Today's Mathematics: Concepts, Methods, and Classroom Activities, (Shrinkwrapped with CD inside envelop inside front cover of Text), 12th Edition

Chapter 1 Learning Mathematics 1

Societal Needs 2

Calls for Change 3

National and International Achievement 3

The Identification of Standards 5

Principles and Standards for School Mathematics 6

Implementing the Process Standards 8

Describing A Contemporary Mathematics Program 10

Levels of Abstraction 11

Theoretical Foundations for a Contemporary

Mathematics Program 12

Research Snapshot 13

Theory into Practice 17

Closure 18

Teaching Competencies and Self-Assessment Tasks 19

Chapter 2 Teaching Mathematics 21

The NCTM Principles and Standards for School Mathematics 22

The NCTM Professional Teaching Standards: Mathematics Teaching Today 23

An Example of a Teaching Standard 25

Lesson Planning Processes and Purposes 29

Issues in Designing Mathematics Lessons 33

Mathematics Objectives 35

The Role of Motivation and Follow-Up 36

The Assessment of Learning and Teaching 37

Research Snapshot 38

Adjusting Instruction to Meet Individual Needs 38

Classroom Instructional Aids 39

Closure 40

Teaching Competencies and Self-Assessment Tasks 41

Chapter 3 Assessing Mathematics 43

NCTM Assessment Standards for School Mathematics 44

An Example of an Assessment Standard 47

A Classroom Assessment Vignette 48

Purposes for Assessment 49

Assessment Strategies 51

Research Snapshot 53

Closure 58

Teaching Competencies and Self-Assessment Tasks 59

Chapter 4 Technology in K–8 Mathematics 61

A Brief History of Technology’s Influence on Education 62

Calculators and Exploration of Mathematical Concepts 63

Research Snapshot 64

Calculator Features and Functions 66

Examples of Effective Calculator Use 66

Tools for Measuring Motion 68

Computers and Mathematics Instruction 69

Instructional Software in the Mathematics Classroom 71

Application Software in the Mathematics Classroom 72

Virtual Manipulatives 73

Design Issues and Advantages of Virtual Manipulatives 74

Classification Attributes for Virtual Manipulatives 75

Capsule Descriptions of the National Library of Virtual Manipulatives 76

Research Snapshot 80

Multimedia in the Mathematics Classroom 81

The Internet in the Mathematics Classroom 82

Programming Computers and Calculators 83

Closure 84

Teaching Competencies and Self-Assessment Tasks 85

Chapter 5 Problem Solving and Mathematical Language 87

The Nature of Problem Solving 88

Problem-Solving Strategies 91

Research Snapshot 93

Approaching Word Problems Effectively 98

Logic and Reasoning 101

The Language of Logic 101

The Language of Mathematics 103

Closure 107

Practice Exercises for Teachers 108

Teaching Competencies and Self-Assessment Tasks 111

Sample Instructional and Assessment Activities 112

Chapter 6 Number Sense, Numeration, and Place Value 115

A Foundation for Mathematics Development 116

Patterns and Other Relationships in the Primary Curriculum 117

Number Sense 118

Number Relations 123

Extending Numberness Concepts 125

Place-Value Numeration 125

Decimal Numeration 126

Ancient Numeration Systems 131

Research Snapshot 133

Number Bases Other Than Ten 134

Closure 137

Practice Exercises for Teachers 138

Teaching Competencies and Self-Assessment Tasks 141

Sample Instructional and Assessment Activities 142

Chapter 7 Addition and Subtraction of Whole Numbers 145

Creating a Sound Base for Addition and Subtraction 146

Meaning and Models for Addition 147

Developing Basic Addition Facts 148

Memorizing Basic Addition Facts Using Structures 149

Extending Basic Addition Facts Using Place Value 155

Regrouping in the Addition Process 156

Meaning and Models for Subtraction 157

Research Snapshot 158

Developing Basic Subtraction Facts 160

Memorizing Basic Subtraction Facts Using Structures 161

Extending Basic Subtraction Facts Using Place Value 162

Regrouping in the Subtraction Process 163 Closure 164

Practice Exercises for Teachers 166

Teaching Competencies and Self-Assessment Tasks 167

Sample Instructional and Assessment Activities 167

Chapter 8 Multiplication and Division of Whole Numbers 171

Meaning and Models for Multiplication 172

Developing and Memorizing Basic Multiplication Facts 175

Expanding Basic Multiplication Facts Through Place Value 178

Regrouping in Multiplication 181

Meaning and Models for Division 183

Research Snapshot 183

Developing and Memorizing Basic Division Facts 186

Remainders in Division 187

Expanding Basic Division Facts Through Place Value 187

