Elementary and Mid. School Mathematics -field . Guide (7TH 10 - Old Edition)

“It is fun to figure out the puzzle of how children go about making sense of mathematics and then how to help teachers help kids.”  John A. Van de Walle, Late of Virginia Commonwealth University

This is the philosophy behind Elementary and Middle School Mathematics:  Teaching Developmentally.   John A. Van de Walle wrote this book to help students understand mathematics and become confident in their ability to teach the subject to children in kindergarten through eighth grade.  Although he could not have foreseen the changes in mathematics teaching over the last three decades, he was at the forefront of the movement towards a constructivist view of teaching, or teaching developmentally.  Constructivism says that children construct their own knowledge.  They are not blank slates waiting to absorb whatever the teacher tells them.  Teachers must understand both mathematics itself and how students learn mathematics in order to teach it effectively. 

Learning through problem solving is another major theme of this book.  Students solve problems not just to apply mathematics, but also to learn new mathematics.  Effective problems will take into account where students are, the problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn and not be diluted by non-mathematical activities such as cutting or pasting, and the problem must require justifications and explanations for answers and methods.  Learning then becomes an outcome of the problem solving process. 

The book also addresses in more detail than any other book on the market the effect that the trends of standards-based education, increased pressure to test, and increased teacher accountability have had on teaching mathematics.  He addresses the 2000 NCTM Standards in depth, in Chapter 1 on Teaching Mathematics in the Era of the NCTM Standards, through the NCTM icon that appears in the margins throughout the text, and in two appendices in the back of the book.  Chapter 5 on Building Assessment into Instruction has also been heavily revised to focus on increased testing pressure, creating more explicit links between objectives and assessment, and including assessments for students with special needs. 

Elementary and Middle School Mathematics:  Teaching Developmentally is a book for doing math today–for both students who want to become teachers, and the students they will eventually teach. 

New To This Edition:

NEW!  Revises Chapter 5 on assessment--Discusses increased testing pressure and accountability, adds more information on equitable assessments, creates more explicit links between objectives and assessment, and includes assessments for students with special needs.

NEW!  Updates the Literature Connections feature to remove all out of print children’s literature and include more non-fiction, poetry, and other types of readings.

NEW!  Weaves the Focal Points throughout the chapters as well as links them with the Big Ideas feature–Focal Points have also been added to the Appendix. 

NEW!  Includes expanded coverage of working with diverse learners. 

NEW!  Gives greater emphasis on dealing with math anxiety.

The Field Experience Guide is for field experiences, practicums, and/or student teaching experiences at the elementary and middle school levels. This guide contains three parts. Part I, Menu of Field Experiences, provides tasks for preservice teachers to do in the field. Part II, Resources for Teaching, provides three types of activities: Expanded Lessons, Mathematics Activities, and Balanced Assessment Tasks. Part III, Black Line Masters, features reproducibles, along with suggestions regarding the use and construction of many of these materials.

Every chapter in Part I includes field-based tasks that align to the National Council for Accreditation of Teacher Education (NCATE) standards; National Council of Teachers of Mathematics (NCTM) standards; and the textbook Elementary and Middle School Mathematics: Teaching Developmentally Seventh Edition by John A. Van de Walle, Karen S. Karp, and Jennifer M. Bay-Williams. For example, Chapter 6, "Teaching Mathematics Equitably to All Children," includes a menu of field experiences that provide evidence that you can meet the needs of diverse learners. New rubrics are provided in each chapter to help you and your professor assess your progress on the topic of that particular chapter.

Part II features fully updated, reformatted, and revised Expanded Lessons. Increased attention is given to assessment and to questioning in these new lessons. In addition to these 25 effective lessons, Part II has a collection of problem-based tasks that can be developed into engaging lessons. Finally, three balanced assessment tasks are provided, which can be used as a lesson or an assessment of student learning. The lessons and activities in Part II can be used to complete the field experiences in Part I.

Enjoy this collection of experiences as they support you in your journey towards being an effective teacher of mathematics.

John A. Van de Walle, Late of Virginia Commonwealth University

Karen S. Karp, University of Louisville

Jennifer M. Bay-Williams, University of Louisville

Written by leaders in the field of mathematics education, this best-selling book will help teachers and K-8 students make sense of math. For each strand of the mathematics curriculum, numerous problem-based activities are interwoven with a discussion of the mathematical content and how children develop their understanding of that content.

