In the Classroom / Oakland / Teaching Residency / Uncategorized

The Value of Mistakes

It’s mid-August and the building buzzes with teachers preparing for the first day of school. I find myself wondering what to do with this big, empty room that feels sterile and uninviting. The pressure to have a space worthy of Instagram or Pinterest weighs on me. How can I welcome my freshmen into an Algebra 1 classroom that screams Algebra Fun? I search online for motivational quotes about math and academic habits and settle on, “It’s okay not to know, but it’s not okay not to try.” As I walk to the printer with my neon card stock in hand, I begin questioning what this statement truly communicates. After all, I want to stand behind whatever words I put on my wall. Just as I’m about to push “Print,” I realize that the message I hope my students take away from the quote isn’t really the value of hard work, though of course that’s important, but rather the importance of mistakes.

“Mistakes are proof that you are trying.”

At the time, I had no idea how important these seven words would be for me and my students.


My “mistake wall” with student work and our problem solving strategies


My classroom before the arrival of students

It’s first week of school. Beginning the year with “A Week of Inspirational Math,” motivated by Jo Boaler’s work at YouCubed, students across the Leadership Public Schools network engage with pattern-seeking activities that ask them to consider math from a different perspective. My students explore Pascal’s Triangle and engage with neuroscience about the impact of mistakes and struggle on our brains. We talk about growth versus fixed mindsets and evaluate where each of us fall on the mindset spectrum. We learn how mistakes make our brains grow and how fixed mindsets hinder our potential. We reflect on our past failures and remind ourselves how those moments of struggle and defeat taught us important lessons about how we think, learn, and understand. I tell my students that mistakes, not answers, are my favorite part of learning mathematics. Mistakes help us reinforce concepts. Mistakes provide us opportunities to consider and adapt our thinking. Mistakes allow us to re-frame failure and reflect on what we tried rather than where or how we failed.


Drawings my students made after we watched a TedTalk and looked at research about the ways mistakes help our brain grow

My first big assignment asked students to consider their Mathematical Autobiography. What experiences affect how you think and feel about math? In their essays, word clouds, and drawings, my students reflected on the moments, big and small, that shape their understanding of themselves as learners. I saw students whose academic experiences reinforced the importance of being right and obscured the value of mistakes. I also saw students whose resilience and belief in their ability allowed them to achieve success and helped them recognize their own potential. The insights of my 13-15 year-old Algebra 1 students surpassed what I understood at their age. Their autobiographies resonated with me deeply, and I knew I had to share their words:

“I didn’t think I could do it until I tried. That’s when I learned that I can be good at something if I actually try.”

“When I was in a community of people who didn’t care, I stopped doing my work.”

“You have to take a risk on answering the question to know if you’re right or wrong.”

A word cloud Math Autobiography

A visual Math Autobiography with a written description.

Fast forward to October. In retrospect, it feels like it happened almost by accident. I did not plan to make mistakes the central focus of Algebra 1 from the outset, but now I could not imagine what class would be like without this emphasis. The words of 23 of my students hang as posters on my wall; in each class we reflect on the insights of one of our peers. We remind ourselves of the value of mistakes, the importance of hard work, and the need for failure in math. We celebrate the errors we make, and we remind each other that mistakes are a part of learning. I admit my mistakes openly and proudly. I ask students to find the errors in my work and remind my students that making mistakes means progress, because we can turn mistakes into new learning.


Posing in front of the number line I made at the front of my classroom

As a teacher, I realize how important and integral mistakes are to student learning, but the “student” in me still recognizes the discomfort and embarrassment I feel whenever I fail. Everyday, I see my students try to hide their confusion, concealing their mistakes from their peers and from me. Maybe it’s just high school, but there’s a part of me that knows deep down it’s human nature to want to appear successful and competent in front of others. Though I remind my students that their mistakes and failures provide rich opportunities to learn and grow, I sometimes struggle to take my own advice. As a first-year teacher, I make mistakes every day that impact my students. I try a new routine or design a creative lesson plan that leaves my students confused and frustrated. I give a consequence to the student whom I catch, rather than to the one who instigated. As I reflect on my first month and a half of teaching, I try to re-frame my classroom challenges and missteps as moments of personal and professional growth. I made a bad call; I wrote a mediocre lesson; I assigned a poorly written task. It happens and will happen again. What I must trust is that I am a better teacher today than I was yesterday, and I’ll be an even better teacher tomorrow. My mistakes in the classroom define me insofar as they provide me with opportunities to evolve both as a teacher and as a human being. My students’ learning will be deepened by their mistakes, and our capacity to rise in the face of adversity and defeat will increase as we continue to admit and celebrate our failures openly.

Caroline Murphy is a Harvard Teacher Fellow from Cohort II who recently began her residency year at Leadership Public Schools – Richmond in Richmond, CA. Caroline teaches Algebra 1 and Math Game Lab, co-advises the Music Club, and serves as an advisor for twenty 9th grade girls. She shares her love of math (and mistakes) with her students and hopes to foster in them an appreciation for the subject and for the critical thinking and problem solving skills it develops. As a graduate with a degree in Music, Caroline reminds her students that a love of math and quantitative reasoning can connect to their interests in other subjects and outside the classroom.


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