Guiding Children's Learning of Mathematics (11TH)

Guiding Children's Learning of Mathematics (11TH)

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  • 言語 ENG,ENG
  • 商品コード 9780495091912
  • DDC分類 372.7

Table of Contents

        List of Activities                         xv
Preface xix
PART ONE Guiding Elementary Mathematics with 1 (110)
Standards
Elementary Mathematics for the 21st Century 3 (8)
Solving Problems Is Basic 4 (1)
A Comprehensive Vision of Mathematics 5 (4)
Principles of School Mathematics 6 (1)
The Mathematics Curriculum Principle 7 (1)
The Equity Principle 7 (1)
The Learning Principle 8 (1)
The Teaching Principle 8 (1)
The Assessment Principle 8 (1)
The Technology Principle 8 (1)
Implementing the Principles and Standards 9 (1)
Study Questions and Activities 9 (1)
Teacher's Resources 9 (2)
Defining a Comprehensive Mathematics 11 (16)
Curriculum
Connecting Concepts, Skills, and 12 (1)
Application
What Elementary Children Need to Know in 12 (7)
Mathematics
Numbers and Number Operations 13 (1)
Geometry 14 (1)
Measurement 15 (1)
Data Analysis and Probability 16 (1)
Algebra 17 (2)
Learning Mathematical Processes 19 (4)
Problem Solving 19 (1)
Reasoning and Proof 20 (1)
Communication 21 (1)
Connection 21 (1)
Mathematical Representation 22 (1)
Integrating Process and Content Standards 23 (2)
Finding Focus 25 (1)
Summary 26 (1)
Study Questions and Activities 26 (1)
Teacher's Resources 26 (1)
Mathematics for Every Child 27 (20)
Equity in Mathematics Learning 28 (1)
Gender 29 (1)
Ethnic and Cultural Differences 30 (4)
Multiculturalism 31 (1)
Ethnomathematics 31 (3)
Students Who Have Limited English 34 (3)
Proficiency
Technological Equity 37 (1)
Students Who Have Difficulty Learning 37 (3)
Mathematics
Gifted and Talented Students 40 (2)
Individual Learning Styles 42 (2)
Multiple Intelligences 43 (1)
Learning Styles 43 (1)
Summary 44 (1)
Study Questions and Activities 44 (1)
Teacher's Resources 44 (1)
For Further Reading 45 (2)
Learning Mathematics 47 (10)
Theories of Learning 48 (1)
Behaviorism 48 (1)
Cognitive Theories 48 (1)
Key Concepts in Learning Mathematics 48 (4)
Focus on Meaning 48 (1)
Developmental Stages 49 (1)
Social Interactions 50 (1)
Concrete Experiences 50 (1)
Levels of Representation 50 (1)
Procedural Learning 51 (1)
Short-Term to Long-Term Memory 51 (1)
Pattern Making 51 (1)
Thinking to Learn 52 (1)
Research in Learning and Teaching 52 (4)
Mathematics
Reviews of Research 54 (2)
Teachers and Action Research 56 (1)
Summary 56 (1)
Study Questions and Activities 56 (1)
Teacher's Resources 56 (1)
Organizing Effective Instruction 57 (22)
What Is Effective Mathematics Teaching? 58 (2)
Using Objectives to Guide Mathematics 58 (2)
Instruction
Becoming an Effective Teacher 60 (1)
Using Objectives in Planning Mathematics 60 (3)
Instruction
Long-Range Planning 61 (1)
Unit Planning 61 (1)
Daily Lesson Planning 62 (1)
Varying Teaching Approaches 63 (5)
Informal or Exploratory Activities 63 (1)
Directed Teaching/Thinking Lessons 63 (3)
Problem-Based Projects and 66 (2)
Investigations
Integrating Multiple Approaches 68 (1)
Delivering Mathematics Instruction 68 (4)
Practice 69 (1)
Homework 69 (1)
Grouping 70 (1)
Cooperative Group Learning 70 (2)
Encouraging Mathematical Conversations 72 (1)
Managing the Instructional Environment 72 (5)
Time 72 (1)
Space 73 (1)
Learning Centers 73 (1)
Manipulatives 74 (1)
Textbooks and Other Printed Materials 75 (2)
Children's Literature 77 (1)
Summary 77 (1)
Study Questions and Activities 77 (1)
Teacher's Resources 78 (1)
