Celebrating Mathematical Mistakes: How to Use Students' Thinking to Unlock Understanding (Celebrate Mathematics Mistakes)

In this practical guide, authors Wessman-Enzinger and Gerstenschlager provide a foundation for celebrating mathematical mistakes and offer several strategies and task structures that encourage creative and flexible mathematical reasoning. Part of the Growing the Mathematician in Every Student collection, this book moves beyond the correct–incorrect paradigm by acknowledging the beauty, power, and ubiquity of mistakes, supporting more meaningful student learning.

This book will help educators:

• Learn three types of mistakes and their roles in mathematical reasoning
• Understand how mathematical errors encourage creativity
• Support students’ invented notation and language as demonstrations of their learning
• Apply strategies and task structures with real-life vignettes
• Reflect on chapter content with prompts

Contents:
Introduction
Part 1: Celebrating Mathematical Mistakes
Chapter 1: Shifting Our Views of Mistakes
Chapter 2: Beautiful and Powerful Mistakes
Chapter 3: Factual, Procedural, and Conceptual Mistakes
Chapter 4: Mistakes by Mathematicians
Part 2: Mathematical Mistakes in Action
Chapter 5: Two Foundational Instructional Strategies for Examining Mistakes
Chapter 6: Changing Minds in Mathematics
Chapter 7: This or That Tasks
Chapter 8: Invented Notation and Language
Chapter 9: Mathematical Games
Chapter 10: Mistakes in Action
Epilogue
References and Resources
Index

Nicole M. Wessman-Enzinger, PhD, is an associate professor of education at George Fox University in Newberg, Oregon. She teaches mathematics content to future teachers. Her main role at the university is preparing future teachers (K–12) to teach mathematics, but her favorite part of this work is helping her future teachers redefine their relationships with mathematics. She enjoys exploring mathematics deeply and creatively with them. She is a former high school mathematics teacher from Illinois, where she learned from her students and colleagues (like the incredible mathematics teachers at the Metropolitan Mathematics Club of Chicago).
Nicole is a member of various professional organizations, like the Psychology of Mathematics Education and the National Council of Teachers of Mathematics. She regularly presents at national and international mathematics education conferences. Various journals publish her work on students’ conceptions of numbers, mathematical mistakes, and joy in mathematics. She most enjoys studying children’s thinking about numbers as a way of recognizing children as mathematicians in classrooms.
Nicole received a bachelor’s degree in mathematics and mathematics education from Olivet Nazarene University (Bourbonnais, Illinois), a master’s degree in mathematics education from DePaul University (Chicago, Illinois), and a PhD from Illinois State University (Normal, Illinois).
The best part of Nicole’s day is supporting her own young mathematician, Mathilda, in experiencing the beauty and joy in mathematics.

Natasha E. Gerstenschlager, PhD, is an efficacy research manager for Imagine Learning, where she studies the impact of educational products on student outcomes. She is a former associate professor in mathematics education in Kentucky, where she taught mathematics courses for current and prospective teachers and developed and led professional development sessions on innovative, research-based teaching practices.
Natasha is a member of the American Educational Research Association and the National Council of Teachers of Mathematics, where she serves as a department editor. She has presented her work at national and international conferences, and her ideas around improving mathematics teaching across grade levels have been published in various journals. She enjoys connecting the ideas in research to the application of practice for mathematics educators.
In addition to her work, and more importantly, Natasha delights in helping her two children experience mathematics in their daily lives (particularly during camping adventures and while playing board games) so that they can develop a love and a joy for mathematics that go beyond the classroom.
Natasha received a bachelor’s degree and a master’s degree in mathematics and a doctorate of philosophy in mathematics and science education, all from Middle Tennessee State University.