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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