Closure 190

Practice Exercises for Teachers 191

Teaching Competencies and Self-Assessment Tasks 192

Sample Instructional and Assessment Activities 193

Chapter 9 Number Theory and Number Systems 197

The Language of Number Theory 199

The Sieve of Eratosthenes 200

Factor Trees 202

Prime Factorization 203

Divisibility ‘‘Rules’’ 205

Research Snapshot 207

Least Common Multiples and Greatest Common Factors 207

Number Systems 209

Closure 218

Practice Exercises for Teachers 218

Teaching Competencies and Self-Assessment Tasks 221

Sample Instructional and Assessment Activities 222

Chapter 10 Algebraic Reasoning: Generalizing

Patterns and Relationships 225

The Content of Algebra 226

Research Snapshot 227

Algebra in Problem Solving 228

Promoting Algebraic Thinking in the Lower Elementary Grades 229

Enhancing Algebraic Thinking in the Upper Elementary and Middle Grades 232

Closure 236

Practice Exercises for Teachers 237

Teaching Competencies and Self-Assessment Tasks 240

Sample Instructional and Assessment Activities 241

Chapter 11 Rational Numbers Expressed as Fractions: Concepts 245

A Fraction of the History of Fractional Numbers 246

Rational Numbers—A Definition and Description 247

Research Snapshot 247

The Regions Model for Fractional Numbers 248

The Groups of Objects Model for Fractional Numbers 250

The Number Line Model for Fractional Numbers 251

Knowledge and Understandings Prior to Operations on Rational Numbers Expressed as Fractions 253

Closure 258

Practice Exercises for Teachers 260

Teaching Competencies and Self-Assessment Tasks 262

Sample Instructional and Assessment Activities 263

Chapter 12 Rational Numbers Expressed as Fractions: Operations 267

Research Snapshot 268

Addition of Fractional Numbers 269

Subtraction of Fractional Numbers 274

Multiplication of Fractional Numbers 278

Division of Fractional Numbers 282

Closure 285

Practice Exercises for Teachers 286

Teaching Competencies and Self-Assessment Tasks 288

Sample Instructional and Assessment Activities 288

Chapter 13 Rational Numbers Expressed as Decimals 291

Models That Give Decimals Meaning 292

Place Value—A Foundation for Decimals 293

Exponential Notation 295

Addition with Decimal Numbers 296

Subtraction with Decimal Numbers 297

Multiplication with Decimal Numbers 299

Division with Decimal Numbers 300

Relating Decimals and Fractions 301

Scientific Notation 303

Ratio, Proportion, and Percent 304

Research Snapshot 305

Closure 311

Practice Exercises for Teachers 312

Teaching Competencies and Self-Assessment Tasks 313

Sample Instructional and Assessment Activities 314

Chapter 14 Data Analysis: Graphs, Statistics, and Probability 317

A Child’s View of Statistics 318

Measures of Central Tendency in Data 319

Research Snapshot 320

Organizing and Interpreting Data 321

Taking a ‘‘Chance’’ 326

Experimental Probability 326

Theoretical Probability 327

Permutations and Combinations 328

Models for Exploring Probability 330

Closure 331

Practice Exercises for Teachers 332

Teaching Competencies and Self-Assessment Tasks 334

Sample Instructional and Assessment Activities 335

Chapter 15 Measurement 339

The Historical Development of Measurement Systems 340

Contemporary Measurement Systems 341

The Process of Measurement 345

Computing with Denominate Numbers 349

Money and Time as Measures 350

Research Snapshot 352

Closure 354

Practice Exercises for Teachers 354

Teaching Competencies and Self-Assessment Tasks 356

Sample Instructional and Assessment Activities 357

Chapter 16 Geometry: Basic Concepts and Structures 361

Research Snapshot 362

Early Experiences in Geometry 363

The ‘‘Building Blocks’’ of Geometry 364

Extending the Basics—Curves, Regions, and Rays 366

Angles and Angle Measure 369

Exploring Geometric Constructions 372

Symmetry and Transformational Geometry 374

Other Devices for Exploring Geometric Concepts 376

Closure 377

Practice Exercises for Teachers 378

Teaching Competencies and Self-Assessment Tasks 381

Sample Instructional and Assessment Activities 382

Chapter 17 Geometry: Polygons and Polyhedra 385

Defining Polygons 386

Research Snapshot 386

A Closer Look at Triangles 388

A Closer Look at Quadrilaterals 394

A Closer Look at Circles 395

Area, Perimeter, and Circumference Measurement 397

Defining Polyhedra 401

Closure 409

Practice Exercises for Teachers 410

Teaching Competencies and Self-Assessment Tasks 414

Sample Instructional and Assessment Activities 415

Index 417