Ann Haltom Singleton is Associate Dean of the School of Education at Union University in Jackson, Tennessee. She earned her EdD in Special Education from the University of Memphis.  Her research areas include leadership development and mathematics instruction, especially in inclusive settings. She has contributed to numerous articles and has made over 30 national presentations. She was recognized as the Union University 2003 Faculty of the Year.

Terry L. Weaver honed his teaching skills in the Miami-Dade County School System. He received his PhD in Special Education from George Peabody College for Teachers at Vanderbilt University. Dr. Weaver then shared his teaching skills at Carson-Newman College and Union University where he continues to teach. Dr. Weaver has served as an item writer for and participated in the revalidation of the Praxis II Specialty Area Test in SE (Core Knowledge). He is a co-author of Teaching Mathematics to All Children, Designing and Adapting Instruction to Meet the Needs of Diverse Learners, has presented on differentiated instruction and assessment, universal design, inclusion, and adapting instruction for diverse learners, and recently lead the revision of a chapter on mathematics in Vaughn’s and Bos’s Strategies for Teaching Students with Learning and Behavior Problems. Drs. Tucker, Singleton, and Weaver have published numerous articles on teaching mathematics.

About the authors x

Preface xi

1 Instructional Activities:

T he Building Blocks for Effective Instruction 1

Exploratory Developmental Activities 2

Consolidating Developmental Activities 2

Think-Time Practice Activities 3

Speed-Drill Practice Activities 3

Classroom Applications 3

Real-World Problems 4

Varied Assessment Methods 4

Monitoring and Assessment 4

2 Less on Design:

C reating Lessons That Meet the Needs of a Diverse Classroom 10

What Is a Lesson? 10

A Traditional Lesson Plan 11

A Lesson Adapted for Diverse Learners 16

Adapting Another Lesson 19

contents

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vi C o n t e n t s

3 Beginnings:

M athematics Learning in Early Childhood 25

Comparison 29

Seriation 32

Matching and Prenumber Comparisons 33

Matching and Prenumber Seriation 33

4 Whole Nu mbers and Nu meration:

N aming and Writing Quantity 42

Development of Numbers and Numeration 45

Adapting the Lesson for a Diverse Group of Students 61

5 Adding and Subtracting Whole Nu mbers:

C ombining and Separating Quantities 65

The Meaning of the Operation 65

The Basic Facts 66

The Algorithm(s) 66

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C o n t e n t s vii

Developing the Meaning of Addition 67

Developing the Easy Basic Addition Facts 69

Activities for Exploring Relationships 73

Developing the Hard Basic Addition Facts 76

Teaching the Addition Algorithm 82

Summary of the Developmental Sequence for Addition 85

Developing the Meaning of Subtraction 86

Developing the Easy Basic Subtraction Facts 87

Developing the Hard Basic Subtraction Facts 90

Teaching the Subtraction Algorithm 92

Summary of the Developmental Sequence for Subtraction 93

6 Mu ltiplying and Dividing Whole Nu mbers:

C ombining Equal-Sized Groups and Separating Quantities

into Equal-Sized Groups 101

Developing the Meaning of Multiplication 101

Developing the Easy Basic Multiplication Facts 103

Developing the Hard Basic Multiplication Facts 107

Teaching the Multiplication Algorithm 111

Summary of the Developmental Sequence for Multiplication 121

Adapting a Multiplication Lesson 121

Developing the Meaning of Division 127

Developing the Easy Basic Division Facts 129

Developing the Hard Basic Division Facts 131

Teaching the Division Algorithm 133

Adapting a Division Lesson 144

7 Fractions:

Working with Units Smaller Than One 150

Three Sides of Fractions 151

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viii C o n t e n t s

Beyond Unit Fractions 154

8 Decimals:

Working with Base-Ten Units Smaller Than One 172

9 Measu rement:

A ssigning a Number to a Quantity 189

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C o n t e n t s ix

10 Geometry:

L earning the Names and Characteristics of Shapes 216

Straightness 217

Congruence 217

Similarity 218

Parallelism 218

Perpendicularity 219

Symmetry 220

Rectangles in Elementary School 220

Circles in Elementary School 225

Angles in Elementary School 228

Prisms in Elementary School 230

11 Data Analysis and Probability:

G etting Information from Data and Measuring Likelihood 237

Emphasizing the Big Ideas of Data Analysis 238

From Exploratory Experiences toward Conceptual Understanding:

