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

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 2012-04-13
  • Publisher: Pearson

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Supplemental Materials

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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 Authorp. iii
Video Clipsp. x
Prefacep. xi
Why Whole Class Discussions?p. 1
Common Core and NCTM Standardsp. 2
Whole Class Discussion and Student Achievementp. 3
Communication and Mathematical Learningp. 4
"Math Talk" with Partners, Small Groups, and Whole Classp. 5
Case Study: Problem Solving with Partnersp. 5
Video Clip 1.1: Student Interview: Student Perspectives on "Math Talkö and Math Learningp. 7
Video Clip 1.2: Fifth & Sixth Grade Teacher Perspectives on Class Discussionsp. 8
Characteristics of Effective Whole Class Discussionsp. 9
Planning a Whole Class Discussionp. 10
Planning Prior to Discussionp. 11
Video Clip 1.3: Fifth & Sixth Grade Teacher Interview on Lesson Planningp. 11
Planning the Discussion During the Lessonp. 12
The Whole Class Discussion: Facilitating Mathematical Connectionsp. 12
Video Clip 1.4: Fifth & Sixth Grade Problem-Solving Lessonp. 12
Additional Considerations for Facilitating Effective Discussionsp. 17
Chapter Summaryp. 17
Study Guidep. 18
Video Case Studyp. 19
Problem-Solving Using Schematic Drawingsp. 19
Strategies for Your Classroomp. 20
How and When to Use Whole Class Discussion to Support Learningp. 20
Reflecting on Video Clipsp. 21
Reflecting on Practicep. 22
Using Whole Class Discussionsp. 22
Designing the Physical Classroom Space for Discussionsp. 23
Design Elements for Classroom Spacep. 23
Designing a Functional Space for Discussionsp. 25
Designing Space for Small Group Discussionp. 26
Designing a Functional Space for Whole Class Discussionsp. 26
Creating a Focal Pointp. 27
Visualization and Representationsp. 28
Access to Materials for Students' Workp. 29
Access to Technologyp. 29
Displaying and Saving Students' Workp. 30
Further Suggestions for Classroom Layoutsp. 31
Chapter Summaryp. 32
Study Guidep. 33
Strategies for your Classroomp. 34
Considerations for Creating Physical Spacep. 34
Reflecting on Practicep. 35
Designing Classroom Spacep. 35
Physical Layouts for Classroom Discussions Checklistp. 36
Developing Classroom Routines for Whole Class Discussionsp. 37
Building a Supportive Classroom Communityp. 38
Establish Mutual Respectp. 39
Video Clip 3.1: Student Interview: Cultivating a Classroom Communityp. 39
Value Students' Experiences and Home Languagep. 39
Use Small Groups/Partnersp. 40
Video Clip 3.2: Fifth & Sixth Grade Teacher Interview: Using Flexible Groupingp. 40
Physical Classroom Routines to Prepare for Whole Class Discussionsp. 41
Strategies and Social Routines for Whole Class Discussionsp. 42
Routines for Communicationp. 43
Communicating and Listening During Whole Class Discussionsp. 44
Active Listening During Whole Class Discussionsp. 45
Using Representations to Record Thinkingp. 46
Create, Share, and Explain Representationsp. 46
Using Representations to Connect to Another Student's Methodp. 47
Video Clip 3.3: Second Grade Measurement Lesson and Teacher Interviewp. 47
Case Study 1: Examining an Unsuccessful Discussionp. 49
Case Study 2: Examining a Successful Discussionp. 52
Chapter Summaryp. 53
Study Guidep. 55
Video Case Studyp. 57
Second Grade Measurement Lesson and Teacher Interviewp. 57
Video Clip 3.4: Second Grade Teacher Interview: Teaching Measurementp. 57
Strategies for Your Classroomp. 60