This book is uniquely designed to help your students:

• Prepare for mathematics instruction in today’s classroom:
  • NEW!  MyEducationLab website for this text presents classroom video, clips of teacher workshops presented by John Van de Walle, expanded lessons, real curriculum materials, children’s literature resources, and more. Margin notes throughout the text seamlessly integrate website material for instructors and readers.
  • NEW!  Field Experience Guide Connections at the end of each chapter showcase specific classroom-based tasks, activities, and resources available to readers in the popular Field Experience Guide.
• Develop a constructivist and problem solving approach to the learning and teaching of mathematics
• NEW! Use the 2000 NCTM Principles and Standards and Curriculum Focal Points to inform their instruction by providing the most complete coverage of the NCTM guidelines available.
• UPDATED! Effectively integrate technology to support teaching and learning with comprehensive coverage of new technologies and teaching strategies.
• Practice doing the mathematics that they will teach through numerous activities in each of the 16 content chapters
• NEW! Meet the needs of all learners through discussion of differentiating instruction, adaptation of the response to intervention (RTI) model for use with students with special needs in the mathematics classroom, and more.

Part II Resources Organized by Content vii

NCATE Standards ix

Design of Field Experience Guide x

PART I Menu of Field Experiences 1

    Field Experience Cover Sheet 2

    Field Experience Activity Log 3

CHAPTER 1 Professional and Pedagogical Knowledge: Classroom Environment 4

    Standards Alignment 4 • Rubric 5

        1.1 Observation: Physical Environment 6

        1.2 Observation: NCTM Professional Teaching Standards 7

        1.3 Teacher Interview: An Environment for Learning 8

        1.4 Student Interview: Attitudes and Environment 9

        1.5 Teaching: Establishing Your Environment 10

        1.6 Project: Assessing School Environment 12

CHAPTER 2 Professional and Pedagogical Knowledge: Planning 13

    Standards Alignment 13 • Rubric 14

        2.1 Teacher Interview: Selecting Goals and Objectives 15

        2.2 Observation: Evidence of Higher-Level Thinking 16

        2.3 Teaching: Mathematics Task Analysis 17

        2.4 Teaching: Worthwhile Task Evaluation 18

        2.5 Teaching: Planning a Problem-Based Lesson 19

        2.6 Teaching: Using Children’s Literature in Math Teaching 21

CHAPTER 3 Content Knowledge 23

    Standards Alignment 23 • Rubric 25

        3.1 Observation: Conceptual and Procedural Knowledge 26

        3.2 Observation: Mathematical Proficiency 27

        3.3 Teacher Interview: Selecting a Worthwhile Task 28

        3.4 Student Interview: Conceptual and Procedural Knowledge 29

        3.5 Teaching: Create a Web of Ideas 31

        3.6 Teaching: Design (and Teach) a Lesson 32

        3.7 Reflection: Student Understanding 33

CHAPTER 4 Pedagogical Content Knowledge: Instruction 34

    Standards Alignment 34 • Rubric 35

        4.1 Observation: The Process Standards 36

        4.2 Observation: Classroom Discourse 38

        4.3 Observation: Cooperative Groups 39

        4.4 Teacher Interview: Teaching for Understanding 41

        4.5 Student Interview: Learning Mathematics Developmentally 42

        4.6 Teaching: Teaching a Small Group 43

        4.7 Teaching: Teaching a Standards-Based Lesson 44

        4.8 Reflection: Reflecting on Teaching and Learning 45

        4.9 Feedback on Teaching 46

CHAPTER 5 Pedagogical Content Knowledge: Technology 47

    Standards Alignment 47 • Rubric 48

        5.1 Project: Learning Online 49

        5.2 Project: Evaluating Mathematics Software or Websites 50

        5.3 Teaching: Using the Calculator to Support Learning 51

        5.4 Teaching: Develop a Calculator Learning Center 52

        5.5 Reflection: Reactions to Learning with Technology 54

CHAPTER 6 Dispositions 55

    Standards Alignment 55 • Rubric 56

        6.1 Teacher Interview: Communicating with Parents 57

        6.2 Parent Interview: What Is Important to You? 59

        6.3 Teaching: Prepare a Family Math Take-Home Activity 60

        6.4 Reflection: Professional Growth 61

CHAPTER 7 Student Learning 62

    Standards Alignment 62 • Rubric 63

        7.1 Classroom Observation: Assessing to Inform Instruction 64

        7.2 Diagnostic Interview: Assessing for Understanding 65

