Guiding Children's Learning of Mathematics, 11th Edition

Front Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Contents......Page 8
List of Activities......Page 16
Preface......Page 20
PART ONE: Guiding Elementary Mathematics with Standards......Page 24
CHAPTER 1: Elementary Mathematics for the 21st Century......Page 26
Solving Problems Is Basic......Page 27
A Comprehensive Vision of Mathematics......Page 28
Teacher’s Resources......Page 32
CHAPTER 2: Defining a Comprehensive Mathematics Curriculum......Page 34
What Elementary Children Need to Know in Mathematics......Page 35
Learning Mathematical Processes......Page 42
Integrating Process and Content Standards......Page 46
Finding Focus......Page 48
Teacher’s Resources......Page 49
CHAPTER 3: Mathematics for Every Child......Page 50
Equity in Mathematics Learning......Page 51
Gender......Page 52
Ethnic and Cultural Differences......Page 53
Students Who Have Limited English Proficiency......Page 57
Students Who Have Difficulty Learning Mathematics......Page 60
Gifted and Talented Students......Page 63
Individual Learning Styles......Page 65
Teacher’s Resources......Page 67
For Further Reading......Page 68
CHAPTER 4: Learning Mathematics......Page 70
Key Concepts in Learning Mathematics......Page 71
Research in Learning and Teaching Mathematics......Page 75
Teacher’s Resources......Page 79
CHAPTER 5: Organizing Effective Instruction......Page 80
What Is Effective Mathematics Teaching?......Page 81
Using Objectives in Planning Mathematics Instruction......Page 83
Varying Teaching Approaches......Page 86
Delivering Mathematics Instruction......Page 91
Managing the Instructional Environment......Page 95
Study Questions and Activities......Page 100
Teacher’s Resources......Page 101
CHAPTER 6: The Role of Technology in the Mathematics Classroom......Page 102
Calculators......Page 103
Computers......Page 106
The Internet......Page 108
Computer Games......Page 111
Teacher’s Resources......Page 113
For Further Reading......Page 114
CHAPTER 7: Integrating Assessment......Page 116
Planning for Assessment......Page 117
Implementing Assessment with Instruction......Page 124
Interpreting and Using Standardized Tests in Classroom Assessment......Page 130
Study Questions and Activities......Page 132
For Further Reading......Page 133
PART TWO: Mathematical Concepts, Skills, and Problem Solving......Page 134
CHAPTER 8: Developing Problem-Solving Strategies......Page 136
Approaches to Teaching Problem Solving......Page 138
Implementing a Problem-Solving Curriculum......Page 155
Take-Home Activities......Page 156
Children’s Bookshelf......Page 158
For Further Reading......Page 159
CHAPTER 9: Developing Concepts of Number......Page 160
Primary Thinking-Learning Skills......Page 161
Beginning Number Concepts......Page 166
Number Types and Their Uses......Page 168
Counting and Early Number Concepts......Page 169
Linking Number and Numeral......Page 174
Other Number Skills......Page 178
Teacher’s Resources......Page 181
For Further Reading......Page 182
CHAPTER 10: Extending Number Concepts and Number Systems......Page 184
Number Sense Every Day......Page 185
Understanding the Base-10 Numeration System......Page 186
Working with Larger Numbers......Page 190
Thinking with Numbers......Page 195
Other Number Concepts......Page 201
Take-Home Activities......Page 205
Using the Technology Center......Page 207
For Further Reading......Page 208
CHAPTER 11: Developing Number Operations with Whole Numbers......Page 210
What Students Need to Learn About Number Operations......Page 211
What Teachers Need to Know About Addition and Subtraction......Page 213
Developing Concepts of Addition and Subtraction......Page 215
What Teachers Need to Know About Properties of Addition and Subtraction......Page 223
What Teachers Need to Know About Multiplication and Division......Page 231
Developing Multiplication and Division Concepts......Page 235
What Teachers Need to Know About Properties of Multiplication and Division......Page 242
Learning Multiplication and Division Facts with Strategies......Page 243
Take-Home Activities......Page 248
Study Questions and Activities......Page 249
Technology Resources......Page 250
For Further Reading......Page 251
CHAPTER 12: Extending Computational Fluency with Larger Numbers......Page 252
Number Operations with Larger Numbers......Page 253
Number Sense, Estimation, and Reasonableness......Page 270
Take-Home Activities......Page 273
Study Activities and Questions......Page 274
For Further Reading......Page 275
CHAPTER 13: Developing Understanding of Common and Decimal Fractions......Page 276
What Teachers Need to Know About Teaching Common Fractions and Decimal Fractions......Page 278
Five Situations Represented by Common Fractions......Page 279
Introducing Common Fractions to Children......Page 282
Introducing Decimal Fractions......Page 290
Comparing Fractional Numbers......Page 295
Rounding Decimal Fractions......Page 300
Take-Home Activities......Page 304
Teacher’s Resources......Page 305
Technology Resources......Page 306
For Further Reading......Page 307
CHAPTER 14: Extending Understanding of Common and Decimal Fractions......Page 310
