Get them talking: Your formula for bringing math concepts to life!
Want your middle schoolers to intelligently engage with mathematical ideas? Ready to help them construct and critique viable arguments that meet tough Standards for Mathematical Practice 3 standards? Look no further. This research-based gem will help you foster the critical reasoning and argumentation skills every student needs for intelligent discourse within our modern society. Learn how to bring mathematical argumentation alive in your classroomall within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.
Filled with content-focused and classroom-ready games, activities, vignettes, sample tasks, and links to online tools and a rich companion website, this innovative guide will help you
Immediately engage students in fun, classroom-ready argumentation activities Plan lessons that foster lively, content-driven, viable argumentation Help students explore mathematical ideas and take ownership of their learning Facilitate deep mathematical understanding Promote students precise use of mathematical language to construct, justify, and critique mathematical ideas and mathematical statements or the arguments of others. Encourage logical, clear connections between abstract ideas for enhanced 21st century skills
This guide delivers all the tools you need to get serious about mathematical argumentation and bring well-planned, well-constructed mathematical discourse to life in your classroom today!
Arvustused
If you share my belief that "construct viable arguments and critique the reasoning of others" are perhaps the nine most important words in the Common Core era, then Mathematical Argumentation in Middle School is just what you need. This powerful and practical book takes us through an accessible process of generating cases, making conjectures, and justifying that fully supports bringing SMP #3 to life in our classrooms. -- Steve Leinwand This great resource gives teachers tools to implement the four cycles of mathematical argumentation and help students develop a "variety of expertise," as described in the Standards of Mathematical Practice. As students cycle through the phases, they are guided in building "mathematical authority" as independent thinkers and creators of mathematical ideas. I recommend this book to any teacher who wants to amp up the math discussion in their classroom. -- Annette Hilts Now more than ever, we need to provide all children with opportunities to learn to think critically and participate in thoughtful, productive debate in todays society. This book translates the mathematical practice of argumentation into a four-stage process that can be applied across a wide range of mathematical content. This process utilizes an innovative, research-based approach based on improv games that opens access for all students to participate in the process of mathematical argumentation. Finally, there is a practical guide for making argumentation an everyday practice in mathematics classrooms! -- Kristen Bieda
| Preface |
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ix | |
| Acknowledgments |
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xiii | |
| About the Authors |
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xv | |
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Chapter 1 Mathematical Argumentation: Why and What |
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1 | (18) |
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Argumentation Is Important! |
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2 | (1) |
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What Argumentation Is---and Is Not |
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3 | (1) |
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A Four-Part Model of Argumentation |
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4 | (3) |
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7 | (1) |
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Teaching as Disciplined Improvisation |
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8 | (1) |
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Improvisation for Argumentation and Norm Setting |
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9 | (3) |
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Sharing Mathematical Authority |
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12 | (1) |
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Getting Started With Argumentation |
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13 | (2) |
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Argumentation Lessons Versus Argumentation in Lessons |
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15 | (1) |
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15 | (4) |
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Chapter 2 Generating Cases |
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19 | (20) |
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What Does It Mean to Generate Cases? |
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20 | (1) |
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An Activity Rich in Argumentation and Content |
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20 | (2) |
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Vignette: Small Groups Generate Cases |
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22 | (5) |
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27 | (2) |
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29 | (2) |
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31 | (3) |
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Tasks for Different Grade Levels |
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34 | (2) |
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36 | (3) |
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39 | (22) |
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What Does It Mean to Conjecture? |
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40 | (1) |
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Vignette: Conjecturing Together |
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40 | (4) |
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44 | (5) |
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49 | (2) |
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Vignette: Norms for Conjecturing Through Gift Giving |
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51 | (1) |
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52 | (2) |
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Tasks for Different Grade Levels |
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54 | (3) |
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57 | (1) |
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58 | (3) |
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61 | (24) |
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What Does It Mean to Justify? |
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62 | (1) |
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Vignette: Justifying Multiple Conjectures |
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62 | (7) |
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Teaching Moves for Eliciting Justifications |
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69 | (4) |
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Vignette: Critiquing and Connecting Arguments |
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73 | (3) |
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Teaching Moves for Critiquing and Connecting Arguments |
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76 | (2) |
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78 | (1) |
