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