9780132101288

Offering an innovative framework, this book helps teachers learn how to use classroom artifacts to assess students'mathematical thinking and students' understanding of mathematical content. Teachers need to be able to diagnose what their students do and don't understand about mathematics. Examining Mathematics Practice through Classroom Artifactshelps teachers become more analytic about their students'thinking by showing them how to use student artifacts to evaluate what is happening in the classroom. Focusing on elementary through middle grades, chapters investigate what classroom artifacts are, how to interpret them and ways to use this data to improve mathematics instruction.

Lynn Goldsmith began her career as a developmental psychologist, where her major research interests lay in understanding the formal and informal systems that support the development of extreme talent. For the past 20 years, she has worked in the field of mathematics education, investigating factors contributing to successful professional development, the role of curriculum in educational reform, and the emotional aspects of learning. She has co-authored Choosing a Standards-Based Mathematics Curriculum (Heinemann, 2000), served as series co-editor of the Guiding Middle-Grades Curriculum Decisions series (Heinemann, 2000), and co-authored Nature's Gambit: Child Prodigies and the Development of Human Potential (Teachers College Press, 1991). Nanette Seago was the primary author of Learning and Teaching Linear Functions: Video Cases for Mathematics Professional Development, 6-12. She has been working in mathematics professional development for twenty years. Currently, she is working at WestEd as a Principal Investigator for a National Science Foundation project focused on the research and design of video case materials for middle school teachers-Learning and Teaching Geometry.