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79 | (2) |
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Tasks for Upper Grade Levels |
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81 | (2) |
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83 | (1) |
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83 | (2) |
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Chapter 5 Representations in Justifications |
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85 | (20) |
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What Are Representations? |
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86 | (1) |
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Vignette: Visual Representations Foster Participation |
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86 | (4) |
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Vignette: Gestures Enable a Unique Contribution |
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90 | (3) |
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93 | (2) |
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Using Dynamic Digital Tools |
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95 | (2) |
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97 | (1) |
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98 | (2) |
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Tasks for Different Grade Levels |
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100 | (3) |
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103 | (2) |
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Chapter 6 Levels of Justification |
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105 | (16) |
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Four Levels of Justification |
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106 | (1) |
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106 | (2) |
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Level 1 Case-Based Justifications |
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108 | (2) |
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Level 2 Partially Generalized Justifications Based on Cases |
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110 | (3) |
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Level 3 Fully Generalized Justifications |
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113 | (2) |
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115 | (1) |
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Teaching Moves for Transitions Between Levels |
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116 | (2) |
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118 | (3) |
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121 | (16) |
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What Does It Mean to Conclude? |
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122 | (1) |
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122 | (2) |
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124 | (5) |
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129 | (2) |
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131 | (1) |
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132 | (2) |
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134 | (3) |
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137 | (16) |
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How Can You Plan for Students' Argumentation? |
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138 | (1) |
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138 | (4) |
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142 | (1) |
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Vignette: Visualizing Justification |
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143 | (3) |
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146 | (1) |
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Updating and Sharing Lesson Plans |
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146 | (1) |
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146 | (4) |
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150 | (3) |
| Glossary |
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153 | (2) |
| References |
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155 | (4) |
| Index |
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159 | |
Jennifer Knudsen has been working in mathematics education since her days as a Peace Corps volunteer in Kenya and as a teacher in in New York City Public Schools. She has focused on students engagement in mathematics as an equity issue throughout her career, including work on numerous curriculum and professional development projects. She directs the Bridging Professional Development project as part of her role as a senior mathematics educator at SRI International. She holds a B.A. from The Evergreen State College, where she learned to love mathematical argumentation. She lives in Austin, Texas with her husband and daughter.
Harriette S. Stevens attended the University of Kansas where she received her Bachelor of Arts in Applied Mathematics and Master of Arts in Education, with a concentration in Mathematics. She received her Doctorate in Education, with a focus on curriculum and instructional design, from the University of San Francisco. She was the director of a mathematics professional development program for K-12 teachers at the University of California, Berkeleys Lawrence Hall of Science. In this capacity, she worked in partnership with several urban-school districts, and designed PD and instructional materials to help improve teachers understanding of mathematics content and their students preparation for success in college and careers. Currently, she is a consultant with the Mathematics Education Group, San Francisco and co-director of the Bridging professional development project at SRI International, Menlo Park. Her interests include a focus on strengthening teachers knowledge of mathematics content and the ways in which this knowledge is used to advance classroom discourse and problem solving in urban schools.
Teresa Lara-Meloy is passionate about finding better ways of teaching middle school math and improving ways to support teachers. As Math Ed Researcher at SRI International, she designs technology-integrated curricular and professional development materials. She received her M.Ed. from Harvards Graduate School of Education. She is a member of the NCSM and TODOS. She has co-authored articles on technology in education and the role of technology in supporting the participation of English Language Learners in math class.
Hee-Joon Kim, Ph.D. is a mathematics education researcher at SRI International located in Menlo Park, CA. Her research focuses on understanding classroom discourse that supports mathematical argumentation in middle school. She has expertise in designing curriculum materials with dynamic tools for students in middle grades. She has been involved in research-based professional development projects that focus on improving classroom practices that support conceptual understanding and promote equity. She received a B.S. in Mathematics at Ewha Womans University in South Korea and a Ph.D. in Mathematics Education at the University of Texas at Austin.
Nicole Shechtman, Ph.D., is a senior educational researcher at SRI International located in Menlo Park, CA. Her research and evaluation work explores critical issues in mathematics teaching and learning, innovative uses of educational technology, and the development of social and emotional competencies, such as effective communication, teamwork, and everyday problem-solving. She holds a PhD in psychology from Stanford University.
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