Making Algebra Meaningful

Learn how to design algebra lessons that are responsive to all students’ experiences.

An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher 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: (1) students’ algebraic reasoning and representing; (2) goal-directed classroom practices with technology; (3) culturally and historically responsive algebra literacy; and (4) teachers’ journeys toward antiracism. The author makes connections among research in algebra education; teaching algebra; and leading ambitious, equitable, and antiracist visions for algebra education.

By the end of this book, you will:

• Learn how to support students to fluently reason and represent expressions, equations, and functions.
• Learn how to design algebra lessons that are culturally and historically responsive to students’ experiences and social justice issues.
• Learn to use sketchnotes to reflect on and communicate complex ideas in teaching and learning algebra.
• Have a set of tools for guiding the design of instruction to support meaningful algebra learning for all students.

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.

“ Making Algebra Meaningful is a thoughtful, impeccably researched, and inspiring work…. An excellent resource for aspiring and practicing teachers as well as teacher educators and leaders. Highly recommended”

—CHOICE Reviews

“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

“In Making Algebra Meaningful, Nicole Fonger takes the reader on a journey to understand algebra learning from a variety of perspectives. Throughout the book, she effectively incorporates the metaphor of a lens, and the process of zooming in and out, to support readers with seeing mathematics teaching and learning differently. The author also affords readers opportunities to make connections through multiple representations, as the text is accompanied by the author's sketchnotes throughout the book. Readers are invited to sketchnote while reading to develop their ideas further.”
—Amanda Jansen, professor, School of Education, University of Delaware

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