Guiding Children’s Learning of Mathematics (with CD-ROM and InfoTrac)

by Kennedy, Leonard M.; Tipps, Steve; Johnson, Art

• ISBN13: 9780534608767
• ISBN10: 0534608760
• Edition: 10th
• Format: Paperback
• Copyright: 2003-07-21
• Publisher: Wadsworth Publishing

Summary

Preface. 1. New Standards for a New Century. Part I: TEACHING AND LEARNING ELEMENTARY MATHEMATICS. 2. Foundations for Effective Instruction in Elementary Mathematics. 3. Implementing Effective Instruction. 4. Implementing Integrated Assessment. Part II: CONCEPTS AND SKILLS IN ELEMENTARY MATHEMATICS. 5. Problem-Solving and Algebraic Reasoning. 6. Developing Number Concepts and Systems. 7. Understanding Operations of Addition and Subtraction with Whole Numbers. 8. Understanding Operations of Multiplication and Division with Whole Numbers. 9. Developing Geometric Concepts and Systems. 10. Developing Concepts of Common and Decimal Fractions. 11. Extending Concepts of Common and Decimal Fractions. 12. Developing Measurement Concepts. 13. Understanding Concepts of Data. 14. Understanding Concepts of Chance. Appendices. NCTM Standards. Endnotes.

Author Biography

Leonard M. Kennedy is Professor Emeritus, California State University, Sacramento.

