Learning math often feels like it’s all about right or wrong, like success or failure are the only two possible options and that all of your math expertise is visible as soon as you take a test. What I experienced as a student studying math and now as a math teacher is that this couldn’t be further from the truth. Some of my greatest learning experiences in math and truest moments of understanding have come out of failures. I’ve had many kinds of failures: tests, quizzes, homework assignments, most any assignment that you can think of. This may seem counterintuitive or it may make you question why I would be qualified to tutor math, but I see this as one of the most valuable assets I have as a mathematician. The act of failing a test, getting a problem wrong, or simply doing worse on something than you had hoped is often an amalgamation of mistakes and misunderstandings. Oftentimes this feels devastating, humiliating, and pushes people to think they’re “just not a math person.” However, if you take the time to learn from those mistakes and not just be afraid of them, you will have a deeper understanding of the math than you ever could have gotten from succeeding on your first attempt.
I remember taking my first ever quiz in Calculus and getting a C, a grade I was devastated and embarrassed by. However, once I was able to move past some of the shame, I knew that I needed to renew my studying as I knew I still had a test coming up and I was determined not to repeat this grade. I met with my teacher to discuss the mistakes I had made and learn about what I wasn’t yet understanding. My teacher re-teaching me this material gave me the insight that a lot of what I already knew was applicable to the questions I had missed on the quiz, and this second learning opportunity gave me the chance to connect my knowledge in a way I hadn’t before. At the end of the year when I was studying for the AP test this was the topic I felt most comfortable with and had the most ownership of, no doubt because of the fact that I had taken the time to pause and really take a second look from a new perspective.
Now, as a classroom teacher, I tell students from the very first day of school that mistakes are welcome and encouraged in my classroom. I highlight the mistakes that I make so that students can see me appreciating my own imperfections and see the ways in which I learn from messing up. The mistakes that my students make are often even more interesting to me than my own. Seeing the ways in which they think about a problem and make a wrong turn allows me to work with them not only on seeing the typical way of thinking about the math but how they can use their new idea/solution path as a strength to inform that problem and future work.
Mistakes are not something to shy away from in math class; they are something to be encouraged, appreciated, and revered as some of the greatest sources of knowledge. Without mistakes, we wouldn’t be able to see so many solution paths and creative ways of thinking that are invaluable to mathematical knowledge; so next time you make a mistake in math, work not to feel badly about it but instead celebrate it for the new knowledge it is helping you to create!