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

by Heddens, James W.; Speer, William R.; Brahier, Daniel J.

• ISBN13: 9780470286906
• ISBN10: 0470286903
• Edition: 12th
• Format: Paperback
• Copyright: 2009-01-09
• Publisher: WILEY

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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