A Typical K—4 Development of Data Analysis 238

Adapting a Data Analysis Lesson 245

Using Data Analysis to Solve Problems 250

Emphasizing the Big Ideas of Probability 250

From Exploratory Experiences toward Conceptual Understanding:

A Typical K—4 Development of Probability 251

Using Probability to Solve Problems 256

A ctivities to Take to Your Class room 258

I ndex 260

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about the authors

Benny F. Tucker earned his Ph.D. at the University of Illinois in 1975. He has authored

or co-authored more than 50 books, on topics ranging from teaching methods for elementary

school mathematics to the use of instructional activities in the mathematics

classroom. He has authored or co-authored more than 20 articles in professional journals

and has made more than 30 presentations at professional conferences.

Ann Haltom Singleton is Associate Dean of the School of Education at Union University

in Jackson Tennessee. She earned her Ed.D. in Special Education from the University

of Memphis. Her research areas include leadership development and mathematics

instruction, especially in inclusive settings. She has contributed to numerous articles and

has made over 30 national presentations. She was recognized as the Union University

2003 Faculty of the Year.

Terry L. Weaver honed his teaching skills in the Miami-Dade County School System.

He received his Ph.D. in Special Education from George Peabody College for Teachers

at Vanderbilt University. Dr. Weaver then shared his teaching skills at Carson-Newman

College and Union University where he continues to teach. Dr. Weaver has served as an

item writer for and participated in the revalidation of the Praxis II Specialty Area Test

in SE (Core Knowledge). He is a co-author of Teaching Mathematics to All Children:

Designing and Adapting Instruction to Meet the Needs of Diverse Learners, has presented

on differentiated instruction and assessment, universal design, inclusion, and adapting

instruction for diverse learners, and recently lead the revision of a chapter on mathematics

in Vaughn’s and Bos’s Strategies for Teaching Students with Learning and Behavior

Problems.

x

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xi

Why This Book?

The diversity of students in K—4 classrooms is extensive. The children in a typical classroom

are diverse in gender, diverse in race and ethnicity, and diverse in religion and

culture. They are diverse in ability, diverse in interests, and diverse in preferred learning

styles. And they are diverse in family background, and diverse with respect to resources

in the home such as books and technology. In the face of such diversity, how can the

teacher expect to plan for effective instruction?

Although teachers must certainly be aware of student diversity and the need to

accommodate that diversity, it is perhaps more important for K—4 teachers to be aware of

the ways in which their students are alike. For example, almost universally, children are

kinesthetic

learners. It is natural for them to be active and move around. They love classroom

activities that allow (even require) them to be energetic and animated. Children

are also naturally inquisitive. They are interested in what, why, and how. It is the nature

of children to be curious about things. They like to talk to one another, to exchange

ideas, and to discuss the things that they are experiencing and learning. Children are

concrete learners. They enjoy handling things, seeing how things are related. They

like to understand.

In this text, we provide an approach to the planning and teaching of K—4 mathematics

that is based on the nature of children. We believe that the teaching suggestions in

this text will help teachers be more effective as they plan and teach mathematics in diverse

classrooms, grades K—4.

Structure of the Book

The book begins with two introductory chapters that provide a basic understanding

of instructional activities and lesson planning. Then there are nine chapters devoted to

teaching the content that most commonly appears in K—4 mathematics textbooks. We

do not attempt to provide comprehensive coverage of every topic that might appear in

a K—4 textbook. Rather, our intent is to emphasize a way of teaching effectively that

will result in learning, understanding, retention of important concepts and skills, and

an ability to apply those concepts and skills to solve problems. Important to that way of

teaching is effective planning. Therefore, we have made planning for effective teaching

an important part of this text.

preface

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