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

**by**James W. Heddens (Emeritus, Kent State University); William R. Speer (University of Nevada, Las Vegas); Daniel J. Brahier (Bowling Green State University)

12th

### 9780470286906

0470286903

Paperback

1/1/2009

WILEY

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## Questions About This Book?

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This is the 12th edition with a publication date of 1/1/2009.

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## Summary

Elementary school math teachers need a resource that provides a valuable set of ideas and reference materials for actual classroom use. Now in its 12 th edition, this successful book will help them thoroughly understand today's NCTM standards and how to present them in the most effective way possible. It includes increased coverage of diversity while integrating the latest NCTM guidelines. Readers will also find improved and increased coverage of technology. And they'll benefit from a new feature that addresses math anxiety. Elementary math teachers will quickly discover how to put the principles of mathematics to work in the classroom.

## Author Biography

**James Heddens**is a Professor Emeritus from Kent State University.

## Table of Contents

Chapter 1 | |

Learning Mathematics | p. 1 |

Societal Needs | p. 2 |

Calls for Change | p. 3 |

National and International Achievement | p. 3 |

The Identification of Standards | p. 5 |

Principles and Standards for School Mathematics | p. 6 |

Implementing the Process Standards | p. 8 |

Describing A Contemporary Mathematics Program | p. 10 |

Levels of Abstraction | p. 11 |

Theoretical Foundations for a Contemporary Mathematics Program | p. 12 |

Theory into Practice | p. 17 |

Closure | p. 18 |

Teaching Competencies and Self-Assessment Tasks | p. 19 |

Chapter 2 | |

Teaching Mathematics | p. 21 |

The NCTM Principles and Standards for School Mathematics | p. 22 |

The NCTM Professional Teaching Standards: Mathematics Teaching Today | p. 23 |

An Example of a Teaching Standard | p. 25 |

Lesson Planning Processes and Purposes | p. 29 |

Issues in Designing Mathematics Lessons | p. 33 |

Mathematics Objectives | p. 35 |

The Role of Motivation and Follow-Up | p. 36 |

The Assessment of Learning and Teaching | p. 37 |

Adjusting Instruction to Meet Individual Needs | p. 38 |

Classroom Instructional Aids | p. 39 |

Closure | p. 40 |

Teaching Competencies and Self-Assessment Tasks | p. 41 |

Chapter 3 | |

Assessing Mathematics | p. 43 |

NCTM Assessment Standards for School Mathematics | p. 44 |

An Example of an Assessment Standard | p. 47 |

A Classroom Assessment Vignette | p. 48 |

Purposes for Assessment | p. 49 |

Assessment Strategies | p. 51 |

Closure | p. 58 |

Teaching Competencies and Self-Assessment Tasks | p. 59 |

Chapter 4 | |

Technology in K-8 Mathematics | p. 61 |

A Brief History of Technology's Influence on Education | p. 62 |

Calculators and Exploration of Mathematical Concepts | p. 63 |

Calculator Features and Functions | p. 66 |

Examples of Effective Calculator Use | p. 66 |

Tools for Measuring Motion | p. 68 |

Computers and Mathematics Instruction | p. 69 |

Instructional Software in the Mathematics Classroom | p. 71 |

Application Software in the Mathematics Classroom | p. 72 |

Virtual Manipulatives | p. 73 |

Design Issues and Advantages of Virtual Manipulatives | p. 74 |

Classification Attributes for Virtual Manipulatives | p. 75 |

Capsule Descriptions of the National Library of Virtual Manipulatives | p. 76 |

Multimedia in the Mathematics Classroom | p. 81 |