Standards and Fractional Numbers......Page 311
Teaching Children About Fractional Numbers in Elementary and Middle School......Page 312
Extending Understanding of Decimal Fractions......Page 313
Extending Concepts of Common and Decimal Fraction Operations......Page 315
Addition and Subtraction with Common Fractions......Page 316
Addition and Subtraction with Decimal Fractions......Page 327
Multiplication with Common Fractions......Page 328
Developing Understanding of Division Algorithms......Page 338
Developing Number Sense About Operations with Common Fractions......Page 341
Renaming Fractions in Simpler Terms......Page 342
Multiplying and Dividing with Decimal Fractions......Page 343
Using a Calculator to Develop Understanding of Decimal Fractions......Page 348
Take-Home Activity......Page 351
Study Questions and Activities......Page 352
Children’s Bookshelf......Page 353
Technology Resources......Page 354
For Further Reading......Page 355
CHAPTER 15: Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent......Page 356
What Teachers Should Know About Teaching Proportional Reasoning......Page 357
Ratios as a Foundation of Proportional Reasoning......Page 358
Teaching Proportional Reasoning......Page 359
Developing Proportional Reasoning Using Rate Pairs and Tables......Page 361
Working with Proportions......Page 362
Developing and Extending Concepts of Percent......Page 367
Take-Home Activities......Page 376
Using Children’s Literature......Page 377
Technology Resources......Page 378
For Further Reading......Page 379
CHAPTER 16: Thinking Algebraically......Page 380
What Teachers Should Know About Teaching Algebra......Page 381
Variables and Equations in Mathematics and Algebraic Thinking......Page 386
Equations in Algebraic Thinking......Page 391
Functions in Algebraic Thinking......Page 392
Extending Algebraic Thinking......Page 396
Extending Understanding of Equations......Page 401
Extending the Meaning of Functions......Page 402
Take-Home Activities......Page 407
Using Children’s Literature......Page 409
Technology Resources......Page 410
For Further Reading......Page 411
CHAPTER 17: Developing Geometric Concepts and Systems......Page 412
Children’s Development of Spatial Sense......Page 413
What Teachers Need to Know About Teaching Geometry......Page 415
Development of Geometric Concepts: Stages of Geometry Understanding......Page 419
Teaching and Learning About Topological Geometry......Page 420
Teaching and Learning About Euclidean Geometry......Page 423
Teaching and Learning About Transformational Geometry......Page 434
Teaching and Learning About Coordinate Geometry......Page 435
Extending Geometry Concepts......Page 437
Take-Home Activities......Page 454
Study Questions and Activities......Page 455
Children’s Bookshelf......Page 456
Technology Resources......Page 457
For Further Reading......Page 458
CHAPTER 18: Developing and Extending Measurement Concepts......Page 460
Measuring Processes......Page 462
What Teachers Should Know About Teaching Measurement......Page 463
A Teaching/Learning Model for Measurement......Page 467
Activities to Develop Measurement Concepts and Skills......Page 469
Teaching Children How to Measure Length......Page 473
Teaching Children About Measuring Area......Page 474
Teaching Children About Measuring Capacity and Volume......Page 475
Teaching Children About Measuring Angles......Page 476
Teaching Children to Measure Time......Page 477
Teaching Children to Use Money......Page 481
Extending Measurement Concepts......Page 483
Extending Concepts About Length......Page 484
Extending Concepts About Area......Page 488
Extending Volume Concepts......Page 493
Extending Mass and Weight Concepts......Page 496
Expanding Angle Concepts......Page 498
Expanding Temperature Concepts......Page 501
Extending Concepts of Time......Page 502
Measurement Problem Solving and Projects......Page 503
Take-Home Activities......Page 504
Study Questions and Activities......Page 507
Teacher’s Resources......Page 508
Technology Resources......Page 509
For Further Reading......Page 510
CHAPTER 19: Understanding and Representing Concepts of Data......Page 512
Data Collection......Page 513
What Teachers Should Know About Understanding and Representing Concepts of Data......Page 514
Extending Data Concepts......Page 522
Histograms......Page 525
Extending Children’s Understanding of Statistics......Page 533
Take-Home Activity......Page 540
Study Questions and Activities......Page 542
Children’s Bookshelf......Page 543
For Further Reading......Page 544
CHAPTER 20: Investigating Probability......Page 546
Two Types of Probability......Page 547
What Teachers Should Know About Teaching Probability......Page 548
Extending Probability Understanding......Page 551
Probability Investigations......Page 552
Geometric Probability......Page 556
Expected Value......Page 559
Simulations......Page 562
Take-Home Activities......Page 563
Using Children’s Literature......Page 564
For Further Reading......Page 565
Appendix A: NCTM Table of Standards and Expectations......Page 568
Appendix B: Black-Line Masters......Page 580
Glossary......Page 588
References......Page 594
Index......Page 600