"Mathematics instruction typically involves a correct answer. But what if, instead of penalizing students' mathematical mistakes, we use their errors as vehicles for deeper mathematical understanding? In Celebrating Mathematical Mistakes: How to Use Students' Thinking to Unlock Understanding, Nicole M. Wessman-Enzinger and Natasha E. Gerstenschlager posit that students' mathematical errors can be ripe teaching opportunities that allow for more meaningful learning. In this practical guide, Wessman-Enzinger and Gerstenschlager define three types of mathematical mistakes and offer several strategies and task structures-including play and games-that encourage creative and flexible mathematical reasoning. Part of the Growing the Mathematician in Every Studentcollection, Celebrating Mathematical Mistakes moves beyond the correct-incorrect paradigm by acknowledging the beauty, power, and ubiquity of mathematical errors"--
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 MistakesChapter 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 ActionChapter 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
