Making Algebra Meaningful

Nicole L. Fonger is an associate professor of mathematics and mathematics education at Syracuse University, and recipient of the Linking Research and Practice Award from the National Council of Teachers of Mathematics.

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