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