Learning to Fail, Not Failing to Learn
Why Is One Greater Than Zero?
I entered college as a physics major. I had never considered anything else until I met a second year who waxed poetic about an introductory proof based calculus class. I was intrigued but nervous. I had never done anything of the sort before, and being in a class with mostly math majors sounded daunting.
I am now a math major.
It happened unexpectedly, and quite accidentally. I took the first quarter of the proof based math class, and I was intrigued. So, I took the second. And the third. Suddenly, I found myself needing to continue to take math major courses so I could gain the required credit needed to major in physics. At this point, it was actually easier for me to double major than not. It worked out, though. I am enamored by the world of math.
Before taking a proof based math class, I never wondered why 1 is greater than zero. It just is, right? I rolled my eyes right out of my head when we were asked to prove this. Hold up a fist. Now hold up one finger. Is it not clear that the one finger you are holding up now is greater than the zero fingers you were holding up a second ago? It turns out there is a lot more to the story than that. The proof rests on definitions of ordered fields and field axioms- both concepts we proceeded to flesh out into a deep understanding of calculus.
Throughout the year, we proved calculus from the ground up. Math is a fascinating subject, and I am so grateful to have the opportunity to engage with it in such a unique way. I began and continue this major out of curiosity, not necessity, and it’s become clear that I am at my best when I am learning for its own sake.
Failure
Admittedly, though, I don’t always have such feelings of good will toward my accidental major. The problem sets are long, the exams are hard, and I get tired sometimes. Nothing takes the wind out of my sail like an exam. I am a terrible test taker, so I am frustrated with exams regardless of whether I am taking one or not. But, when my grade is on the line as well, the anxiety becomes hard to ignore. I am no longer excited to understand the zany world of functions. Instead, I would rather not be a math student at all.
Unfortunately, I feel this way very often. My life as a student is a constant struggle to balance my need to perform with my desire to learn. I wish I could doff the pressure of exams, but the reality is that they do matter. Right now, perhaps more than learning.
Of course, performance doesn’t matter more than learning to me. I am a student because I am curious. I work hard because I want to understand. This is a mentality I work hard to cultivate. But, if I want to reach the next level of understanding — an interesting summer internship or the next course in my majors — I need prove somehow that I have learned the material. The selected metric is performance on tests. But, the pressure of performance makes me anxious, and I consistently underperform. As such, I never really feel like my performance accurately represents my understanding.
The problem, then, is that it is so easy to loose sight of that spark of curiosity that made me love these subjects in the first place. If I am constantly worried about performance, then I can never appreciate learning for its own sake.
For instance, I recently got a terrible grade on my physics midterm. I have been living the class, enjoying the the homework, and I feel like I am really understanding the material. My grade does not reflect this feeling in the slightest.
Getting this grade back pushed me into panic mode. Now, I have to perform exceptionally on the homework. Instead of working to learn, I am working toward precision by constantly checking my answers with classmates and online sources. The question I ask myself is no longer ‘am I learning this’? Now, I am stuck asking myself ‘is this correct’? The excitement I felt for this class a mere week ago is now fleeting.
Learning to Fail, Not Failing to Learn
But why should one bad grade cause this much grief? Unfortunately, anyone who considers themselves a perfection or has received criticism when they felt their best understands how discouraging anything analogous to a bad grade can feel. It’s hard to remember how cool it was to first learn why one must be greater than zero when your exam bled so much it looks like a murder scene. It’s hard to retain passion when you fail.
These are the moments when a mental reset is in order. Just like how in math it’s easy to get lost in the weeds of complex theorems and proofs, it’s easy to get lost in the world of performance. So, take a step back? What were the assumptions you began your project with? What are your axioms — those things you know to be true without needing to prove them to yourself?
For me, it is my curiosity and love of learning. I entered college knowing that physics might be too hard for me to tackle, but I was simply too curious not to. Physics and math excite me, and though it is hard to remember that when I enter performance mode, it is unequivocally true. It is what drives me to continue and what makes me feel purposeful in my studies.
Once you understand the axioms you’re working with, it becomes a little easier to step back and apply them. My physics midterm grade was bad — really bad. And now I need to focus a little more on performance to make up for it. But, this doesn’t mean I can’t also learn while I do this. Physics is fascinating. That is why I am taking these classes, not to feel smart because I perform on an exam.
It certainly won’t be easy to keep this in mind. Failure is hard, and the rapid pace of life leaves little time for reflection and self-love. But, I know that without making time to return to my axioms, academics become work — not play — and I will lose the curiosity that makes late nights at the library not just worth it but also enjoyable. This is a reflection on the way I approach failure in my own life, but it is also a problem to myself to hold my axioms in mind while I continue to learn. It is an imperfect solution — performance is still important and promising my professors that I want to learn will not suffice to prove that I have learned — but it is important nonetheless. After all, I am at my best when I am learning for its own sake. This is my axiom. What are yours?
