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 HigherLevel 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 ProblemBased 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 110733 00 i-xii r0 as.indd iii 29/11/11 8:20 PM 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 StandardsBased 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 TakeHome 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 DotPaper 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 MoreorLess Cards Number Cards Dot Cards FiveFrame TenFrame Double TenFrame 10 × 10 Multiplication Array MissingPart Worksheet BaseTen Materials Little TenFrames PlaceValue Mat (with TenFrames) BaseTen 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 LookAlike Rectangles LookAlike Rectangles Recording Sheet Degrees and Wedges Clock Faces 2cm Square Grid 1cm Square Grid 0.5cm Square Grid 1cm Square Dot Grid 2cm Isometric Grid 1cm Isometric Dot Grid 1cm 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

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 use in the classroom; Part II, Resources for Teaching, provides three types of activities: Expanded Lessons, Mathematics Activities, and Balanced Assessment Tasks; Part III, Blackline Masters, features reproducibles, along with suggestions for 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, 8/e by John A. Van de Walle, Karen S. Karp, and Jennifer M. Bay-Williams. New field experiences have also been added to include a focus on Common Core State Standards content. Revised rubrics in each chapter help you and your professor assess your progress on the topic of that particular chapter.   Part II features updated Expanded Lessons. Each lesson now opens with a Grade Level Guide based on Common Core State Standards, as well as NCTM Curriculum Focal Points. Strategies for English language learners (ELLs) and Students with Disabilities have also been added to each lesson. In addition to these 24 effective lessons, Part II has a collection of Mathematics Activities that can be developed into engaging lessons. This edition includes three new problem-based tasks for a more comprehensive coverage of content. Finally, three balanced assessment tasks are provided, which can be used as lessons or assessment of student learning. The lessons and activities in Part II can be used to complete the field experiences in Part I.   Part III contains reproducible Blackline Masters referenced in Elementary and Middle School Mathematics: Teaching Developmentally, 8/e and Expanded Lessons in Part II.   Enjoy this collection of experiences as they support you in your journey toward effective mathematics teaching.

Part I is organised by specific knowledge, skills, or dispositions for teacher candidates outlined in NCATE, such as pedagogical knowledge and assessment. Within each is a menu of possible tasks for teacher candidates to use. In one setting, it may be appropriate to focus on one or two of the NCATE categories, such as assessment and content knowledge, using numerous activities from those sections. In another setting, it may be more useful to use one or two activities from each category. An instructor might select the tasks or allow students to pick from a selection of tasks that have the same goal. It is also important to note that although many of the activities in the field guide are placed in one chapter, they are also applicable to other areas. Each section includes a rubric that can be used with any experience in that section.   Part II has a collection of lessons and activities for each of the content standards: Number, Algebra, Geometry, Measurement, Data Analysis, and Probability. Each content area has at least one lesson for each grade band (K—2, 3—5, 6—8). See p. vii for a detailed list of lessons and grade bands. These lessons can be linked to the experiences described in Part I. For example, if students are designing appropriate accommodations for a student with special needs, they might select a task or lesson from this collection, use a lesson that is provided by the methods instructor or the classroom teacher, or find a lesson on their own.   Part III of this guide contains a full set of reproducible Blackline Masters referenced in the 7th edition of Elementary and Middle School Mathematics as well as additional Blackline Masters for use with the Expanded Lessons in Part II.

This fourth edition of the Field Experience Guide has a number of new features:   √ Focus on Common Core State Standards content throughout. First, there are a number of field experiences throughout Part I that include a focus on the Standards for Mathematical Practice . All lessons and activities have grade level recommendations that are consistent with the CCSS content recommendations. These lessons are now listed at the beginnings of Chapters 9 and 10 for easy reference. √ New Field Experience Activities. New activities were added to several of the Part I chapters (see, for example, 2.3, Level of Cognitive Demand, and 4.7, Classroom Discussions—Talk Moves ). As noted previously, several new field experiences are focused on the Common Core State Standards ( 2.5, 3.4, 7.8 ). √ Revised rubrics in Part I chapters . These focus on teaching skills and are intended to be broad enough that they can be used with any task in that chapter. √ More activities. Three new activities were added to Chapter 10 to provide more choices and to provide a more comprehensive content coverage in Chapters 9 and 10 . √ Increased focus on diversity. Lessons now have specific strategies for English language learners (ELLs) and students with disabilities.