The Role of Technology in the Mathematics 79 (14)
Classroom
Calculators 80 (3)
Calculator Use 80 (1)
Benefits of Using a Calculator 81 (1)
Research on Calculators in the Classroom 82 (1)
Computers 83 (2)
Research About Computers in the 83 (1)
Classroom
Computer Software 83 (2)
The Internet 85 (3)
Virtual Manipulatives 86 (2)
Computer Games 88 (2)
Video Technology 90 (1)
Summary 90 (1)
Study Questions and Activities 90 (1)
Teacher's Resources 90 (1)
For Further Reading 91 (2)
Integrating Assessment 93 (18)
Connecting Curriculum, Instruction, and 94 (1)
Assessment
Planning for Assessment 94 (7)
Performance Objectives and Tasks 94 (2)
Creating Assessment Tasks 96 (1)
Collecting and Recording Assessment 96 (3)
Information
Analyzing Student Performance and 99 (2)
Making Instructional Decisions
Implementing Assessment with Instruction 101(6)
Preassessment 101(1)
During Instruction 102(2)
Self-Assessment During Instruction 104(1)
Writing as Assessment 104(1)
Assessment at the End of Instruction 105(2)
Interpreting and Using Standardized Tests 107(2)
in Classroom Assessment
Summary 109(1)
Study Questions and Activities 109(1)
Teacher's Resources 110(1)
For Further Reading 110(1)
PART TWO Mathematical Concepts, Skills, and 111(434)
Problem Solving
Developing Problem-Solving Strategies 113(24)
Approaches to Teaching Problem Solving 115(17)
Teaching About, Teaching for, and 115(1)
Teaching via Problem Solving
The Four-Step Problem-Solving Process 115(1)
Eleven Problem-Solving Strategies: 116(16)
Tools for Elementary School Students
Implementing a Problem-Solving Curriculum 132(1)
Take-Home Activities 133(2)
Summary 135(1)
Study Questions and Activities 135(1)
Teacher's Resources 135(1)
Children's Bookshelf 135(1)
For Further Reading 136(1)
Developing Concepts of Number 137(24)
Primary Thinking-Learning Skills 138(5)
Matching and Discriminating, Comparing 138(3)
and Contrasting
Classifying 141(1)
Ordering, Sequence, and Seriation 142(1)
Beginning Number Concepts 143(2)
Number Types and Their Uses 145(1)
Counting and Early Number Concepts 146(5)
Number Constancy 148(3)
Linking Number and Numeral 151(4)
Writing Numerals 153(1)
Misconceptions and Problems with 154(1)
Counting and Numbers
Introducing Ordinal Numbers 154(1)
Other Number Skills 155(3)
Skip Counting 155(1)
One-to-One and Other Correspondences 155(1)
Odd and Even Numbers 156(2)
Summary 158(1)
Study Questions and Activities 158(1)
Teacher's Resources 158(1)
Children's Bookshelf 159(1)
For Further Reading 159(2)
Extending Number Concepts and Number Systems 161(26)
Number Sense Every Day 162(1)
Understanding the Base-10 Numeration 163(4)
System
Exchanging, Trading, or Regrouping 165(1)
Assessing Place-Value Understanding 165(2)
Working with Larger Numbers 167(5)
Thinking with Numbers 172(6)
Rounding 174(1)
Estimation 175(3)
Other Number Concepts 178(4)
Patterns 178(1)
Prime and Composite Numbers 178(1)
Integers 179(3)
Take-Home Activities 182(2)
Summary 184(1)
Study Questions and Activities 184(1)
Using the Technology Center 184(1)
Teacher's Resources 185(1)
Children's Bookshelf 185(1)
Technology Resources 185(1)
For Further Reading 185(2)
Developing Number Operations with Whole 187(42)
Numbers
Building Number Operations 188(1)
What Students Need to Learn About Number 188(2)
Operations
What Teachers Need to Know About Addition 190(2)
and Subtraction
Developing Concepts of Addition and 192(8)
Subtraction
Introducing Addition 192(4)
Introducing Subtraction 196(3)
Vertical Notation 199(1)
What Teachers Need to Know About 200(8)