Ideas for Developing Classroom Routinesp. 60
Reflecting on Video Clipsp. 61
Reflecting on Practicep. 62
Building a Supportive Classroom Communityp. 62
Thinking about Physical and Social Routines for Discussionp. 63
Routines for Listeningp. 65
Student Self-Evaluation Checklist for Participation in Whole Class Discussionp. 67
Whole Class Student Participation Checklistp. 67
What Do We Talk About? Planning the Discussionp. 68
Planning the Lesson to Optimize Learningp. 69
Mathematical Goals, Concepts, and Skillsp. 70
What Does It Mean to Understand a Concept or "Big Idea"?p. 71
Using a Concept Map to Show Connectionsp. 72
Curriculum Tasks and Sequencingp. 75
Sequencing Lessonsp. 75
Anticipating Student Reasoning: The 5E Lesson Planp. 76
Chapter Summaryp. 78
Study Guidep. 79
Level 1: Identify Long-Term Goals, Short-Term Goals, and Interconnectionsp. 79
Level 2: Plan the Individual Lessonp. 81
Level 3: Examine Student Work to Build Whole Class Discussionp. 81
Classroom Case Studyp. 83
Analyzing Student Work to Plan Discussionp. 83
Student Work Sample A: Richard's Solutionp. 84
Student Work Sample B: Katie's Solutionp. 85
Student Work Sample C: Juan's Solutionp. 86
Student Work Sample D: Samantha's Solutionp. 87
Student Work Sample E: Conner's Solutionp. 88
An Overall Analysis of Students' Solutionsp. 89
Strategies for Your Classroomp. 91
Three Levels of Planningp. 91
Reflecting on Practicep. 92
Level 1 Planningp. 92
Rubric For Unit Planning: Level 1p. 93
Rubric For The 5E Lesson Plan: Level 2p. 94
Rubric For Planning the Discussion: Level 3p. 95
Teacher Questioning and Mathematical Connectionsp. 96
Posing a Question to Start the Whole Class Discussionp. 97
Using Questions to Identify Discussion Topicsp. 97
The Three Levels of Sense-Making in Discussionp. 98
Phase 1: Making Thinking Explicitp. 99
Case Study 1: Clarifying an Explanationp. 99
Phase 2: Analyzing Each Other's Solutions to Make Connectionsp. 101
Phase 3: Developing New Mathematical Insights by Making Generalizationsp. 103
Case Study 2: Writing a Number Sentence to Represent a Fair Sharing Problemp. 103
Chapter Summaryp. 108
Study Guidep. 109
Video Case Studyp. 110
Third Grade Lesson: Using Arrays to Find Area and Perimeterp. 110
Sixth Grade Problem-Solving Lessonp. 112
Strategies for Your Classroomp. 116
The Three Levels of Sense-Making in Discussionp. 116
Sequence of a Whole Class Discussionp. 117
Reflecting on Video Clipsp. 118
Reflecting on Practicep. 119
Making Mathematical Connectionsp. 119
Strategies for Evaluating and Improving Your Discussionp. 120
Improving Whole Class Discussionsp. 121
Making Classroom Teaching Visible to Improve Discussionp. 121
Signs of Effective Whole Class Discussionsp. 123
Chapter Summaryp. 123
Study Guide Part 1p. 124
Video Case Studyp. 126
Second Grade Lesson on Two-Digit Addition with Regroupingp. 126
Strategies for Your Classroomp. 130
Refining Your Whole Class Discussion: Long-Term Strategiesp. 130
Refining Your Whole Class Discussion: Making Teaching Visiblep. 130
Reflecting on Video Clipsp. 131
Reflecting on Practicep. 132
Next Steps after Holding a Whole Class Discussionp. 132
Improving Your Discussionp. 133
Whole Class Discussion Checklist: Informal Assessment of Student Understandingp. 134
Student Rubric for Self-Evaluation of Whole Class Discussionp. 135
Whole Class Discussion Participation Checklistp. 136
Classroom Observation Rubricp. 137
Math Discussion Rubricp. 138
Self-Reflection Rubric for Evaluating Whole Class Discussionsp. 140
Referencep. 141
Indexp. 144
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