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! 


academics study skills MCAT medical school admissions SAT expository writing college admissions English MD/PhD admissions GMAT LSAT GRE writing strategy chemistry physics math biology ACT graduate admissions language learning law school admissions test anxiety interview prep MBA admissions academic advice premed homework help personal statements AP exams creative writing MD career advice study schedules summer activities Common Application history test prep philosophy computer science secondary applications organic chemistry economics supplements PSAT admissions coaching grammar law statistics & probability psychology ESL research 1L CARS SSAT covid-19 legal studies logic games reading comprehension dental admissions mathematics USMLE Spanish calculus engineering parents Latin verbal reasoning DAT excel mentorship political science French Linguistics Tutoring Approaches academic integrity case coaching chinese AMCAS DO MBA coursework PhD admissions Social Advocacy admissions advice biochemistry classics diversity statement genetics geometry kinematics medical school mental health quantitative reasoning skills time management Anki English literature IB exams ISEE MD/PhD programs algebra algorithms art history artificial intelligence astrophysics athletics business business skills careers cold emails data science internships letters of recommendation poetry presentations resume science social sciences software engineering study abroad tech industry trigonometry work and activities 2L 3L Academic Interest DMD EMT FlexMed Fourier Series Greek Health Professional Shortage Area Italian Lagrange multipliers London MD vs PhD MMI Montessori National Health Service Corps Pythagorean Theorem Python STEM Sentence Correction Step 2 TMDSAS Zoom acids and bases amino acids analysis essay architecture argumentative writing brain teaser campus visits cantonese capacitors capital markets cell biology central limit theorem chemical engineering chess chromatography class participation climate change clinical experience community service constitutional law consulting cover letters curriculum demonstrated interest dental school distance learning electricity and magnetism enrichment european history executive function finance first generation student freewriting fun facts functions gap year genomics harmonics health policy history of medicine history of science hybrid vehicles hydrophobic effect ideal gas law induction information sessions institutional actions integrated reasoning intern international students investing investment banking lab reports logic mandarin chinese mba mechanical engineering medical physics meiosis microeconomics mitosis music music theory neurology neuroscience office hours operating systems organization pedagogy phrase structure rules plagiarism pre-dental proofs pseudocode psych/soc quantum mechanics resistors resonance revising scholarships school selection simple linear regression slide decks sociology software stem cells stereochemistry study spots synthesis teaching technical interviews transfer typology units virtual interviews writer's block writing circles