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Field Experience Guide for Elementary and Middle School Mathematics : Teaching Developmentally

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The Field Experience Guide,a supplement to Elementary and Middle School Mathematics, 8th Edition, is for observation, practicum, and student teaching experiences at the elementary and middle school levels. The guidebook contains three parts: Part I provides tasks for preservice teachers to do in the field; Part II provides three types of activities: Expanded Lessons, Mathematics Activities, and Balanced Assessment Tasks. Part III of this guide contains a full set of reproducible Blackline Masters referenced in the 8th edition of Elementary and Middle School Mathematicsas well as additional Blackline Masters for use with the Expanded Lessons in Part II. A convenient Field Experience Guide Connectionssection at the end of each chapter in the 8th Edition will help you better integrate the information from the text with the Field Experience Guideto support with your work in schools.

Table of Contents


Part II Resources Organized by Content vii

What Is New in the Field Experience Guide? ix

Design of Field Experience Guide x

NCATE Standards xi

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 Observation: Productive Classroom Culture 8

1.4 Teacher Interview: An Environment for Learning 9

1.5 Student Interview: Attitudes and Environment 10

1.6 Teaching: Implementing Mathematical Practice 1 11

1.7 Project: Assessing School Environment 13

CHAPTER 2 Professional and Pedagogical Knowledge: Planning 14

Standards Alignment 14 • Rubric 15

1.1 Teacher Interview: Selecting Goals and Objectives 16

2.2 Observation: Evidence of Higher Level Thinking 17

2.3 Teaching: Level of Cognitive Demand 18

2.4 Teaching: Worthwhile Task Evaluation 19

2.5 Teaching: Incorporating the Standards for Mathematical Practice 20

2.6 Teaching: Planning a Problem Based Lesson 21

2.7 Teaching: Using Children’s Literature in Math Teaching 23

CHAPTER 3 Content Knowledge 25

Standards Alignment 25 • Rubric 26

3.1 Observation: Conceptual and Procedural Knowledge 28

3.2 Observation: Mathematical Proficiency 29

3.3 Teacher Interview: Selecting a Worthwhile Task 31

3.4 Student Interview: Assessing Mathematical Proficiency 32

3.5 Teaching: Create a Web of Ideas 34

3.6 Teaching: Design (and Teach) a Lesson 35

3.7 Reflection: Student Understanding 36

CHAPTER 4 Pedagogical Content Knowledge: Instruction 37

Standards Alignment 37 • Rubric 38

4.1 Observation: The Process Standards 39

4.2 Observation: Classroom Discourse 41

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4.3 Observation: Cooperative Groups 42