Foreword	p. xiii
Preface	p. xvii
Acknowledgments	p. xxii
Turning to the Evidence	p. 1
What Are Artifacts, and Why Analyze Them?	p. 3
Learning to See through Multiple Lenses	p. 4
Our Vision of Mathematics Learning and Teaching	p. 6
A Framework for Using Artifacts Skillfully	p. 10
Attention to Thinking	p. 13
Describing and Interpreting Classroom Artifacts	p. 14
Why Focus on Evidence?	p. 16
Creating a Description of Student Work	p. 16
Exercise 1: Danny	p. 19
Process for Analyzing Danny's Work	p. 20
Commentary on Danny's Work	p. 21
Exercise 2: Melissa	p. 23
Process for Viewing and Analyzing the Melissa Video	p. 24
Commentary on Melissa's Interview	p. 27
Reflecting on Exercise 2	p. 30
Using Artifacts in Your Own Classroom	p. 30
Warm-Ups	p. 30
Homework, Quizzes, and Tests	p. 31
Exercise 3: Sorting Homework	p. 32
Process for Sorting the Homework Samples	p. 32
Commentary on Exercise 3	p. 33
Making Videos of Your Own	p. 35
Wrapping Up	p. 37
Additional Exercises: Video Clips of Two Math Interviews	p. 37
Exercise 4: Kasage	p. 37
Process for Viewing and Analyzing the Kasage Video	p. 37
Exercise 5: Myrna	p. 43
Process for Viewing and Analyzing the Myrna Video	p. 43
Seeing the Potential in Students' Thinking	p. 48
Why Focus on Errors?	p. 49
Using Errors to See Potential Instead of Just Deficits in Students' Thinking	p. 49
Exercise 1: Lemonade Lesson Part 1-Alberto and Kisha	p. 51
Process for Viewing and Analyzing Lemonade Lesson Part 1	p. 52
Commentary on Lemonade Lesson Part 1	p. 55
Reflecting on Exercise 1	p. 56
Exercise 2: Lemonade Lesson Part 2-Rosa and Maria	p. 56
Process for Viewing and Analyzing Lemonade Lesson Part 2	p. 57
Commentary on Lemonade Lesson Part 2	p. 58
Reflecting on Exercise 2	p. 59
General Commentary About Errors	p. 59
Working with Errors in Your Own Practice	p. 60
Homework	p. 60
Warm-Ups	p. 61
Class Discussions	p. 61
Periodic Diagnostic Interviews	p. 61
Wrapping Up	p. 62
Attention to Content	p. 63
Keeping an Eye on Rigorous Mathematics: Big Ideas and Habits of Mind	p. 64
Naming and Framing Mathematical Rigor	p. 65
Mathematical Frameworks: Big Ideas and Habits of Mind	p. 66
Big Ideas	p. 67
Habits of Mind	p. 69
Choosing and Using a Mathematical Framework for Analyzing Artifacts	p. 71
Exercise 1: Identifying Big Ideas in Your Math Textbook	p. 71
Process for Analyzing Your Textbook	p. 72
Commentary on Exercise 1	p. 74
Exercise 2: A Tale of Two Lessons-Using Mathematical Frameworks to Think About Rigor and Cognitive Demand	p. 76
Process for Analyzing the Lessons	p. 77
Commentary on Exercise 2	p. 80
General Commentary on Using Mathematical Frameworks to Consider Mathematical Rigor	p. 82
Using Mathematical Frameworks in Your Lessons	p. 83
Lesson Planning	p. 83
Teaching the Lesson	p. 84
Wrapping Up	p. 84
Choosing, Using, and Connecting Mathematical Representations	p. 85
General Commentary About Representations	p. 88
Exercises	p. 89
Exercise 1: Larry's Seventh-Grade Classroom Scenario	p. 90
Process for Analyzing Larry's Classroom Scenario	p. 92
Commentary on Larry's Classroom Scenario	p. 93
Reflecting on Exercise 1: Implications for Practice	p. 100
Your Own Practice and Work with Representations	p. 101
Using Artifacts to Examine Representations in Your Classroom	p. 101
Homework	p. 101
Warm-Ups	p. 101
Class Discussion	p. 102
Diagnostic Interviews	p. 102
Wrapping Up	p. 102
Additional Exercises	p. 102
Exercise 2: Video Games Fraction Lesson	p. 103
Process for Analyzing the Video Game Fractions Lesson Video	p. 103
Exercise 3: Garden Border Task: Student Methods	p. 107
Process for Analyzing the Garden Border Work Samples	p. 107
Putting It All Together in the Classroom	p. 113
Putting It All Together	p. 114
Exercises: Integrated Analysis of Whole Lessons	p. 115
Exercise 1: Building Triangles Lesson	p. 117
Process for Viewing and Analyzing the Building Triangles Lesson	p. 117
Commentary on the Building Traiangles Lesson	p. 122
Some Additional Points of Reflection	p. 123
Exercise 2: Multiplication Lesson	p. 124
Process for Viewing and Analyzing the Multiplication Lesson	p. 124
Commentary on the Multiplication Lesson	p. 130
Some Additional Points of Reflection	p. 132
Linking to Your Own Practice	p. 132
Final Thoughts	p. 134
Appendix	p. 135
Blank Worksheet (Chapter 2)	p. 136
Student Work Samples	p. 137
Blank Worksheets (Chapters 3-6)	p. 144
Lesson Graphs (Chapter 6)	p. 149
Blank Lesson Graph (Chapter 6)	p. 151
References	p. 152
Book Study Guide	p. 156
Deciding on a Facilitator	p. 156
Structuring Your Book Study Sessions	p. 157
Using the Reading Reaction Sheet	p. 157
Chapter Guiding Questions	p. 157
Combination of Structure 1 and 2	p. 158
Guiding Questions for Each Chapter	p. 158
Turning to the Evidence	p. 158
Describing and Interpreting Classroom Artifacts	p. 158
Seeing the Potential in Student Thinking	p. 159
Keeping an Eye on Rigorous Mathematics	p. 160
Choosing, Using, and Connecting Representations	p. 161
Putting It All Together	p. 161
Reading Reaction Sheet	p. 162
Index	p. 163
Table of Contents provided by Ingram. All Rights Reserved.

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Examining Mathematics Practice through Classroom Artifacts

Examining Mathematics Practice through Classroom Artifacts

0132101289

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