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About the Author, ii
Copyright, iv
Preface, xv
Unit 1. What Does It Mean to “Do,” “Teach,” and “Learn” Mathematics?, 1
Chapter 1. Mathematics as a Process, 3
National and International Assessment Data, 5
How Would You React?, 10
The Need for Reform, 11
“Doing” Mathematics, 12
Problem Solving, 12
Reasoning and Proof, 15
SPOTlight on Technology, 17
Communication, 18
Connections, 19
Representation, 21
Classroom Dialogues, 22
Conclusion, 24
Glossary, 25
Discussion Questions and Activities, 26
Chapter 2. Principles of Mathematics Education, 27
The Six Principles, 28
Equity, 28
Curriculum, 29
How Would You React?, 30
Teaching, 31
SPOTlight on Technology, 33
Learning, 33
Assessment, 35
Technology, 35
Classroom Dialogues, 37
Connecting the Principles, 38
Conclusion, 39
Glossary, 40
Discussion Questions and Activities, 40
Chapter 3. Learning Theories and Psychology in Mathematics Education, 43
Research in Mathematics Education, 44
Quantitative and Qualitative Methods, 45
Experimental and Descriptive Research, 46
How Would You React?, 47
Learning Theories in Mathematics, 48
Development of Learning Theory, 49
Bruner’s Stages of Representation, 50
The van Hiele Model, 54
The Inquiry Approach and Constructivist Model, 57
Inductive versus Deductive Teaching, 60
SPOTlight on Technology, 61
Classroom Dialogues, 64
Motivation, 66
Conclusion, 69
Glossary, 70
Discussion Questions and Activities, 72
Unit 2. The Mathematics Curriculum, 75
Chapter 4. Curricular Models, 77
NCTM Curriculum Standards, 78
NCTM Focal Points and Related Documents, 80
How Would You React?, 82
State Models, 83
The Core Curriculum, 84
SPOTlight on Technology, 90
Traditional versus Integrated Sequences, 91
Classroom Dialogues, 95
Conclusion, 98
Glossary, 100
Discussion Questions and Activities, 100
Chapter 5. Implementing a Course of Study, 103
The Course of Study, 104
How Would You React?, 109
Writing Goals and Objectives, 110
Classifying Objectives, 111
SPOTlight on Technology, 118
Selection and Organization of Resources, 119
Textbooks, 119
Print Resources, 122
Classroom Dialogues, 124
The Internet, 126
Organizing a Resource File, 127
Conclusion, 128
Glossary, 129
Discussion Questions and Activities, 130
Unit 3. Teaching Mathematics, 133
Chapter 6. Planning for Instruction, 135
Unit Planning, 136
How Would You React?, 141
Lesson Planning, 142
General Considerations, 145
Goals and Objectives, 145
Materials and Resources, 146
Motivation, 146
Lesson Procedure, 147
Closure, 148
Extension, 149
Assessment, 149
SPOTlight on Technology, 150
Sample Lesson Plans, 151
Classroom Dialogues, 160
Lesson Imaging versus Lesson Planning, 162
Reflecting on a Lesson, 163
Conclusion, 164
Glossary, 165
Discussion Questions and Activities, 166
Chapter 7. Teaching Tools and Strategies, 167
Teaching Standards and Principles, 169
The NCTM Standards for Teaching and Learning Mathematics, 169
Knowledge Standards, 171
The Teaching and Learning Principles, 172
Selecting Activities and Problems, 172
How Would You React?, 175
Classroom Tools, 176
Hands-On Manipulative Materials, 176
Use of Technology, 180
Diagrams, Graphs, and Other Discussion Starters, 182
SPOTlight on Technology, 183
Learning Environment, 186
Classroom Discourse, 191
The Role of Discourse, 191
Questioning Skills, 192
Classroom Dialogues, 195
Cooperative Learning, 197
Reflective Practices, 200
Conclusion, 202
Glossary, 202
Discussion Questions and Activities, 203
Chapter 8. Teaching Specific Mathematics Content, 205
The Teaching of Algebra, 207
Sample Lesson Plan: Algebra, 209
Algebra—Activities Sampler, 211
How Would You React?, 215
The Teaching of Geometry, 216
Sample Lesson Plan: Geometry, 218
Geometry—Activities Sampler, 221
The Teaching of Data Analysis and Probability, 226
SPOTlight on Technology, 227
Sample Lesson Plan: Data Analysis and Probability, 230
Data Analysis and Probability—Activities Sampler, 232
The Teaching of Discrete Mathematics, 238
Sample Lesson Plan: Discrete Mathematics, 241
Classroom Dialogues, 244
Discrete Mathematics—Activities Sampler, 246
A Word on Pre-Calculus and Calculus, 252
Conclusion, 253
Glossary, 254
Discussion Questions and Activities, 255
Unit 4. Assessment in Mathematics, 257
Chapter 9. The Role of Assessment, 259
What Is Assessment?, 260
Purposes for Assessment, 261
Test Construction, 264
Preparing Items, 264
Ensuring Validity and Reliability, 267
Scoring Student Work, 267
How Would You React?, 268
Including Review Items, 269
Limitations to Written Tests, 270
Alternate Strategies for Assessing Student Progress, 270
Journals, 270
Open-Ended Questions and Rubrics, 273
SPOTlight on Technology, 278
Individual and Team Projects, 278
Observations and Checklists, 282
Interviews, 284
Self-Assessment, 286
Classroom Dialogues, 287
Portfolios, 288
Conclusion, 291
Glossary, 292
Discussion Questions and Activities, 293
Chapter 10. Principles of Assessment Practices, 295
NCTM Recommendations on Assessment, 296
The Assessment Standards, 296
How Would You React?, 300
The Assessment Principle, 301
Equity and Assessment, 301
Homework Assignments, 303
Homework Amount and Frequency, 304
Checking Homework Assignments, 308
SPOTlight on Technology, 309
Using Homework Assignments in Assessment, 311
Classroom Dialogues, 313
Evaluation: Maintaining and Determining Final Grades, 315
Conclusion, 321
Glossary, 322
Discussion Questions and Activities, 322
Unit 5. Meeting Individual Student and Teacher Needs, 323
Chapter 11. Meeting the Needs of All Students, 325
Defining and Achieving Equity, 327
Students with Special Needs, 328
How Would You React?, 331
Gender, 333
SPOTlight on Technology, 337
Ethnic and Cultural Issues, 339
Classroom Dialogues, 341
Ideas for Meeting Diverse Student Needs, 343
Differentiated Instruction, 343
General Suggestions for the Classroom, 344
Conclusion, 347
Glossary, 348
Discussion Questions and Activities, 348
Chapter 12. The Teacher of Mathematics in the School Community, 351
Working with Parents, 352
How Would You React?, 357
The Supervision and Evaluation of Teachers, 358
SPOTlight on Technology, 364
Functioning in a Department, 365
Ongoing Professional Development, 366
Making the Case for Long-Term Development, 366
Classroom Dialogues, 368
Opportunities for Professional Development, 370
The Professional Development Plan, 372
Conclusion, 373
Discussion Questions and Activities, 374
Appendix: Recommended Web Sites, 375
Professional Organizations, 375
Curriculum Projects, 375
Activities and Lesson Plan Ideas, 375
General Mathematics Education Sites, 376
Bibliographic References and Resources, 377
Index, 397
Photo Credits, 407

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