9780130270214

With the composition of today's classroom in mind, this book approaches teaching and planning elementary mathematics by using methods that accommodate the diverse learning needs of any student having difficulties with basic math concepts. The authors use personal experience and research that supports a complete set of developmental concepts and skills to outline the effective development of mathematical concepts and skills. It stresses lesson planning that will result in learning, understanding, and retaining important concepts and skills. NCTM's Curriculum and Evaluation Standards for School Mathematics are integrated into every chapter. Other topics include: Diversity in the Classroom; Lesson Design: Creating Lessons That Meet the Needs of a Diverse Classroom; Mathematics Learning in Early Childhood; Whole Numbers and Numeration; Fractions; Decimals and Percents; Measurement; and Geometry.

Instructional Activities: The Building Blocks for Effective Instruction

3

(14)

Basics for the Effective Use of Activities, the Building Blocks for Construction of Effective Lesson

3

(6)

What Are the Students Learning?

3

(1)

Developmental Activities

4

(1)

Practice Activities

5

(1)

Application Activities

5

(1)

Assessment Activities

6

(2)

Level of Involvement

8

(1)

Flexibility

9

(4)

Webs of Activities

9

(2)

Content Flexibility Webs

11

(1)

Procedure Flexibility Webs

12

(1)

Exercises and Activities

13

(1)

References and Related Readings

14

(1)

Web Sites

15

(2)

Diversity in the Classroom: Variations of Individual Needs

17

(16)

Why Diverse Classrooms?

17

(2)

Racial, Linguistic, and Cultural Diversity

19

(1)

Learning Style Preferences

20

(2)

Kinds of Intelligence

22

(1)

Low Cognitive Ability

23

(2)

Learning Disabilities

25

(1)

Visual or Auditory Impairments

25

(1)

Physical Impairments

26

(1)

Summary

26

(1)

Exercises and Activities

26

(4)

References and Related Readings

30

(1)

Web Sites

31

(2)

Lesson Design: Creating Lessons That Meet the Needs of a Diverse Classroom

33

(16)

Combining Activities into a Lesson

34

(2)

What is a Lesson?

34

(1)

A Traditional Lesson Plan

35

(1)

The Nature of Standard Traditional Lessons

36

(1)

Adapting Lessons for Diverse Learning Needs

36

(10)

A Lesson Adapted for Diverse Learners

39

(4)

Adapting Another Lesson

43

(3)

Exercises and Activities

46

(1)

References and Related Readings

47

(1)

Web Sites

47

(2)

Beginnings: Mathematics Learning in Early Childhood

49

(20)

A Common Misconception

50

(1)

About Young Children

50

(1)

Teaching Classification

51

(2)

Teaching Comparison and Seriation

53

(6)

Comparison

53

(3)

Seriation

56

(2)

Matching and Prenumber Comparisons

58

(1)

Matching and Prenumber Seriation

58

(1)

The Beginning of Geometric Concepts: Relative Position

59

(4)

A Revised Lesson

63

(2)

Exercises and Activities

65

(1)

References and Related Readings

66

(1)

Web Sites

67

(2)

Whole Numbers and Numeration: Naming and Writing Quantity

69

(26)

Building on What Children Already Know

70

(2)

The Big Picture

72

(1)

Development of Numbers and Numeration

72

(1)

One-Digit Numbers

73

(5)

Two-Digit Numbers

78

(6)

Three or More Digits

84

(3)

Rounding Numbers

87

(2)

Adapting a Lesson

89

(4)

Adapting the Lesson for a Diverse Group of Students

90

(3)

Exercises and Activities

93

(1)

References and Related Readings

94

(1)

Web Sites

94

(1)

Adding and Subtracting Whole Numbers: Combining and Separating Quantities

95

(44)

Teaching Addition of Whole Numbers

96

(22)

An Overview of the Development of Computation

96

(1)

Developmental Sequence for the Addition of Whole Numbers

97

(3)

Developing the Easy Basic Addition Facts

100

(6)

Memorization of the Easy Basic Addition Facts

106

(2)

