4  (1) 

Goals and Challenges for Secondary Math Teachers Today 


5  (3) 

The Standards: Twelve Years of Growth 


8  (5) 

Professional Development: A Teacher's Resource 


13  (1) 


14  (1) 


15  (3) 

LongRange and ShortRange Planning 


18  (37) 


19  (3) 


22  (1) 


22  (4) 

Examining Lesson Components More Closely 


26  (1) 


26  (2) 

What Is Cooperative Learning? 


28  (1) 

How to Structure Small Learning Groups 


28  (3) 

The Teacher's Role in Managing SmallGroup Learning 


31  (1) 

How to Incorporate SmallGroup Learning Into Mathematics Class 


31  (1) 


32  (7) 


39  (16) 

Teaching More Effective Lessons 


55  (41) 


56  (1) 


56  (1) 

Motivating Students: Eight Techniques 


56  (6) 


62  (1) 

Classroom Questioning Features to Develop 


63  (1) 

Some Precautionary Considerations for Improving Classroom Questioning 


64  (2) 

Ten Types of Questions to Avoid 


66  (3) 

Classroom Questioning as a Means to Generate HigherOrder Thinking 


69  (3) 

Strategies for Teaching More Effective Lessons 


72  (1) 

Using Tree Diagrams, or Branching 


72  (1) 

Using Paper Folding or Cutting 


73  (1) 

A Picture Is Worth a Thousand Words 


74  (2) 


76  (2) 

Using Mathematical Models and Manipulatives 


78  (5) 

Extending Familiar Concepts 


83  (5) 

Using a Graphing Calculator 


88  (1) 

Writing in the Mathematics Classroom 


89  (1) 


89  (1) 


89  (1) 


89  (2) 

Criteria for Evaluating Student Writing Samples 


91  (1) 

Benefits of Writing Activities in the Mathematics Classroom 


91  (5) 

The Role of Problem Solving 


96  (31) 

A Psychological View of Problem Solving 


99  (1) 

ProblemSolving Preliminaries 


100  (2) 

An Introduction to ProblemSolving Strategies 


102  (6) 

The Ten ProblemSolving Strategies 


108  (8) 

Creating Mathematical Problems 


116  (1) 

Creativity in Problem Solving 


117  (10) 

Using Technology to Enhance Mathematics Instruction 


127  (30) 


128  (1) 

Calculators as an Aid to Problem Solving 


128  (1) 

Examples of Calculator Activities 


128  (6) 

Solving Equations Using Matrices 


134  (1) 


135  (2) 


137  (2) 

Using The Geometer's Sketchpad 


139  (14) 

The Geometer's Sketchpad and Enrichment Units 


153  (4) 

Multiple Assessment and Grading Strategies 


157  (35) 

Using Performance Assessment Tasks 


158  (1) 

Using Rubrics to Evaluate Student Work 


158  (13) 

Constructing a Class Test 


171  (12) 


183  (1) 


184  (2) 

Interpreting Test Results 


186  (1) 


186  (1) 


187  (1) 

Parental Responsibilities 


187  (1) 

Determining the Course Grade 


188  (2) 


190  (2) 

Enriching Mathematics Instruction 


192  (24) 

Enriching Mathematics Instruction with a Historical Approach 


193  (8) 

Enrichment Techniques for All Levels 


201  (1) 


202  (3) 

Using Calculators to Enrich Instruction 


205  (2) 

Models and Manipulatives That Enrich Instruction 


207  (9) 

Extracurricular Activities in Mathematics 


216  (17) 


217  (1) 


217  (2) 


219  (1) 


219  (1) 


220  (2) 

Cooperation With a University 


222  (1) 

The School Mathematics Magazine 


222  (1) 

The Mathematics Assembly Program 


222  (1) 


223  (1) 

Class Trips of Mathematical Significance 


223  (1) 


224  (1) 


224  (1) 


224  (9) 
ENRICHMENT UNITS FOR THE SECONDARY SCHOOL CLASSROOM 

233  (242) 

CrossCatalogue of Enrichment Units 


233  (242) 

Constructing OddOrder Magic Squares 


240  (2) 

Constructing EvenOrder Magic Squares 


242  (2) 

Introduction to Alphametics 


244  (2) 

A Checkerboard Calculator 


246  (2) 


248  (2) 


250  (2) 

What Day of the Week Was It? 