        7.3 Student Observation and Interview: Learning Through Problems 69

        7.4 Teaching: Assessing Student Understanding with Rubrics 70

        7.5 Teaching: Creating and Using Rubrics 71

        7.6 Teaching: Using Anecdotal Notes to Assess Students 72

        7.7 Teaching: Using a Checklist to Assess Students 74

CHAPTER 8 Diversity 76

    Standards Alignment 76 • Rubric 77

        8.1 Observation: One Child’s Experience 78

        8.2 Teacher Interview: Student Diversity 80

        8.3 Teacher Interview: Environment and Students 81

        8.4 Teaching: Lesson Adaptations 82

        8.5 Teaching: Sheltering a Lesson for English Language Learners 84

        8.6 Reflection: Meeting the Needs of Individuals 86

PART II Resources for Teaching 89

    CHAPTER 9 Expanded Lessons 91

        9.1 Exploring Subtraction Strategies 93

        9.2 Close, Far, and in Between 95

        9.3 Two More Than/ Two Less Than 97

        9.4 Learning about Division 99

        9.5 Estimating Groups of Tens and Ones 101

        9.6 Dot-Paper Equivalences 103

        9.7 Multiplication of Fractions 105

        9.8 Friendly Fractions to Decimals 107

        9.9 Division of Fractions Using the Partition Concept 109

        9.10 How Close Is Close? 111

        9.11 Comparing Ratios 113

        9.12 One Up and One Down 115iv

        9.13 Predict How Many 117

        9.14 Create a Journey Story 119

        9.15 Crooked Paths 121

        9.16 Fixed Areas 123

        9.17 Shape Sorts 125

        9.18 Diagonal Strips 127

        9.19 Triangle Midsegments 129

        9.20 Using Data to Answer a Question 131

        9.21 Create a Game 133

        9.22 Bar Graphs to Circle Graphs 135

        9.23 Testing Bag Designs 137

        9.24 Toying with Measures 139

CHAPTER 10 Mathematics Activities 141

        10.1 The Find! 143

        10.2 Odd or Even? 145

        10.3 Factor Quest 147

        10.4 Interference 149

        10.5 Target Number 151

        10.6 Fraction Find 153

        10.7 Illustrating Ratios 155

        10.8 Building Bridges 157

        10.9 Compensation Decision 159

        10.10 Solving the Mystery 161

        10.11 Cover All 163

CHAPTER 11 Balanced Assessment Activities 165

        11.1 Magic Age Rings 167

        11.2 Grocery Store 171

        11.3 Bolts and Nuts! 174

PART III Blackline Masters 179

    Suggestions for Use and Construction of Materials 179

        More-or-Less Cards 181

        Number Cards 182

        Dot Cards 3—8 183

        Five-Frame 189

        Ten-Frame 190

        Double Ten-Frame 191

        10 × 10 Multiplication Array 192

        Missing-Part Worksheet 193

        Base-Ten Materials Grid 194

        Little Ten-Frames 15—16 195

        Place-Value Mat (with Ten-Frames) 197

        Base-Ten Grid Paper 198

        Addition and Subtraction Recording Charts 199

        Multiplication and Division Recording Charts 200

        Blank Hundreds Chart (10 × 10 Square) 201

        Hundreds Chart 202

        Four Small Hundreds Charts 203

        Circular Fraction Pieces 24—26 204

        10 × 10 Grids 207

        Rational Number Wheel 208

        10,000 Grid 209

        Look-Alike Rectangles 210

        Look-Alike Rectangles Recording Sheet 211

        Degrees and Wedges 212

        Clock Faces 213

        2-cm Square Grid 214

        1-cm Square Grid 215

        0.5-cm Square Grid 216

        1-cm Square Dot Grid 217

        2-cm Isometric Grid 218

        1-cm Isometric Dot Grid 219

        1-cm Square/Diagonal Grid 220

        Assorted Shapes 42—47 221

        Coordinate Grid 228

        Geoboard Pattern 229

        Geoboard Recording Sheets 230

        Tangrams and Mosaic Puzzle 231

        Motion Man 54—53 232

        Property Lists for Quadrilaterals 54—57 234

        Assorted Triangles 238

        Woozle Cards 239

        Design a Bag 240

        What Are the Chances? 241

        at Collections 242

        2 More Than 243

        2 Less Than 244

        How Long? 245

        Fraction Names 246

        Solving Problems Involving Fractions 247

        It’s a Matter of Rates 248

        Predict How Many 69—70 249

        Create a Journey Story 251

        Crooked Paths 252

        Rectangles Made with 36 Tiles 253

        Fixed Area Recording Sheet 254

        Properties of Quadrilateral Diagonals 255

        Toy Purchases 256

        Toying with Measures 257