Thinking Strategies for Hard Basic Addition Facts

108

(3)

Teaching the Hard Basic Addition Facts

111

(2)

Teaching the Addition Algorithm

113

(5)

Summary of the Development Sequence for Addition

118

(1)

Teaching Substration

118

(11)

Developing the Meaning of Substraction

118

(2)

Developing the Easy Basic Subtraction Facts

120

(5)

Thinking Strategies for Hard Basic Substraction Facts

125

(2)

Teaching the Subtraction Algorithm

127

(1)

Summary of the Developmental Sequence for Subtraction

128

(1)

Adapting a Lesson

129

(2)

Teaching Problem Solving Using Addition and Substraction

131

(3)

Exercises and Activities

134

(3)

References and Related Readings

137

(1)

Web Sites

137

(2)

Multiplying and Dividing Whole Numbers: Combining Equal-Sized Groups and Separating Quantities into Equal-Sized Groups

139

(60)

Teaching Multiplication of Whole Numbers

140

(32)

Developmental Sequence for Teaching Multiplication

140

(1)

Developing the Meaning of Multiplication

140

(4)

Teaching the Easy Basic Multiplication Facts

144

(5)

Thinking Strategies for Hard Basic Multiplication Facts

149

(5)

Teaching the Multiplication Algorithm

154

(12)

Summary of Developmental Sequence for Multiplication

166

(1)

Adapting a Multiplication Lesson

167

(5)

Teaching Division of Whole Numbers

172

(23)

Developmental Sequence for Teaching Division

172

(20)

Adapting a Division Lesson

192

(3)

Using Multiplication and Division to Solve Problems

195

(1)

Exercises and Activities

195

(2)

References and Related Readings

197

(1)

Web Sites

197

(2)

Fractions: Working with Units Smaller Than One

199

(46)

Defining Fractions

200

(1)

Three Sides of Fractions

200

(1)

Fractional Units

201

(2)

Beyond Unit Fractions

203

(2)

Fractions of a Set

205

(1)

Equivalent Fractions

206

(2)

Using the Laboratory Approach

208

(3)

Comparison of Fractions

211

(3)

Adding Fractions

214

(2)

Subtracting Fractions

216

(1)

Least Common Denominators

216

(5)

Improper Fractions and Mixed Numbers

221

(2)

Multiplying Fractions

223

(4)

Dividing Fractions

227

(8)

Adapting a Lesson on Fractions

235

(3)

Solving Problems Using Fractions

238

(3)

Problem-Solving Strategies

239

(2)

Exercises and Activities

241

(1)

References and Related Readings

242

(1)

Web Sites

243

(2)

Decimals and Percents: Working with Base-Ten Units Smaller Than One and Using Hundredths as a Common Denominator

245

(36)

Defining Decimals

246

(1)

Place Value for Decimals

247

(6)

Comparison of Decimals

253

(3)

Addition and Substraction of Decimals

256

(3)

Multiplying Decimals

259

(5)

Division of Decimals

264

(7)

Fraction Comparison Revisited

271

(1)

Defining Percent

272

(1)

Adapting a Lesson on Decimals

272

(4)

Using Decimals to Solve Problems

276

(2)

Exercises and Activities

278

(1)

References and Related Readings

279

(1)

Web Sites

279

(2)

Measurement: Assigning a Number to a Quantity

281

(46)

Measurement and Geometry

281

(1)

Defining Measurement

281

(1)

Measuring Length

281

(14)

Teaching Area Measurement

295

(9)

The Big Idea for Developing Area Formulas

299

(5)

Teaching Volume Measurement

304

(9)

Measuring Angles

313

(3)

Measuring with Indirect Units

316

(1)

Measuring Time

317

(1)

Measuring Weight

318

(1)

Measuring Temperature

319

(1)

Measuring Value

319

(1)

Adapting a Lesson on Volume

319

(3)

Using Measurement to Solve Problems

322

(2)

Exercises and Activities

324

(2)

References and Related Readings

326

(1)

