Whole Class Mathematics Discussions Improving In-Depth Mathematical Thinking and Learning

by Lamberg, Teruni

• ISBN13: 9780132117333
• ISBN10: 0132117339
• Edition: 1st
• Format: Paperback
• Copyright: 2012-04-13
• Publisher: Pearson

Summary

Filled with research-based ideas, practical strategies and tools; this book and the accompanying PDToolkit website supports teachers in facilitating effective whole class discussions to enhance K-8 students'mathematical understanding. NCTM standards and the Common Core standards emphasize communication as an integral part of how students should learn mathematics. This book provides a comprehensive approach to whole class math discussion and addresses how to set up a classroom, cultivate classroom routines, plan for instruction, facilitate discussions, and assess for future improvement. Reflective questions throughout the book enable teachers to develop professionally and support formal workshop or book study experiences. The accompanying PDToolkit website offers video clips from five real classrooms which illustrate whole class math discussions in action, teacher and student interviews, and chapter PPTs for professional development sessions.

Author Biography

Teruni Lamberg, Ph.D. is an Associate Professor of Elementary Education at the University of Nevada, Reno. She teaches graduate and undergraduate mathematics education courses. She is currently the Principal Investigator and Director of the Lemelson Math and Science Master's Cohort Program, serves on the board of the Nevada Math Council and on the board for the North American Chapter of the International Group for the Psychology of Mathematics Education. She taught elementary school prior to receiving her doctorate from Arizona State University and completing her Postdoctorate work at Vanderbilt University.

