Textbook
Today's Mathematics: Concepts, Methods, and Classroom Activities, 12th EditionJanuary 2009, ©2009

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 SelfAssessment
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 FollowUp 36
The Assessment of Learning and Teaching 37
Adjusting Instruction to Meet Individual Needs 38
Classroom Instructional Aids 39
Closure 40
Teaching Competencies and SelfAssessment
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 SelfAssessment
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 SelfAssessment
Tasks 85
Chapter 5
Problem Solving and Mathematical
Language 87
The Nature of Problem Solving 88
ProblemSolving 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 SelfAssessment
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
PlaceValue 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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 SelfAssessment
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 PreK8 mathematics

A listing of the NCTM standards for grades PreK2, 35 and 68 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 PreK8.)

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.
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