Preface 

xv  
UNIT I WHAT DOES IT MEAN TO ``DO,'' ``TEACH,'' AND ``LEARN'' MATHEMATICS? 

1  (54) 


3  (24) 

National and International Assessment Data 


6  (3) 


9  (1) 


10  (13) 


10  (5) 


15  (2) 


17  (2) 


19  (3) 


22  (1) 


23  (1) 


24  (1) 


25  (1) 

Bibliographic References and Resources 


25  (2) 

Learning Theories and Psychology in Mathematics Education 


27  (28) 

Research in Mathematics Education 


28  (4) 

Learning Theories in Mathematics 


32  (16) 

Bruner's Stages of Representation 


32  (4) 


36  (1) 

The Inquiry Approach and Constructivist Model 


37  (4) 

Inductive versus Deductive Teaching 


41  (4) 


45  (3) 


48  (1) 


49  (2) 


51  (1) 

Bibliographic References and Resources 


52  (3) 
UNIT II THE MATHEMATICS CURRICULUM 

55  (54) 


57  (23) 

NCTM Curriculum Standards 


58  (4) 


62  (1) 


63  (7) 

Traditional versus Integrated Sequences 


70  (6) 


76  (1) 


77  (1) 


78  (1) 

Bibliographic References and Resources 


79  (1) 

Implementing a Course of Study 


80  (29) 


81  (5) 

Writing Goals and Objectives 


86  (8) 


88  (1) 


88  (1) 


88  (6) 

Selection and Organization of Resources 


94  (8) 


94  (3) 


97  (1) 


98  (2) 

Organizing a Resource File 


100  (2) 


102  (1) 


103  (1) 


104  (1) 

Bibliographic References and Resources 


105  (1) 

NCTM Addenda Series Resources Books 


105  (1) 

Sample Recommended Resource Books 


106  (1) 

Comap ``HiMap'' (High School Mathematics) Teaching Modules 


106  (1) 

NSFFunded Curricular Materials 


107  (2) 
UNIT III TEACHING MATHEMATICS 

109  (100) 


111  (26) 


112  (5) 


117  (14) 


121  (1) 


121  (1) 


122  (1) 


123  (1) 


123  (1) 


123  (1) 


124  (7) 

Lesson Imaging versus Lesson Planning 


131  (1) 


132  (1) 


133  (1) 


134  (1) 


135  (1) 

Bibliographic References and Resources 


135  (2) 

Responsibilities of the Professional Teacher 


137  (34) 

Teaching Standards and Guiding Principles 


139  (2) 

The NCTM Professional Teaching Standards 


139  (2) 


141  (1) 

Selecting Activities and Problems 


141  (4) 


145  (8) 

Handson Manipulative Materials 


145  (4) 


149  (1) 

Diagrams, Graphs, and Other Discussion Starters 


150  (3) 


153  (7) 

Studnet and Teacher Roels 


153  (1) 


154  (3) 


157  (3) 


160  (6) 


166  (1) 


167  (1) 


168  (1) 


168  (1) 

Bibliographic References and Resources 


169  (2) 

Integrating Technology in Mathematics Instruction 


171  (38) 


173  (7) 


180  (8) 

Laser Discs, CDROMs, and Videos 


188  (3) 

The Internet and the World Wide Web 


191  (10) 


191  (8) 

Student Research Tools and Projects 


199  (2) 

Choosing between Paper and Pencil and Technology 


201  (2) 


203  (2) 


205  (1) 


205  (1) 

Bibliographic References and Resources 


206  (3) 
UNIT IV ASSESSMENT IN MATHEMATICS 

209  (62) 


211  (33) 


212  (1) 


213  (3) 


216  (6) 


216  (3) 

Ensuring Validity and Reliability 


219  (1) 


219  (2) 


221  (1) 

Alternate Strategies for Assessing Student Progress 


222  (16) 


222  (2) 

OpenEnded Questions and Rubrics 


224  (3) 

Individual and Team Projects 


227  (4) 

Observations and Checklists 


231  (3) 


234  (2) 


236  (2) 


238  (1) 


239  (2) 


241  (1) 

Bibliographic References and Resources 


242  (2) 

Standards and Equity in Assessment 


244  (27) 

NCTM Recommendations on Assessment 


245  (5) 


245  (4) 


249  (1) 

Equity through Assessment 


250  (2) 


252  (10) 

Homework Amount and Frequency 


253  (1) 

Laying the Groundwork for the Next Day 


253  (1) 

Completing a Classroom Problem 


254  (2) 

Practicing a Skill Developed in Class 


256  (1) 

Checking Homework Assignments 


257  (2) 

Using Homework Assignments in Assessment 


259  (3) 

Evaluation: Determining Final Grades 


262  (4) 


266  (1) 


267  (1) 


267  (1) 

Bibliographic References and Resources 


268  (3) 
UNIT V THE TEACHING PROFESSION AND APPENDICES 

271  (26) 

The Teacher of Mathematics in the School Community 


273  (24) 


274  (6) 

The Supervision and Evaluation of Teachers 


280  (6) 

Functioning in a Department 


286  (1) 

Ongoing Professional Development 


287  (6) 

Making the Case for LongTerm Development 


287  (2) 

Opportunities for Professional Development 


289  (2) 

The Professional Development Plan 


291  (2) 


293  (1) 


293  (1) 

Bibliographic References and Additional Resources 


294  (3) 
Appendix A Curriculum 

297  (22) 

NCTM Curriculum Standard 2, Grades 68: Patterns, Functions, and Algebra 


298  (5) 

NCTM Curriculum Standard 3, Grades 912: Geometry and Spatial Sense 


303  (10) 

Sample State Model Strand, Grades K12: Data Analysis and Probability 


313  (6) 
Appendix B Teaching 

319  (14) 

NCTM Professional Teaching Standard 1: Worthwhile Mathematical Tasks 


320  (6) 

NCTM Guiding Principle: The Equity Principle 


326  (7) 
Appendix C Assessment 

333  (4) 

NCTM Assessment Standard: The Inferences Standard 


334  (3) 
Appendix D Cases 

337  (20) 

Case 1: The Marble Line (algebra) 


338  (11) 

Case 2: Chances Are (probability) 


349  (8) 
Appendix E Suggested Websites 

357  (10) 

Professional Organizations 


357  (1) 

Activities and Lesson Plan Ideas 


358  (4) 

General Mathematics Education Sites 


362  (2) 

Mathematics History and Miscellaneous 


364  (1) 

OnLine Catalogs of Mathematics Education Materials and Supplies 


365  (1) 

Sample Search Engines for the Internet 


366  (1) 
Appendix F Sample Lessons and Activities 

367  (30) 

AlgebraSample Lesson Plan 


367  (2) 

AlgebraActivities Sampler 


369  (4) 

GeometrySample Lesson Plan 


373  (3) 

GeometryActivities Sampler 


376  (4) 

Statistics and ProbabilitySample Lesson Plan 


380  (2) 

Statistics and ProbabilityActivities Sampler 


382  (6) 

Discrete MathematicsSample Lesson Plan 


388  (3) 

Discrete MathematicsActivities Sampler 


391  (6) 
Index 

397  