Properties of Addition and Subtraction
Learning Strategies for Addition and 201(4)
Subtraction Facts
Developing Accuracy and Speed with 205(3)
Basic Facts
What Students Need to Learn About 208(1)
Multiplication and Division
What Teachers Need to Know About 208(4)
Multiplication and Division
Multiplication Situations, Meanings, 208(2)
and Actions
Division Situations, Meanings, and 210(2)
Actions
Developing Multiplication and Division 212(7)
Concepts
Introducing Multiplication 212(4)
Introducing Division 216(2)
Working with Remainders 218(1)
What Teachers Need to Know About 219(1)
Properties of Multiplication and Division
Learning Multiplication and Division 220(5)
Facts with Strategies
Division Facts Strategies 221(3)
Building Accuracy and Speed with 224(1)
Multiplication and Division Facts
Take-Home Activities 225(1)
Summary 226(1)
Study Questions and Activities 226(1)
Teacher's Resources 227(1)
Children's Bookshelf 227(1)
Technology Resources 227(1)
For Further Reading 228(1)
Extending Computational Fluency with Larger 229(24)
Numbers
Number Operations with Larger Numbers 230(17)
Addition and Subtraction Strategies for 231(8)
Larger Numbers
Multiplying and Dividing Larger Numbers 239(8)
Number Sense, Estimation, and 247(3)
Reasonableness
Take-Home Activities 250(1)
Summary 251(1)
Study Activities and Questions 251(1)
Technology Resources 252(1)
For Further Reading 252(1)
Developing Understanding of Common and 253(34)
Decimal Fractions
What Teachers Need to Know About Teaching 255(1)
Common Fractions and Decimal Fractions
Five Situations Represented by Common 256(3)
Fractions
Unit Partitioned into Equal-Size Parts 256(1)
Set Partitioned into Equal-Size Groups 256(1)
Comparison Model 257(1)
Expressions of Ratios 257(1)
Indicated Division 258(1)
Introducing Common Fractions to Children 259(8)
Partitioning Single Things 259(1)
Assessing Knowledge of Common Fractions 260(5)
Partitioning Sets of Objects 265(1)
Fractional Numbers Greater than 1 265(2)
Introducing Decimal Fractions 267(5)
Introducing Tenths 268(1)
Introducing Hundredths 268(3)
Introducing Smaller Decimal Fractions 271(1)
Introducing Mixed Numerals with Decimal 272(1)
Fractions
Comparing Fractional Numbers 272(5)
Comparing Common Fractions 272(1)
Comparing Common and Decimal Fractions 272(4)
with Number Lines
Equivalent Fractions 276(1)
Ordering Fractions 276(1)
Rounding Decimal Fractions 277(4)
Take-Home Activities 281(1)
Summary 282(1)
Study Questions and Activities 282(1)
Using Children's Literature 282(1)
Teacher's Resources 282(1)
Children's Bookshelf 283(1)
Technology Resources 283(1)
For Further Reading 284(3)
Extending Understanding of Common and 287(46)
Decimal Fractions
Standards and Fractional Numbers 288(1)
Teaching Children About Fractional 289(1)
Numbers in Elementary and Middle School
Extending Understanding of Decimal 290(2)
Fractions
Decimal Fractions and Number Density 290(2)
Expanded Notation for Decimal Fractions 292(1)
Extending Concepts of Common and Decimal 292(1)
Fraction Operations
Addition and Subtraction with Common 292(1)
and Decimal Fractions
Addition and Subtraction with Common 293(11)
Fractions
Adding and Subtracting with Like 294(1)
Denominators
Using Algorithms to Compute with 294(3)
Fractional Numbers
Adding and Subtracting When 297(2)
Denominators Are Different
Adding and Subtracting with Mixed 299(3)
Numerals
Least Common Multiples and Greatest 302(2)
Common Factors
Using a Calculator to Add Common Fractions 304(1)
Addition and Subtraction with Decimal 304(1)
Fractions
Multiplication with Common Fractions 305(10)