The Internet in the Mathematics Classroom | p. 82 |

Programming Computers and Calculators | p. 83 |

Closure | p. 84 |

Teaching Competencies and Self-Assessment Tasks | p. 85 |

Chapter 5 | |

Problem Solving and Mathematical Language | p. 87 |

The Nature of Problem Solving | p. 88 |

Problem-Solving Strategies | p. 91 |

Approaching Word Problems Effectively | p. 98 |

Logic and Reasoning | p. 101 |

The Language of Logic | p. 101 |

The Language of Mathematics | p. 103 |

Closure | p. 107 |

Practice Exercises for Teachers | p. 108 |

Teaching Competencies and Self-Assessment Tasks | p. 111 |

Sample Instructional and Assessment Activities | p. 112 |

Chapter 6 | |

Number Sense, Numeration, and Place Value | p. 115 |

A Foundation for Mathematics Development | p. 116 |

Patterns and Other Relationships in the Primary Curriculum | p. 117 |

Number Sense | p. 118 |

Number Relations | p. 123 |

Extending Numberness Concepts | p. 125 |

Place-Value Numeration | p. 125 |

Decimal Numeration | p. 126 |

Ancient Numeration Systems | p. 131 |

Number Bases Other Than Ten | p. 134 |

Closure | p. 137 |

Practice Exercises for Teachers | p. 138 |

Teaching Competencies and Self-Assessment Tasks | p. 141 |

Sample Instructional and Assessment Activities | p. 142 |

Chapter 7 | |

Addition and Subtraction of Whole Numbers | p. 145 |

Creating a Sound Base for Addition and Subtraction | p. 146 |

Meaning and Models for Addition | p. 147 |

Developing Basic Addition Facts | p. 148 |

Memorizing Basic Addition Facts Using Structures | p. 149 |

Extending Basic Addition Facts Using Place Value | p. 155 |

Regrouping in the Addition Process | p. 156 |

Meaning and Models for Subtraction | p. 157 |

Developing Basic Subtraction Facts | p. 160 |

Memorizing Basic Subtraction Facts Using Structures | p. 161 |

Extending Basic Subtraction Facts Using Place Value | p. 162 |

Regrouping in the Subtraction Process | p. 163 |

Closure | p. 164 |

Practice Exercises for Teachers | p. 166 |

Teaching Competencies and Self-Assessment Tasks | p. 167 |

Sample Instructional and Assessment Activities | p. 167 |

Chapter 8 | |

Multiplication and Division of Whole Numbers | p. 171 |

Meaning and Models for Multiplication | p. 172 |

Developing and Memorizing Basic Multiplication Facts | p. 175 |

Expanding Basic Multiplication Facts Through Place Value | p. 178 |

Regrouping in Multiplication | p. 181 |

Meaning and Models for Division | p. 183 |

Developing and Memorizing Basic Division Facts | p. 186 |

Remainders in Division | p. 187 |

Expanding Basic Division Facts Through Place Value | p. 187 |

Closure | p. 190 |

Practice Exercises for Teachers | p. 191 |

Teaching Competencies and Self-Assessment Tasks | p. 192 |

Sample Instructional and Assessment Activities | p. 193 |

Chapter 9 | |

Number Theory and Number Systems | p. 197 |

The Language of Number Theory | p. 199 |

The Sieve of Eratosthenes | p. 200 |

Factor Trees | p. 202 |

Prime Factorization | p. 203 |

Divisibility ''Rules'' | p. 205 |

Least Common Multiples and Greatest Common Factors | p. 207 |

Number Systems | p. 209 |

Closure | p. 218 |

Practice Exercises for Teachers | p. 218 |

Teaching Competencies and Self-Assessment Tasks | p. 221 |

Sample Instructional and Assessment Activities | p. 222 |

Chapter 10 | |

Algebraic Reasoning: Generalizing Patterns and Relationships | p. 225 |

The Content of Algebra | p. 226 |

Algebra in Problem Solving | p. 228 |

Promoting Algebraic Thinking in the Lower Elementary Grades | p. 229 |

Enhancing Algebraic Thinking in the Upper Elementary and Middle Grades | p. 232 |

