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

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

ISBN: 978-0-470-28690-6

Jan 2009

456 pages

In Stock

$204.95

## Description

Combining theory, methods and instructional activities in one convenient volume, Heddens, Speers and Brahier’s Twelfth Edition of "Today’s Mathematics" provides a valuable set of ideas and reference materials for actual classroom use. This combined coverage of content and methods creates a long-lasting resource, helping pre-service and in-service teachers see the relationship between what they teach and how they teach. Reflecting recent recommendations from the NCTM Standards, the text emphasizes how to introduce a concept at a given level to expand and reinforce it at successive levels.## Related Resources

**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

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

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

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

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

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

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

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

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

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

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

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 238

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

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

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

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

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

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

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

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

- Revision and reorganization of material into chapters that reflect the vision of mathematics learning, teaching and assessment present in the NCTM Curriculum Focal Points (2006) and the most recent NCTM Teaching Standards entitled, Mathematics Teaching Today: Improving Practice, Improving Student Learning (2007).
- A discussion of changes in content and emphasis in Pre-K-8 mathematics
- A listing of the NCTM standards for grades Pre-K-2, 3-5 and 6-8 and a supporting set of references.
- An example of a complete NCTM standard (see chapter on Technology in Mathematics, a discussion of the role of the computer technology in elementary/middle grades is supported by the complete text of the NCTM position paper on technology in the classroom and a set of activities for grades Pre-K-8.)
- On the CD that accompanies the text, each chapter has both primary and intermediate sample lesson plans for each of the content chapters to aid in putting research theory into classroom practice.