Making mistakes in math class

academic advice academics mathematics

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! 

Comments

topicTopics
academics study skills MCAT medical school admissions SAT college admissions expository writing English strategy MD/PhD admissions writing LSAT GMAT physics GRE chemistry biology math graduate admissions academic advice law school admissions ACT interview prep test anxiety language learning career advice premed MBA admissions personal statements homework help AP exams creative writing MD test prep study schedules computer science Common Application mathematics summer activities history philosophy secondary applications organic chemistry economics supplements research grammar 1L PSAT admissions coaching law psychology statistics & probability dental admissions legal studies ESL CARS PhD admissions SSAT covid-19 logic games reading comprehension calculus engineering USMLE mentorship Spanish parents Latin biochemistry case coaching verbal reasoning AMCAS DAT English literature STEM admissions advice excel medical school political science skills French Linguistics MBA coursework Tutoring Approaches academic integrity astrophysics chinese gap year genetics letters of recommendation mechanical engineering Anki DO Social Advocacy algebra art history artificial intelligence business careers cell biology classics data science dental school diversity statement geometry kinematics linear algebra mental health presentations quantitative reasoning study abroad tech industry technical interviews time management work and activities 2L DMD IB exams ISEE MD/PhD programs Sentence Correction adjusting to college algorithms amino acids analysis essay athletics business skills cold emails finance first generation student functions graphing information sessions international students internships logic networking poetry proofs resume revising science social sciences software engineering trigonometry units writer's block 3L AAMC Academic Interest EMT FlexMed Fourier Series Greek Health Professional Shortage Area Italian JD/MBA admissions Lagrange multipliers London MD vs PhD MMI Montessori National Health Service Corps Pythagorean Theorem Python Shakespeare Step 2 TMDSAS Taylor Series Truss Analysis Zoom acids and bases active learning architecture argumentative writing art art and design schools art portfolios bacteriology bibliographies biomedicine brain teaser campus visits cantonese capacitors capital markets central limit theorem centrifugal force chemical engineering chess chromatography class participation climate change clinical experience community service constitutional law consulting cover letters curriculum dementia demonstrated interest dimensional analysis distance learning econometrics electric engineering electricity and magnetism escape velocity evolution executive function fellowships freewriting genomics harmonics health policy history of medicine history of science hybrid vehicles hydrophobic effect ideal gas law immunology induction infinite institutional actions integrated reasoning intermolecular forces intern investing investment banking lab reports letter of continued interest linear maps mandarin chinese matrices mba medical physics meiosis microeconomics mitosis mnemonics music music theory nervous system