Table of Contents

Preface	p. xiii
Elementary Mathematics for 2000 and Beyond	p. 1
New Standards for a New Century	p. 3
Renewing School Mathematics for the 21st Century	p. 4
Leadership in Mathematics Education	p. 5
New Standards for 2000	p. 7
Principles for Mathematics Education	p. 8
The Mathematics Curriculum Principle	p. 8
The Equity Principle	p. 18
The Teaching Principle and the Learning Principle	p. 18
The Assessment Principle	p. 19
The Technology Principle	p. 19
Meeting the Challenge of the Standards	p. 20
Summary	p. 20
Mathematical Thinking Is Basic	p. 23
Brain-Wise Learning	p. 24
Built to Think	p. 24
Thinking to Learn and Learning to Think	p. 26
Thinking/Learning Skills	p. 27
Matching and Discriminating	p. 27
Sorting and Classifying	p. 30
Ordering and Seriation	p. 34
Sequencing	p. 36
Patterning	p. 38
Process Skills and Process Standards	p. 40
Mathematics as Problem Solving	p. 41
Problem-Solving Strategies	p. 44
Act It Out	p. 45
Build a Model	p. 46
Draw a Picture or Diagram	p. 47
Make a Table and/or Graph	p. 49
Write a Mathematical Sentence	p. 52
Look For and Use a Pattern	p. 53
Guess-and-Check, or Trial-and-Error	p. 55
Account for All Possibilities	p. 57
Solve a Simple Problem, or Break into Parts	p. 59
Work Backwards	p. 60
Change Your Point of View	p. 61
Combining Strategies	p. 62
Classroom Problems	p. 62
Reasoning in Mathematics	p. 64
Communication in Mathematics	p. 65
Mathematical Representation	p. 69
Connections	p. 70
Interdisciplinary Connections	p. 72
Real-World Connections	p. 74
Algebra Is Thinking	p. 74
Implementing the Thinking Curriculum	p. 74
Summary	p. 75
Teaching and Learning Elementary Mathematics	p. 81
Foundations for Effective Instruction in Elementary Mathematics	p. 83
Mathematics for Every Child	p. 84
Equity in Mathematics	p. 85
Students with Learning Disabilities	p. 87
Gifted and Talented Students	p. 89
Individual Differences in All Learners: Multiple Intelligences and Learning Styles	p. 90
Theories of Learning and Mathematics	p. 92
Research into Mathematics Teaching	p. 100
Directed Instruction	p. 100
Cooperative Learning	p. 101
Induction (Guided Discovery) and Concept Attainment	p. 102
Use of Manipulatives	p. 104
Technology in the Classroom	p. 104
Calculators	p. 104
Computers	p. 106
Video Programs	p. 107
Summary	p. 107
Implementing Effective Instruction	p. 111
Implementing a Mathematics Curriculum	p. 112
The Role of Performance Objectives	p. 112
Using Performance Objectives to Plan Lessons	p. 113
Teaching Mathematics	p. 117
Informal Activities	p. 118
Cooperative Learning	p. 119
Teacher-Directed Activities	p. 123
Mathematical Investigations	p. 128
Preparing and Using Lesson Plans	p. 130
Arranging the Classroom	p. 134
Summary	p. 136
Implementing Integrated Assessment	p. 141
Changes in Classroom Assessment	p. 142
Standards and Objectives	p. 143
Concepts, Skills, and Attitudes	p. 144
Instruction and Instructional Decisions	p. 144
Multiple Assessment Tools and Procedures	p. 145
Involvement with Students and Parents	p. 145
Example of Integrated Assessment	p. 146
Assessment, Evaluation, and Grading	p. 147
Organizing Assessments	p. 148
Designing Performance Tasks	p. 148
Selecting Data Collection Tools	p. 150
Recording Assessments	p. 150
Anecdotal Records	p. 151
Checklists and Rating Scales	p. 154
Rubrics	p. 156
Implementing Classroom Assessments	p. 161
Assessing Prior Knowledge and Skills	p. 161
Monitoring Children's Thinking	p. 163
Conducting Classroom Conferences	p. 168
Using Written Work for Assessments	p. 168
Incorporating Journals in Assessment	p. 170
Assessment of Projects and Problem-Solving Performance Tasks	p. 171
Assessment Portfolios	p. 173
Enhancing Student Self-Assessment	p. 174
Assessing Mastery	p. 176
Understanding Standardized Testing	p. 178
Interpreting Standardized Tests	p. 178
Accountability Issues	p. 179
Summary	p. 180
Concepts and Skills in Elementary Mathematics	p. 185
Developing Number Concepts and Systems	p. 187
Thinking with Numbers	p. 188
Number Sense	p. 188
The Base-10 Numeration System	p. 190
Number Concepts and Symbols	p. 193
Principles of Counting and Number Constancy	p. 193
Developing Early Number Concepts	p. 194
Linking Number and Numeral	p. 200
Introducing Ordinal Numbers	p. 203
Writing Numerals	p. 204
Special Problems with Counting and Writing Numerals	p. 205
Understanding the Base-10 Numeration System	p. 208
Unlocking Place Value	p. 209
Exchanging, Trading, or Regrouping	p. 215
Working with Larger Numbers	p. 217
Estimation as a Number Skill	p. 222
Expressing Larger Numbers with Expanded Notation	p. 224
Rounding	p. 226
Algebraic Thinking Through Patterns and Relationships	p. 229
Skip Counting	p. 229
One-to-Many, Many-to-One, and Many-to-Many Correspondences	p. 230
Odd and Even Numbers	p. 232
Prime and Composite Numbers	p. 233
Integers	p. 237
Mathematical Symbols and Expressions	p. 239
Take-Home Activities	p. 243
Summary	p. 245
Understanding Operations of Addition and Subtraction with Whole Numbers	p. 251
Standards and Operations with Whole Numbers	p. 252
Suggested Sequence for Teaching Addition and Subtraction	p. 252
Three Computation Processes	p. 255
Addition and Subtraction Situations	p. 257
Developing Readiness for Addition and Subtraction	p. 257
Introducing Addition and Subtraction	p. 260
Initial Addition Activities	p. 260
Strategies for Learning Addition Facts	p. 264
Initial Subtraction Activities	p. 266
Introducing the Vertical Notation Form	p. 269
Committing the Basic Facts to Memory	p. 274
Helping Children Learn Some Properties of Addition and Subtraction	p. 277
The Commutative Property	p. 277
The Associative Property	p. 277
The Identity Element for Addition	p. 278