Closure | p. 236 |

Practice Exercises for Teachers | p. 238 |

Teaching Competencies and Self-Assessment Tasks | p. 240 |

Sample Instructional and Assessment Activities | p. 241 |

Chapter 11 | |

Rational Numbers Expressed as Fractions: Concepts | p. 245 |

A Fraction of the History of Fractional Numbers | p. 246 |

Rational Numbers-A Definition and Description | p. 247 |

The Regions Model for Fractional Numbers | p. 248 |

The Groups of Objects Model for Fractional Numbers | p. 250 |

The Number Line Model for Fractional Numbers | p. 251 |

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

Closure | p. 258 |

Practice Exercises for Teachers | p. 260 |

Teaching Competencies and Self-Assessment tasks | p. 262 |

Sample Instructional and Assessment Activities | p. 263 |

Chapter 12 | |

Rational Numbers Expressed as Fractions: Operations | p. 267 |

Addition of Fractional Numbers | p. 269 |

Subtraction of Fractional Numbers | p. 274 |

Multiplication of Fractional Numbers | p. 278 |

Division of Fractional Numbers | p. 282 |

Closure | p. 285 |

Practice Exercises for Teachers | p. 286 |

Teaching Competencies and Self-Assessment Tasks | p. 288 |

Sample Instructional and Assessment Activities | p. 288 |

Chapter 13 | |

Rational Numbers Expressed as Decimals | p. 291 |

Models That Give Decimals Meaning | p. 292 |

Place Value-A Foundation for Decimals | p. 293 |

Exponential Notation | p. 295 |

Addition with Decimal Numbers | p. 296 |

Subtraction with Decimal Numbers | p. 297 |

Multiplication with Decimal Numbers | p. 299 |

Division with Decimal Numbers | p. 300 |

Relating Decimals and Fractions | p. 301 |

Scientific Notation | p. 303 |

Ratio, Proportion, and Percent | p. 304 |

Closure | p. 311 |

Practice Exercises for Teachers | p. 312 |

Teaching Competencies and Self-Assessment Tasks | p. 313 |

Sample Instructional and Assessment Activities | p. 314 |

Chapter 14 | |

Data Analysis: Graphs, Statistics, and Probability | p. 317 |

A Child's View of Statistics | p. 318 |

Measures of Central Tendency in Data | p. 319 |

Organizing and Interpreting Data | p. 321 |

Taking a ''Chance'' | p. 326 |

Experimental Probability | p. 326 |

Theoretical Probability | p. 327 |

Permutations and Combinations | p. 328 |

Models for Exploring Probability | p. 330 |

Closure | p. 331 |

Practice Exercises for Teachers | p. 332 |

Teaching Competencies and Self-Assessment Tasks | p. 334 |

Sample Instructional and Assessment Activities | p. 335 |

Chapter 15 | |

Measurement | p. 339 |

The Historical Development of Measurement Systems | p. 340 |

Contemporary Measurement Systems | p. 341 |

The Process of Measurement | p. 345 |

Computing with Denominate Numbers | p. 349 |

Money and Time as Measures | p. 350 |

Closure | p. 354 |

Practice Exercises for Teachers | p. 354 |

Teaching Competencies and Self-Assessment Tasks | p. 356 |

Sample Instructional and Assessment Activities | p. 357 |

Chapter 16 | |

Geometry: Basic Concepts and Structures | p. 361 |

Early Experiences in Geometry | p. 363 |

The ''Building Blocks'' of Geometry | p. 364 |

Extending the Basics-Curves, Regions, and Rays | p. 366 |

Angles and Angle Measure | p. 369 |

Exploring Geometric Constructions | p. 372 |

Symmetry and Transformational Geometry | p. 374 |

Other Devices for Exploring Geometric Concepts | p. 376 |

Closure | p. 377 |

Practice Exercises for Teachers | p. 378 |

Teaching Competencies and Self-Assessment Tasks | p. 381 |

Sample Instructional and Assessment Activities | p. 382 |

Chapter 17 | |

Geometry: Polygons and Polyhedra | p. 385 |

Defining Polygons | p. 386 |

A Closer Look at Triangles | p. 388 |

A Closer Look at Quadrilaterals | p. 394 |

A Closer Look at Circles | p. 395 |

Area, Perimeter, and Circumference Measurement | p. 397 |

Defining Polyhedra | p. 401 |

Closure | p. 409 |

Practice Exercises for Teachers | p. 410 |

Teaching Competencies and Self-Assessment Tasks | p. 414 |

Sample Instructional and Assessment Activities | p. 415 |

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