As a tutor at the secondary level, I get an inside look at the various issues that students face within mathematics. While the specific issues are different from person to person, I’ve come to see a pattern emerging. Anecdotally, I think that most of the issues students face could be summarized with one sentence.

Last summer, the site Brilliant ran a program where participants tried to answer one new problem every day, within varying topics and of different difficulty. One in particular was interesting. Unfortunately, I can’t seem to find it on the site, but this is roughly how it goes:

Physical balance has always fascinated me. We do it unconsciously, and yet it is an essential part of movement. Balance is what keeps us from wiping out, or from getting our legs tangled in a mess of movement. Balance let’s us reach on one leg for an item that’s just out of reach, and it also lets us do complex movements when playing sports.

As someone who likes to learn new concepts, I’m guilty of “knowing” a bunch of mathematical concepts without knowing the “why” behind them. In other words, I’ve come across many neat bits of mathematics, yet I only understand them at a surface level. However, as I continue through my mathematical education, every now and then I’ll formally learn something that I came across before, and the explanation makes the concept that much more interesting in my mind.