I recently participated in a psychology study in which I was asked a series of questions about people’s limits. The questions were along the lines of “Do you think that people are born with certain abilities? Do you think there is a point at which one can no longer improve at something?” The questions reminded me of something I was told last year, something meant to comfort me after I failed a calculus test that I had studied fervently for: “Some people just can’t do calculus.” I had redone every single homework assignment, I had met with my math teacher for clarification when I didn’t understand something, and I had done everything I thought possible to succeed in preparation, and I failed the test. And I believed what the person told me. I thought that maybe, just maybe, I was born without the ability to do calculus. It broke my heart. I thought I had reached a limit that I had not known existed.
I decided to take an accelerated calculus course (Math 41) fall quarter of my freshman year of college. It would have been easy if it was a repeat of my high school course, but even though I had already been through the material once, Math 41 took the material to further depths than I had gone to in high school. We weren’t just solving problems. We were using symbols I had never seen before to prove why solving problems worked. I found that the course was moving so fast that I didn’t have enough time to process what we were covering. When I didn’t do very well on a test I decided to switch into Math 19, a slower calculus course. I wanted to go slower (it covers the same material as Math 41 but over three quarters instead of two) so that I could thoroughly understand the material.
I spent the majority of my time studying for the Math 19 final. I didn’t just do the homework problems. I took them apart and used them as a starting point to come up with more difficult questions for myself. I would write next to a solved problem, “but what if it was like this…” and I would write a similar equation but with an added element of complexity. I walked into the final exam completely confident in myself. I was actually excited to take the test because I was certain that I would do well. I didn’t do great on the Math 19 final. I did alright. This is also a wonderful thing. Why? Because I IMPROVED. That’s really all that matters.
I may not understand 100% yet, but I am much better at calculus than I was a year ago. I understand it more now. Last year I thought that my brain just could not do calculus that I was born with something missing because other kids were not struggling like I was. But this year I am doing better at calculus. I just needed some more than my peers to get it. As long as I can improve, there is no limit to my abilities.