Teaching Addition with Larger Whole Numbers	p. 279
Alternative Algorithms	p. 284
Estimation and Mental Addition Techniques	p. 286
Estimating Sums	p. 286
Mental Computation	p. 288
Introducing Subtraction with Larger Whole Numbers	p. 290
The Decomposition Algorithm	p. 290
The Equal-Additions Algorithm	p. 294
Estimating Differences and Mental Computation	p. 295
Take-Home Activities	p. 296
Summary	p. 299
Understanding Operations of Multiplication and Division with Whole Numbers	p. 305
Standards and Multiplication and Division	p. 306
Introducing Multiplication	p. 306
Repeated Addition Concept	p. 308
Array Concept	p. 310
Area Concept	p. 311
Cartesian Products	p. 312
Introducing Division	p. 314
Introducing Measurement Situations	p. 314
Introducing Partitive Situations	p. 315
Activities for Learning Multiplication and Division Facts	p. 317
Teaching Properties of Multiplication and Division	p. 321
The Commutative Property	p. 321
The Associative Property	p. 322
The Distributive Property	p. 322
The Identity Element	p. 324
The Role of Zero in Multiplication and Division	p. 324
Multiplying Larger Numbers	p. 325
Multiplication with Regrouping	p. 327
Multiplication with Two Numbers Larger than Ten	p. 327
Estimation and Mental Computation	p. 330
Historical Multiplication Processes	p. 330
Division with Larger Numbers	p. 334
Division with Regrouping	p. 336
Division with Two-Place Divisors	p. 339
Quotients with Two Digits	p. 341
Estimating Quotients	p. 344
Shortened Forms	p. 345
Take-Home Activities	p. 346
Summary	p. 349
Developing Geometric Concepts and Systems	p. 353
Rationale for Geometry	p. 354
Geometry Systems	p. 355
Development of Geometry Concepts	p. 357
Learning About Topological Geometry	p. 358
Proximity and Relative Position	p. 358
Separation	p. 359
Order	p. 360
Topological Mazes and Puzzles	p. 362
Learning About Euclidean Geometry	p. 363
Plane Figures	p. 364
Space Figures	p. 368
Points, Lines, Rays, Line Segments, and Angles	p. 375
Geometric Properties--Congruence and Similarity	p. 377
Geometric Properties--Symmetry	p. 379
Learning About Transformational Geometry	p. 383
Tessellations	p. 386
Learning About Coordinate Geometry	p. 390
Take-Home Activity	p. 392
Summary	p. 394
Developing Concepts of Common and Decimal Fractions	p. 399
Instruction About Common and Decimal Fractions	p. 400
Meanings of Common Fractions	p. 400
Unit Partitioned into Equal-Sized Parts	p. 401
Set Partitioned into Equal-Sized Groups	p. 401
Expressions of Ratios	p. 402
Indicated Division	p. 403
Introducing Common Fraction Concepts	p. 404
Partitioning Single Things	p. 404
Partitioning Sets of Objects	p. 408
Fractional Numbers Greater Than One	p. 414
Understanding Ratios and Proportions	p. 415
Introducing Decimal Fractions	p. 416
Tenths	p. 417
Hundredths	p. 419
Smaller Decimal Fractions	p. 420
Mixed Numerals with Decimal Fractions	p. 420
Comparing Fractional Numbers	p. 421
Comparing Common Fractions	p. 424
Comparing Common and Decimal Fractions with Number Lines	p. 425
Equivalent Fractions	p. 430
Rounding Decimal Fractions	p. 431
Extending Understanding of Decimal Fractions	p. 432
Helping Children Understand Percent	p. 434
Meaning of Percent	p. 435
Learning About Percent	p. 436
Take-Home Activity	p. 438
Summary	p. 439
Extending Concepts of Common and Decimal Fractions	p. 443
Standards and Fractional Numbers	p. 443
Addition and Subtraction with Common and Decimal Fractions	p. 444
Addition and Subtraction with Common Fractions	p. 444
Adding and Subtracting with Decimal Fractions	p. 456
Multiplication with Common Fractions	p. 458
Multiplying a Fractional Number by a Whole Number	p. 458
Multiplying a Whole Number by a Fractional Number	p. 460
Multiplying a Fractional Number by a Fractional Number	p. 461
Division with Common Fractions	p. 466
Developing Understanding of Division Algorithms	p. 468
Developing Number Sense About Operations with Common Fractions	p. 471
Simplifying Answers	p. 472
Multiplying and Dividing with Decimal Fractions	p. 474
Multiplying with Decimal Fractions	p. 474
Dividing with Decimal Fractions	p. 477
Working with Ratios and Proportions	p. 480
Rate Pairs and Tables	p. 480
Working with Proportions	p. 482
Working with Percent	p. 482
Take-Home Activities	p. 485
Summary	p. 486
Developing Measurement Concepts	p. 491
Measuring Processes	p. 492
Direct and Indirect Measurement	p. 492
Approximation, Precision, and Accuracy	p. 494
Selecting Appropriate Units	p. 495
Two Measurement Systems	p. 495
English System	p. 496
Metric System	p. 497
A Teaching/Learning Model for Measurement	p. 499
Activities to Develop Measurement Concepts and Skills	p. 503
Nonstandard Units of Measure	p. 503
Standard Units of Measure	p. 507
Length	p. 508
Area	p. 514
Capacity and Volume	p. 518
Weight (Mass)	p. 521
Angles	p. 525
Assessing Measurement Skills and Concepts	p. 529
Temperature	p. 532
Time	p. 533
Money	p. 539
Measurement Problem Solving and Projects	p. 543
Take-Home Activities	p. 545
Summary	p. 546
Understanding Concepts of Data and Chance	p. 551
Using Graphs to Work with Data	p. 551
Data Collection	p. 552
Organizing Data in Tables	p. 553
Object and Picture Graphs	p. 556
Bar Graphs	p. 560
Line Graphs	p. 560
Circle Graphs	p. 562
Stem-and-Leaf Plots	p. 565
Statistics	p. 567
Probability	p. 573
Two Types of Probability	p. 573
Probability Investigations	p. 575
Take-Home Activity	p. 582
Summary	p. 584
Appendices
Using the Internet	p. 587
Distributors of Mathematics Learning Aids	p. 588
Suppliers of Mathematics Software, CD-ROMs, and Videos	p. 589
Principles and Standards for School Mathematics: Discussion Draft, October 1998	p. 591
Endnotes	p. 610
Index	p. 617
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