Do you hate mathematics? Have you found that the rules you have to follow seem to make no sense? No matter what you do, it never feels obvious, like the teacher says it should. Perhaps you can follow your teacher through a problem, but you know that if you ever had to do the problem on your own, there’s no way you could do it.

As a student and someone who tutors others in science and mathematics, I’ve been able to get a lot of experience on both the teaching and the learning side of education. It has given me a better appreciation of the difficulty of our job as teachers trying to get students to understand. In particular, I’ve learned that being deliberate in my explanations is important if I want students to get what I’m explaining. Sure, I can have them fend for themselves, but the consequence is that they can get confused and frustrated for no good reason.

With a few taps, we can compare ourselves with thousands of other people. The comparisons can be anything we can think of. If there’s some kind of performance metric associated with your activity, you can bet there are places to compare results. It’s the nature of things. Humans like competition and comparison, so we build places where these comparisons are easy to find.

As a student, I’m used to diving right into the technical details of a topic. I don’t mind working through a wall of algebra, because that’s what I’m used to. If I wanted to describe how I learn in my classes, it would be: mathematics first, “high-level” understanding second. This isn’t a bad thing. I don’t mind going through the details first. Sure, I might not know how the concept relates to other ideas immediately, but I can learn that later.