Like many teachers and math coaches, I have often thought about missed opportunities for learning when I see mistakes in students’ work, and I long for ways to have students engage with misconceptions and errors. For as Jo Boaler explains about why mistakes cause your brain to grow:
When teachers ask me how this can be possible, I tell them that the best thinking we have on this now is that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged and the challenge results in growth.
I am excited about Nancy Anderson’s new book, What’s Right About Wrong Answers: Learning from Math Mistakes, Grades 4-5. She provides twenty-two error analysis tasks for students that focus on common misconceptions. Each task, presented on a handout, is part of an activity including independent work, partner work, group discussion tasks and extension problems. The handouts are presented in 3 different engaging formats, comic strips, letters, and sample student work. Teacher notes for using the activities are clear and easy to follow. The combination of discussing the misconceptions of fictionalized students and working on similar problems, invites students to talk about mistakes and reflect on their own misconceptions.
In her introduction, Nancy personalizes the importance of students reflecting on their own errors. Reflecting on her own experiences in math, she writes, “I didn’t need explanations that focused on correct solution strategies but help in finding the flaw in my approach… to identify and unravel my misconceptions and use my mistakes to find correct solutions.” Isn’t that what we want for our students?
Reading the book led me to search for other resources focusing on math mistakes. The format for error-analysis activities in What’s Right About Wrong Answers seems to be unique. But there are many other wonderful resources with insights about students’ mistakes and misconceptions. I found the following books and websites:
Books:
Common Mistakes in Teaching Elementary Math- And How to Avoid Them by Fuchang Liu; 2017
Smarter Than We Think by Cathy Seeley: 2014; specifically Chapter 8 Oops! The Value of Mistakes, Failures, and Wrong Turns
#1 hint: Model how to deal with mistakes
Math Misconceptions, PreK-Grade 5: From Misunderstanding to Deep Understanding by Bamberger and Oberdorf; 2010
Activities to Undo Math Misconceptions, PreK-Grade 2 by Bamberger and Schultz-Ferrell; 2010
Mathematical Misconceptions: A Guide for Primary Teachers edited by Cockburn and Littler; November 2008
Websites:
http://mathsolutions.com/uncategorized/teaching-students-to-learn-from-their-mistakes/ Tips for helping students learn from mistakes:
Examples:
- Make them commonplace topics for discussion
- Give problems with challenges that will be likely to bring up some misconceptions
By NCTM President Linda M. Gojak
NCTM Summing Up, January 8, 2013
Linda quotes Norman Juster’s wonderful book The Phantom Tollbooth. I fondly remember reading this to my third and fourth grade students and discussing the role of making mistakes in learning
“It has been a long trip,” said Milo, climbing onto the couch where the princesses sat; “but we would have been here much sooner if I hadn’t made so many mistakes. I’m afraid it’s all my fault.”
“You must never feel badly about making mistakes,” explained Reason quietly, “as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons.”
― Norton Juster, The Phantom Tollbooth
Let’s keep helping our students engage in learning from mistakes!