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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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