Multiplying a Fractional Number by a 307(1)
Whole Number
Multiplying a Whole Number by a 308(1)
Fractional Number
Multiplying a Fractional Number by a 308(4)
Fractional Number
Multiplying Mixed Numerals 312(3)
Division with Common Fractions 315(1)
Developing Understanding of Division 315(3)
Algorithms
Developing Number Sense About Operations 318(1)
with Common Fractions
Renaming Fractions in Simpler Terms 319(1)
Multiplying and Dividing with Decimal 320(5)
Fractions
Multiplying with Decimal Fractions 320(2)
Dividing with Decimal Fractions 322(1)
Relating Common Fractions to Decimal 323(2)
Fractions
Using a Calculator to Develop 325(3)
Understanding of Decimal Fractions
Using Calculators with Common Fractions 326(2)
Take-Home Activity 328(1)
Summary 329(1)
Study Questions and Activities 329(1)
Using Children's Literature 330(1)
Teacher's Resources 330(1)
Children's Bookshelf 330(1)
Technology Resources 331(1)
For Further Reading 332(1)
Developing Aspects of Proportional 333(24)
Reasoning: Ratio, Proportion, and Percent
Proportional Reasoning 334(1)
What Teachers Should Know About Teaching 334(1)
Proportional Reasoning
Ratios as a Foundation of Proportional 335(1)
Reasoning
Meanings of Ratio 335(1)
Teaching Proportional Reasoning 336(2)
Developing Proportional Reasoning Using 338(1)
Rate Pairs and Tables
Working with Proportions 339(5)
Using Equivalent Fractions 339(1)
Solving Proportions Using a Multiples 340(3)
Table
Solving for Proportion Using the 343(1)
Cross-Product Algorithm
Developing and Extending Concepts of 344(9)
Percent
Meaning of Percent 345(1)
Teaching and Learning About Percent 346(1)
Working with Percent 346(5)
Proportional Reasoning and Percent 351(1)
Working with Percents Greater Than 100 351(2)
Take-Home Activities 353(1)
Summary 354(1)
Study Questions and Activities 354(1)
Using Children's Literature 354(1)
Teacher's Resources 355(1)
Children's Bookshelf 355(1)
Technology Resources 355(1)
For Further Reading 356(1)
Thinking Algebraically 357(32)
What Teachers Should Know About Teaching 358(5)
Algebra
Patterning as Algebraic Thinking 358(1)
Patterns in Mathematics Learning and 359(4)
Teaching
Variables and Equations in Mathematics 363(5)
and Algebraic Thinking
Equations in Algebraic Thinking 368(1)
Functions in Algebraic Thinking 369(4)
Extending Algebraic Thinking 373(5)
Extending Understanding of Patterning 373(5)
Extending Understanding of Equations 378(1)
Extending the Meaning of Functions 379(5)
Take-Home Activities 384(2)
Summary 386(1)
Study Questions and Activities 386(1)
Using Children's Literature 386(1)
Teacher's Resources 387(1)
Children' Bookshelf 387(1)
Technology Resources 387(1)
For Further Reading 388(1)
Developing Geometric Concepts and Systems 389(48)
Children's Development of Spatial Sense 390(2)
What Teachers Need to Know About Teaching 392(4)
Geometry
Development of Geometric Concepts: Stages 396(1)
of Geometry Understanding
Teaching and Learning About Topological 397(3)
Geometry
Proximity and Relative Position 397(1)
Separation 398(1)
Order 398(1)
Enclosure 399(1)
Topological Mazes and Puzzles 400(1)
Teaching and Learning About Euclidean 400(11)
Geometry
Geometry in Two Dimensions 400(3)
Points, Lines, Rays, Line Segments, and 403(3)
Angles
Geometry in Three Dimensions: Space 406(1)
Figures
Geometric Properties: Congruence and 407(2)
Similarity
Geometric Properties: Symmetry 409(2)
Teaching and Learning About 411(1)
Transformational Geometry
Teaching and Learning About Coordinate 412(2)
Geometry
Extending Geometry Concepts 414(17)