Web Sites

326

(1)

Geometry: Learning the Names and Characteristics of Shapes

327

(30)

The Big Ideas of Elementary School Geometry

328

(4)

Straightness

328

(1)

Congruence

328

(1)

Similarity

329

(2)

Parallelism

331

(1)

Perpendicularity

332

(1)

Symmetry

332

(1)

Using the Big Ideas to Study Geometric Shapes

332

(16)

Rectangles in Elementary School

333

(7)

Circles in Elementary School

340

(3)

Angles in Elementary School

343

(3)

Prisms in Elementary School

346

(2)

Adapting a Geometry Lesson

348

(5)

Using Geometry to Solve Problems

353

(2)

Exercises and Activities

355

(1)

References and Related Readings

356

(1)

Web Sites

356

(1)

Effective Practice: Games and Activities for Practice and Fun

357

(22)

Matching Activities

358

(10)

Ordering Activities

368

(5)

Answer/Example Construction Activities

373

(5)

Summary

378

(1)

References and Related Readings

378

(1)

Index

379

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Why This Book? Recently, elementary classrooms have become increasingly diverse. This diversity includes differences in gender, race and ethnicity, religion, culture, ability and interest, learning styles, family background and support, and availability of resources such as books and technology. Furthermore, there is a current trend toward inclusion of special needs children in the regular classroom, a trend unlikely to be reversed in the foreseeable future. Typical preparation of special education teachers and regular classroom teachers does not equip either group to operate effectively in the kind of inclusion settings that they are now likely to see. In this text, we provide an approach to the planning and teaching of elementary school mathematics that will better equip teachers to be successful with diverse groups of students and in inclusion classrooms. We hope the teaching suggestions in this text will help teachers be more effective as they attempt toteach mathematics to all children. Structure of the Book The text begins with three introductory chapters that provide a basic understanding of instructional activities, diversity, and lesson planning. Then there are eight chapters devoted to teaching the content that most commonly appears in elementary school mathematics textbooks. The final chapter is devoted to practice activities that can be adapted to a wide variety of content. We have not attempted to provide comprehensive coverage of every mathematics topic that might appear in an elementary school mathematics textbook. Rather, our intent has been to emphasize a way of teaching effectively that will result in learning, understanding, retention of important concepts and skills, and ability to apply those concepts and skills to solve problems. An important part of that way of teaching is effective planning. Therefore, we have made planning for effective teaching an important part of this text. Emphasis on Concept and Skill Development Based on findings of educational research that support more complete development of concepts and skills, calls from the National Council of Teachers of Mathematics for more effective development in lessons, and our personal experiences, we have chosen to make more effective development of mathematical concepts and skills a major emphasis. As a result of that emphasis, virtually all activities suggested in the chapters related to specific mathematics content are developmental activities. Since we made a conscious choice not to include practice activities in those chapters, the final chapter is devoted to effective practice. In that chapter, we present a selection of practice activities that can be used after the concepts and skills have been taught. Basic Philosophy We believe that successful teaching results in understanding, that understanding provides the most sound basis for skill development, and that understanding results in better retention of what is learned. We believe that the best way to help students understand mathematical ideas is to lead them to connect those ideas to other ideas that they already understand. We believe that, for elementary children, understanding of mathematical concepts and skills depends on the development of appropriate mental imagery for those concepts and skills. And, we believe thatall childrenshould be given the opportunity to develop that kind of understanding of mathematics. Acknowledgments This book evolved over several years from informal conversations with many colleagues about how teachers could plan to teach more effectively, from preservice and inservice teachers who responded to our ideas before they were fully formed, and from reactions of children who demonstrated that the more fully evolved teaching methods really worked. And, of course, invaluable assistance was provided by these professionals, whose reviews of the preliminary manuscript helped to dire

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Teaching Mathematics to All Children : Designing and Adapting Instruction to Meet the Needs of Diverse Learners

Teaching Mathematics to All Children : Designing and Adapting Instruction to Meet the Needs of Diverse Learners

0130270210

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Table of Contents

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