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.

Table of Contents:
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