Table of Contents

About the Author	p. iii
Video Clips	p. x
Preface	p. xi
Why Whole Class Discussions?	p. 1
Common Core and NCTM Standards	p. 2
Whole Class Discussion and Student Achievement	p. 3
Communication and Mathematical Learning	p. 4
"Math Talk" with Partners, Small Groups, and Whole Class	p. 5
Case Study: Problem Solving with Partners	p. 5
Video Clip 1.1: Student Interview: Student Perspectives on "Math Talkö and Math Learning	p. 7
Video Clip 1.2: Fifth & Sixth Grade Teacher Perspectives on Class Discussions	p. 8
Characteristics of Effective Whole Class Discussions	p. 9
Planning a Whole Class Discussion	p. 10
Planning Prior to Discussion	p. 11
Video Clip 1.3: Fifth & Sixth Grade Teacher Interview on Lesson Planning	p. 11
Planning the Discussion During the Lesson	p. 12
The Whole Class Discussion: Facilitating Mathematical Connections	p. 12
Video Clip 1.4: Fifth & Sixth Grade Problem-Solving Lesson	p. 12
Additional Considerations for Facilitating Effective Discussions	p. 17
Chapter Summary	p. 17
Study Guide	p. 18
Video Case Study	p. 19
Problem-Solving Using Schematic Drawings	p. 19
Strategies for Your Classroom	p. 20
How and When to Use Whole Class Discussion to Support Learning	p. 20
Reflecting on Video Clips	p. 21
Reflecting on Practice	p. 22
Using Whole Class Discussions	p. 22
Designing the Physical Classroom Space for Discussions	p. 23
Design Elements for Classroom Space	p. 23
Designing a Functional Space for Discussions	p. 25
Designing Space for Small Group Discussion	p. 26
Designing a Functional Space for Whole Class Discussions	p. 26
Creating a Focal Point	p. 27
Visualization and Representations	p. 28
Access to Materials for Students' Work	p. 29
Access to Technology	p. 29
Displaying and Saving Students' Work	p. 30
Further Suggestions for Classroom Layouts	p. 31
Chapter Summary	p. 32
Study Guide	p. 33
Strategies for your Classroom	p. 34
Considerations for Creating Physical Space	p. 34
Reflecting on Practice	p. 35
Designing Classroom Space	p. 35
Physical Layouts for Classroom Discussions Checklist	p. 36
Developing Classroom Routines for Whole Class Discussions	p. 37
Building a Supportive Classroom Community	p. 38
Establish Mutual Respect	p. 39
Video Clip 3.1: Student Interview: Cultivating a Classroom Community	p. 39
Value Students' Experiences and Home Language	p. 39
Use Small Groups/Partners	p. 40
Video Clip 3.2: Fifth & Sixth Grade Teacher Interview: Using Flexible Grouping	p. 40
Physical Classroom Routines to Prepare for Whole Class Discussions	p. 41
Strategies and Social Routines for Whole Class Discussions	p. 42
Routines for Communication	p. 43
Communicating and Listening During Whole Class Discussions	p. 44
Active Listening During Whole Class Discussions	p. 45
Using Representations to Record Thinking	p. 46
Create, Share, and Explain Representations	p. 46
Using Representations to Connect to Another Student's Method	p. 47
Video Clip 3.3: Second Grade Measurement Lesson and Teacher Interview	p. 47
Case Study 1: Examining an Unsuccessful Discussion	p. 49
Case Study 2: Examining a Successful Discussion	p. 52
Chapter Summary	p. 53
Study Guide	p. 55
Video Case Study	p. 57
Second Grade Measurement Lesson and Teacher Interview	p. 57
Video Clip 3.4: Second Grade Teacher Interview: Teaching Measurement	p. 57
Strategies for Your Classroom	p. 60
Ideas for Developing Classroom Routines	p. 60
Reflecting on Video Clips	p. 61
Reflecting on Practice	p. 62
Building a Supportive Classroom Community	p. 62
Thinking about Physical and Social Routines for Discussion	p. 63
Routines for Listening	p. 65
Student Self-Evaluation Checklist for Participation in Whole Class Discussion	p. 67
Whole Class Student Participation Checklist	p. 67
What Do We Talk About? Planning the Discussion	p. 68
Planning the Lesson to Optimize Learning	p. 69
Mathematical Goals, Concepts, and Skills	p. 70
What Does It Mean to Understand a Concept or "Big Idea"?	p. 71
Using a Concept Map to Show Connections	p. 72
Curriculum Tasks and Sequencing	p. 75
Sequencing Lessons	p. 75
Anticipating Student Reasoning: The 5E Lesson Plan	p. 76
Chapter Summary	p. 78
Study Guide	p. 79
Level 1: Identify Long-Term Goals, Short-Term Goals, and Interconnections	p. 79
Level 2: Plan the Individual Lesson	p. 81
Level 3: Examine Student Work to Build Whole Class Discussion	p. 81
Classroom Case Study	p. 83
Analyzing Student Work to Plan Discussion	p. 83
Student Work Sample A: Richard's Solution	p. 84
Student Work Sample B: Katie's Solution	p. 85
Student Work Sample C: Juan's Solution	p. 86
Student Work Sample D: Samantha's Solution	p. 87
Student Work Sample E: Conner's Solution	p. 88
An Overall Analysis of Students' Solutions	p. 89
Strategies for Your Classroom	p. 91
Three Levels of Planning	p. 91
Reflecting on Practice	p. 92
Level 1 Planning	p. 92
Rubric For Unit Planning: Level 1	p. 93
Rubric For The 5E Lesson Plan: Level 2	p. 94
Rubric For Planning the Discussion: Level 3	p. 95
Teacher Questioning and Mathematical Connections	p. 96
Posing a Question to Start the Whole Class Discussion	p. 97
Using Questions to Identify Discussion Topics	p. 97
The Three Levels of Sense-Making in Discussion	p. 98
Phase 1: Making Thinking Explicit	p. 99
Case Study 1: Clarifying an Explanation	p. 99
Phase 2: Analyzing Each Other's Solutions to Make Connections	p. 101
Phase 3: Developing New Mathematical Insights by Making Generalizations	p. 103
Case Study 2: Writing a Number Sentence to Represent a Fair Sharing Problem	p. 103
Chapter Summary	p. 108
Study Guide	p. 109
Video Case Study	p. 110
Third Grade Lesson: Using Arrays to Find Area and Perimeter	p. 110
Sixth Grade Problem-Solving Lesson	p. 112
Strategies for Your Classroom	p. 116
The Three Levels of Sense-Making in Discussion	p. 116
Sequence of a Whole Class Discussion	p. 117
Reflecting on Video Clips	p. 118
Reflecting on Practice	p. 119
Making Mathematical Connections	p. 119
Strategies for Evaluating and Improving Your Discussion	p. 120
Improving Whole Class Discussions	p. 121
Making Classroom Teaching Visible to Improve Discussion	p. 121
Signs of Effective Whole Class Discussions	p. 123
Chapter Summary	p. 123
Study Guide Part 1	p. 124
Video Case Study	p. 126
Second Grade Lesson on Two-Digit Addition with Regrouping	p. 126
Strategies for Your Classroom	p. 130
Refining Your Whole Class Discussion: Long-Term Strategies	p. 130
Refining Your Whole Class Discussion: Making Teaching Visible	p. 130
Reflecting on Video Clips	p. 131
Reflecting on Practice	p. 132
Next Steps after Holding a Whole Class Discussion	p. 132
Improving Your Discussion	p. 133
Whole Class Discussion Checklist: Informal Assessment of Student Understanding	p. 134
Student Rubric for Self-Evaluation of Whole Class Discussion	p. 135
Whole Class Discussion Participation Checklist	p. 136
Classroom Observation Rubric	p. 137
Math Discussion Rubric	p. 138
Self-Reflection Rubric for Evaluating Whole Class Discussions	p. 140
Reference	p. 141
Index	p. 144
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