Picture this-you’re solving an equation taking up an entire page in your notebook and the answer you manage to find is incorrect. After all the erasing and calculations, you somehow made a mistake. Or maybe you’re rushing through your test in precalculus and when you’re handed the paperback, points were taken off over silly mistakes. You regret making these mistakes and your mind is filled with things you could’ve done differently. 

      You might be shocked to hear this but mistakes (and failure) are quite powerful and life-changing. The mistakes you make in math problems set you up for learning how to bounce back from failure and being alright with seeing that you made a mistake (as most humans do). 

      In a study on neural mechanisms by psychologist Jason Moser, he found that when students made mistakes, synapses (electrical signals that move when the brain is learning something) fire. Moser states that “I tell [teachers] 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” (Moser et al., 2011). 

      Mistakes are completely normal, your thoughts and line of thinking matters even if something went wrong because you are learning from these mistakes. Mistakes should be embraced and valued because they make your brain grow (in layman’s terms). Helping students learn from their mathematical mistakes can enable them to have an even deeper understanding of the material they are learning. Seeing where they went wrong, be it conceptually wise or misreading the problem can also benefit teachers because chances are, if one student had trouble with something then another might’ve too. 

      Now how can you use your mistakes to help you learn better? Copying the answers from a student or the back of a textbook is not fostering your learning nor is it teaching you how to grow from mistakes. While mistakes are essential to growth and moving forward in life, not taking the initiative and trouble to analyze your mistakes will only hold you back. 

      First understand that you are in a mistake-friendly environment, a place where you are not judged for your mistakes. Not only will this help you let go of overthinking your mistakes (maybe you think that someone will make fun of you) ─ you are also helping the people around you learn to be okay with failure. Humans aren’t perfect, math isn’t perfect, and mistakes (by definition, technically) are not perfect and that is one of the most beautiful parts about life and learning. 

      If you are looking for a heartwarming read, check out Beautiful Oops! by Barney Saltzberg. The book highlights the beauty of imperfection, the art you can make from mistakes. Be it a torn piece of paper as demonstrated in this children’s book or a calculation error in your notebook, there is value in making mistakes. 

      Looking at mistakes in a negative light can take a toll on your mental health, not only are you bashing yourself for making mistakes but you are spending time thinking that the work you are doing doesn’t matter. When you adopt a growth mindset when you approach making mistakes in math, you move past thinking that some people are just born being good at math. This growth mindset reduces stress and anxiety over making errors because you are comforted by the knowledge that the people around you make mistakes too. 

      You show less signs of seeking perfectionism and obsessing over getting all the problems correct. A study done by Richard W. Robins and Jennifer L. Pals on the effect of mindset states that people with a fixed mindset do not believe that they can improve themselves academically. If you believe that you can grow from your mistakes, be it big or small, you are pushing your brain to learn more to better yourself, academically and mentally. Your self-esteem is boosted because after leaning from the aforementioned mistakes, you become more confident in solving problems and bouncing back from failure. 

CITATION: Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011). Mind Your Errors Evidence for a Neural Mechanism Linking Growth Mind-Set to Adaptive Posterror Adjustments. Psychological Science, 0956797611419520.

Richard W. Robins & Jennifer L. Pals (2002) Implicit Self-Theories in the Academic Domain: Implications for Goal Orientation, Attributions, Affect, and Self-Esteem Change, Self and Identity, 1:4, 313-336, DOI: 10.1080/15298860290106805

ONLINE: https://europepmc.org/article/med/22042726 

https://www.tandfonline.com/doi/abs/10.1080/15298860290106805