4.4 Teacher Interview: Teaching for Understanding 44

4.5 Student Interview: Learning Mathematics Developmentally 45

4.6 Teaching: Teaching a Small Group 46

4.7 Teaching: Classroom Discussions—Talk Moves 47

4.8 Teaching: Teaching a Standards Based Lesson 48

4.9 Reflection: Reflecting on Teaching and Learning 49

4.10 Feedback on Teaching 50

CHAPTER 5 Pedagogical Content Knowledge: Technology 51

Standards Alignment 51 • Rubric 52

5.1 Project: Learning Online 53

5.2 Project: Evaluating Mathematics Software or Websites 54

5.3 Teaching: Using the Calculator to Support Learning 55

5.4 Teaching: Develop a Calculator Learning Center 56

5.5 Reflection: Reactions to Learning with Technology 58

CHAPTER 6 Dispositions 59

Standards Alignment 59 • Rubric 60

6.1 Teacher Interview: Communicating with Families 61

6.2 Parent Interview: What Is Important to You? 63

6.3 Teaching: Prepare a Family Math Take Home Activity 64

6.4 Reflection: Professional Growth 65

CHAPTER 7 Student Learning and Assessment 66

Standards Alignment 66 • Rubric 67

7.1 Classroom Observation: Assessing to Inform Instruction 68

7.2 Diagnostic Interview: Assessing for Understanding 69

7.3 Student Observation and Interview: Learning Through Problems 73

7.4 Teaching: Assessing Student Understanding with Rubrics 74

7.5 Teaching: Creating and Using Rubrics 75

7.6 Teaching: Using Anecdotal Notes to Assess Students 76

7.7 Teaching: Using a Checklist to Assess Students 78

7.8 Teaching: Assessing the Standards for Mathematical Practice 80

CHAPTER 8 Diversity 82

Standards Alignment 82 • Rubric 83

8.1 Observation: One Child’s Experience 84

8.2 Observation: Culturally Responsive Instruction 86

8.3 Teacher Interview: Student Diversity 87

8.4 Teacher Interview: Environment and Students 88

8.5 Teaching: Lesson Adaptations 89

8.6 Teaching: Sheltering a Lesson for English Language Learners 91

8.7 Reflection: Meeting the Needs of All Learners 93

PART II Resources for Teaching 95

CHAPTER 9 Expanded Lessons 96

9.1 Exploring Subtraction Strategies 98

9.2 Close, Far, and In Between 100

9.3 Two More Than/Two Less Than 102

9.4 Learning about Division 104

9.5 Estimating Groups of Tens and Ones 106

9.6 Dot Paper Fraction Equivalences 109

9.7 Multiplication of Fractions Stories 111

9.8 Friendly Fractions to Decimals 113

9.9 Division of Fractions Stories 115

9.10 How Many In Between? 117

9.11 Comparing Ratios 119

9.12 One Up and One Down 121

9.13 Geometric Growing Patterns: Predict How Many 123

9.14 Create a Journey Story 125

9.15 Crooked Paths 127

9.16 Fixed Areas 129

9.17 Shape Sorts 131

9.18 Diagonals of Quadrilaterals 133

9.19 Triangle Midsegments 135

9.20 Using Data to Answer a Question 137

9.21 Design a Fair Game 140

9.22 Bar Graphs to Circle Graphs 142

9.23 Testing Bag Designs 144

9.24 Toying with Measures of Central Tendency 146

CHAPTER 10 Mathematics Activities 148

10.1 The Find! 150

10.2 Move It, Move It 152

10.3 Odd or Even? 155

10.4 Factor Quest 157

10.5 The Other Part of 100 159

10.6 Interference 162

10.7 Target Number 164

10.8 Building Bridges 166

10.9 Compensation Decision 168

10.10 Solving the Mystery 170

10.11 Fraction Find 172

10.12 Illustrating Ratios 174

10.13 Cover All 176

10.14 Find the Zero 178

CHAPTER 11 Balanced Assessment Tasks 180

11.1 Magic Age Rings 181

11.2 Grocery Store 186

11.3 Bolts and Nuts! 190

PART III Blackline Masters 000

Suggestions for Use and Construction of Materials

More or Less Cards

Number Cards

Dot Cards

Five Frame

Ten Frame

Double Ten Frame

10 × 10 Multiplication Array

Missing Part Worksheet

Base Ten Materials

Little Ten Frames

Place Value Mat (with Ten Frames)

Base Ten Grid Paper

Addition and Subtraction Recording Charts

Multiplication and Division Recording Charts

Blank Hundreds Chart (10 × 10 Square)

Hundreds Chart

Four Small Hundreds Charts

Circular Fraction Pieces

10 × 10 Grids

Rational Number Wheel

10,000 Grid

Look Alike Rectangles

Look Alike Rectangles Recording Sheet

Degrees and Wedges

Clock Faces

2 cm Square Grid

1 cm Square Grid

0.5 cm Square Grid

1 cm Square Dot Grid

2 cm Isometric Grid

1 cm Isometric Dot Grid

1 cm Square/Diagonal Grid

Assorted Shapes

Coordinate Grid

Geoboard Pattern

Geoboard Recording Sheets

Tangrams and Mosaic Puzzle

Motion Man

Property Lists for Quadrilaterals

Assorted Triangles

Woozle Cards

Design a Bag

What are the Chances?

Looking at Collections

2 More Than

2 Less Than

How Long?

Fraction Names

Solving Problems Involving Fractions

It’s a Matter of Rates

Predict How Many

Create a Journey Story

Crooked Paths

Rectangles Made with 36 Tiles

Fixed Area Recording Sheet

Properties of Quadrilateral Diagonals

Toy Purchases

Toying with Measures

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