An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade algebra classrooms.

Contents Acknowledgments  xi 1.  What Counts as Meaningful Algebra Learning  1 The Importance of Algebra  1 Big Question  2 My “Why?”  3 What’s My Angle? No Angle, but Many Frameworks or Lenses  3 Structure of the Book  6 2.  Learn to Sketch, Sketch to Learn  15 Why Should I Sketchnote?  15 Sketchnoting 101  21 Deepening Your Sketchnoting Practice  25 Math Ed Sketchnotes  29 3.  Algebra Is Something You Do  32 Mainstream Approaches to Doing Algebra  33 Responsive Approaches to Doing Algebra  36 Big Ideas of Algebra as a Course of Study  44 A Recap—What Is Algebra?  49 4.  Zoom Setting 1: A Focus on Students’ Reasoning and Representing in Learning Algebra  51 Learning to “See” Students’ Representational Fluency  53 Representational Fluency in Equivalence and Equation Solving  58 Learning to “See” Students’ Quantitative Reasoning  62 “Seeing” Students’ Functional Thinking  66 5.  Zoom Setting 2: Supporting Students’ Meaningful Algebra Learning Over Time in Classrooms  71 Supporting Meaningful Equation Solving  72 Visual Story 1: Supporting Students’ Representational Fluency in Determining Equivalent Expressions With Technology  73 Visual Story 2: Supporting a Functions Approach to Equation Solving  82 Visual Story 3: Supporting the Core Concept of Equations as Equivalence Relations  85 Reflecting on Frameworks of Instructional Supports for Meaningful Learning  90 6.  Zoom Setting 3: People, Place, and Algebra as a Tool for Critical Literacy  96 What Is Historically Responsive Literacy?  97 Visual Story 1: Historically Responsive Literacy Begins With Relationships and Identities  99 Visual Story 2: Thinking Like City Planners (Intellect) and Modeling Trends (Skills)  104 Visual Story 3: Criticality and Emotion  107 Practical Path Forward: People, Place, and Algebra as a Tool for Critical Literacy  108 7.  Journeying Toward Antiracism in Algebra  112 Disproportionality in Algebra for All: An Opportunity Gap  113 Journeying to See Racist Structures (Antiracism 101)  115 Practical Path Forward  118 8.  Tools and Practices for Advancing Algebra Education Together  122 Theme 1: Co-Visioning Meaningful Algebra Learning and Teaching  125 Theme 2: Building Effective Communication  126 Theme 3: Centering the Context, Place, and People of Where You Seek to Understand and Change Students’ Opportunities to Learn Meaningful Algebra  128 Theme 4: Co-Creating Knowledge in Community-Engaged Scholarship  129 Centering Equity (An Epilogue)  133 References  139 Appendix A. Chapter 2: Additional Sketchnoting Resources  147 Appendix B. Chapter 4: Additional Research  149 Appendix C. Chapter 5: Additional Activity Design Notes  151 Appendix D. Chapter 6: Research and Resources on Historically Responsive Literacy in Math  153 Appendix E. Chapter 7: Toward Antiracism  159 Index  169 About the Author  173

“Making Algebra Meaningful uses sketchnotes to share a vision of teaching that invites students to be curious, ask questions, and interrogate mathematical and social ideas. This book humanizes algebra as something that all people can do, and Fonger shows us how to support students’ identities as powerful, competent learners of mathematics.” —Amy Ellis, professor of mathematics education, UGA Mary Frances Early College of Education, University of Georgia