252  (5) 


257  (1) 

The Fascinating Number Nine 


258  (2) 

Unusual Number Properties 


260  (2) 

Enrichment with a HandHeld Calculator 


262  (2) 


264  (2) 

Variations on a ThemeMultiplication 


266  (2) 

Ancient Egyptian Arithmetic 


268  (2) 


270  (1) 


271  (1) 

Successive Discounts and Increases 


272  (2) 

Prime and Composite Factors of a Whole Number 


274  (1) 


275  (2) 

Repeating Decimal Expansions 


277  (2) 

Peculiarities of Perfect Repeating Decimals 


279  (1) 


280  (2) 


282  (2) 

Mathematics of Life Insurance 


284  (2) 


286  (2) 


288  (1) 

The Four Color Map Problem 


289  (2) 


291  (3) 


294  (2) 


296  (2) 


298  (1) 

The Structure of the Number System 


299  (2) 

Excursions in Number Bases 


301  (2) 


303  (2) 

Reflexive, Symmetric, and Transitive Relations 


305  (2) 

Bypassing an Inaccessible Region 


307  (1) 


308  (2) 


310  (2) 

The Criterion of Constructibility 


312  (2) 

Constructing Radical Lengths 


314  (1) 


315  (1) 

Investigating the Isosceles Triangle Fallacy 


316  (2) 


318  (1) 

The Minimum Distance Point of a Triangle 


319  (2) 

The Isosceles Triangle Revisited 


321  (2) 

Reflective Properties of the Plane 


323  (2) 

Finding the Length of a Cevian of a Triangle 


325  (2) 


327  (2) 

Making Discoveries in Mathematics 


329  (1) 


330  (2) 

Introducing the Pythagorean Theorem 


332  (2) 


334  (2) 


336  (2) 


338  (1) 


339  (2) 

Angle Measurement with a Circle 


341  (2) 


343  (1) 


344  (2) 


346  (2) 


348  (2) 


350  (1) 


351  (2) 


353  (1) 


354  (2) 


356  (2) 

The Inscribed Circle and the Right Triangle 


358  (2) 


360  (2) 


362  (2) 


364  (2) 


366  (2) 

An Introduction to Topology 


368  (1) 


369  (2) 

Averaging RatesThe Harmonic Mean 


371  (2) 


373  (2) 


375  (1) 


376  (2) 

A Method for Factoring Trinomials of the Form: ax2 + bx + c 


378  (1) 

Solving Quadratic Equations 


379  (2) 


381  (2) 


383  (2) 


385  (2) 

Sum Derivations with Arrays 


387  (2) 


389  (2) 


391  (2) 


393  (2) 


395  (1) 

Continued Fractions and Diophantine Equations 


396  (2) 

Simplifying Expressions Involving Infinity 


398  (2) 

Continued Fraction Expansions of Irrational Numbers 


400  (2) 


402  (2) 


404  (2) 

Application of Congruence to Divisibility 


406  (2) 

Problem SolvingA Reverse Strategy 


408  (3) 

Decimals and Fractions in Other Bases 


411  (1) 


412  (3) 


415  (2) 

Angle TrisectionPossible or Impossible? 


417  (1) 


418  (2) 


420  (2) 


422  (2) 

Algebraic Solution of Cubic Equations 


424  (2) 


426  (2) 

Calculating Sums of Finite Series 


428  (2) 

A General Formula for the Sum of a Series of the Form 


430  (3) 


433  (2) 


435  (2) 

Constructing the Parabola 


437  (2) 

Using Higher Plane Curves to Trisect an Angle 


439  (2) 

Constructing Hypocycloid and Epicycloid Circular Envelopes 


441  (2) 


443  (1) 

Transformations and Matrices 


444  (3) 

The Method of Differences 


447  (1) 

Probability Applied to Baseball 


448  (2) 

Introduction to Geometric Transformations 


450  (2) 

The Circle and the Cardioid 


452  (3) 

Complex Number Applications 


455  (2) 


457  (2) 

Proving Numbers Irrational 


459  (1) 

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


460  (2) 

The Three Worlds of Geometry 


462  (3) 


465  (1) 


466  (2) 


468  (2) 


470  (2) 


472  (3) 
Appendix A Additional Exercises 

475  (6) 
Appendix B Assigning Homework 

481  (11) 
Index 

492  (4) 
About the Authors 

496  