Mathematical Mindsets: Chapter 2

Last week, I began participating in a collaborative book study with 12 other bloggers focusing on the book Mathematical Mindsets by Jo Boaler. Chapter 1 described what happens in the brain when we learn new things and illustrated the difference between a fixed mindset and a growth mindset. (Read Chapter 1's post here.) Chapter 2 discusses the power of mistakes in mathematics. 

Chapter 2 Summary

Making a mistake is good! It lights up our brains causing it to "spark and grow" (p. 12) even when we don't know a mistake was made. Coupled with a growth mindset, when an individual believes he or she has the ability to learn and that mistakes are just part of the learning process, mistakes will cause our brains to grow, especially when we participate in challenging tasks.  

My Big Takeaway

Mistakes should be valued, celebrated even. When I read this chapter, I immediately began thinking about my years as a classroom teacher and how many times I may have given the impression that making a mistake at a certain point in the year with curriculum that we had learned months earlier was wrong. I know that my intention was to build proficiency, but I'm not sure that is the message my students received. 

After reading this chapter, I understand the power that was in the mistakes my students made with curriculum we had learned sometime earlier and how taking the time to analyze them carefully may have led us down a new path. A path that may have led to a deep misunderstanding that the students still had-- an opportunity I missed to help them become more successful learners.  

Ways to Use this New Knowledge to Support Our Students in the Classroom

1. When we are reviewing assignments, move from analyzing assignments for correctness and begin to analyze them for mistakes. We should ask ourselves, "What do the mistakes reveal about where my students are in the learning process?" Then create an appropriate plan of action to address the mistakes.  

2. Use Jean Piaget's concept of "disequilibrium" to promote a growth mindset. Helping students understand this concept will send two important messages: 1.) It's okay not to know the answer right away and 2.) It's okay to struggle (Carter, 2008). Providing tasks that put students in a state of disequilibrium will help them develop and understand the role of productive struggle in the successful learning of mathematics.  

3. Celebrate and highlight mistakes! "My Favorite No" is a teaching strategy that does just that. Click the video link below to see the strategy in action in a real math classroom. Don't see the video? Click here. 

As we prepare to return to school for the fall semester, it's important to consider the role mistakes will play in our classrooms. Will our students hide and shyly respond to questions of which they are unsure of the answer or will they be proud of their thinking, even when it is wrong? While this way of thinking about the role of mistakes may be foreign to many of us, it's imperative to helping our students find success in mathematics.  

       Sound Off! How will you celebrate mistakes this year?

References: 

• Boaler, J. (2016). Mathematical Mindsets. San Francisco, CA: Jossey-Bass 
• Carter, S. (2008). Disequilibrium and questioning in the primary classroom: Establishing routines that help students learn. Teaching Children Mathematics, 15(3), pp. 134-37. 

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