Classifying Polygons 417(3)
Extending Geometry in Three Dimensions 420(1)
Extending Congruence and Similarity 421(1)
Extending Concepts of Symmetry 422(2)
Extending Concepts of Transformational 424(7)
Geometry
Take-Home Activities 431(1)
Summary 432(1)
Study Questions and Activities 432(1)
Using Children's Literature 433(1)
Teacher's Resources 433(1)
Children's Bookshelf 433(1)
Technology Resources 434(1)
For Further Reading 435(2)
Developing and Extending Measurement 437(52)
Concepts
Direct and Indirect Measurement 439(1)
Measuring Processes 439(1)
What Teachers Should Know About Teaching 440(4)
Measurement
Approximation, Precision, and Accuracy 440(1)
Selecting Appropriate Units and Tools 441(3)
A Teaching/Learning Model for Measurement 444(2)
Activities to Develop Measurement 446(4)
Concepts and Skills
Nonstandard Units of Measure 446(3)
Standard Units of Measure 449(1)
Teaching Children How to Measure Length 450(1)
Perimeters 450(1)
Teaching Children About Measuring Area 451(1)
Teaching Children About Measuring 452(1)
Capacity and Volume
Teaching Children About Measuring Weight 453(1)
(Mass)
Teaching Children About Measuring Angles 453(1)
Teaching Children About Measuring 454(1)
Temperature
Teaching Children to Measure Time 454(4)
Clocks and Watches 456(2)
Calendars 458(1)
Teaching Children to Use Money 458(2)
Extending Measurement Concepts 460(1)
Extending Concepts About Length 461(4)
Estimation and Mental Models of Length 464(1)
Extending Concepts About Area 465(5)
Measuring and Estimating Area 465(1)
Inventing Area Formulas 466(4)
Extending Capacity Concepts 470(1)
Extending Volume Concepts 470(3)
Extending Mass and Weight Concepts 473(2)
Estimating Weights and Weighing with 473(1)
Scales
Exploring Density 474(1)
Expanding Angle Concepts 475(3)
Expanding Temperature Concepts 478(1)
Extending Concepts of Time 479(1)
Measurement Problem Solving and Projects 480(1)
Take-Home Activities 481(3)
Summary 484(1)
Study Questions and Activities 484(1)
Using Children's Literature 485(1)
Teacher's Resources 485(1)
Children's Bookshelf 486(1)
Technology Resources 486(1)
For Further Reading 487(2)
Understanding and Representing Concepts of 489(34)
Data
Data Collection 490(1)
What Teachers Should Know About 491(8)
Understanding and Representing Concepts
of Data
Organizing Data in Tables 491(3)
Object and Picture Graphs 494(1)
Bar Graphs 495(3)
Statistics 498(1)
Extending Data Concepts 499(3)
Using Graphs to Work with Data 499(3)
Histograms 502(8)
Line Graphs 502(2)
Circle Graphs 504(2)
Stem-and-Leaf Plots 506(2)
Box-and-Whisker Plots 508(2)
Extending Children's Understanding of 510(7)
Statistics
Take-Home Activity 517(2)
Summary 519(1)
Study Questions and Activities 519(1)
Using Children's Literature 520(1)
Teacher's Resources 520(1)
Children's Bookshelf 520(1)
Technology Resources 521(1)
For Further Reading 521(2)
Investigating Probability 523(22)
Two Types of Probability 524(1)
What Teachers Should Know About Teaching 525(3)
Probability
Extending Probability Understanding 528(1)
Probability Investigations 529(4)
Combinations 532(1)
Sampling 533(1)
Geometric Probability 533(3)
Expected Value 536(3)
Simulations 539(1)
Take-Home Activities 540(1)
Summary 541(1)
Study Questions and Activities 541(1)
Using Children's Literature 541(1)
Teacher's Resources 542(1)
Children's Bookshelf 542(1)
Technology Resources 542(1)
For Further Reading 542(3)
Appendix A NCTM Table of Standards and 545(12)
Expectations
Appendix B Black-Line Masters 557(8)
Glossary 565(6)
References 571(6)
Index 577