If you’ve ever taken a physics class on waves, the first type of mathematical wave you learn is the one due to what is called simple harmonic motion. The idea is pretty simple, so I’ll go through a rough derivation here.

One of the unfortunate side effects of having a curriculum and set schedule in mathematics is that one never gets to think about concepts for too long. Instead, the goal of a class is to simply throw a bunch of ideas to students and let them “ponder” the ideas on their own time. This is seriously backwards, and it’s at the heart of what is wrong with a lot of mathematics education today.

If you want to get a concept across, the best thing to do is to start simple. Learning can be difficult and many parts initially might not make sense, so it’s important to make the “jump” to that knowledge in a way that we can follow. If not, it will simply be too difficult to make that conceptual leap.

If you think about what students learn in mathematics at an early age, it isn’t too difficult to realize why many kids find it useless.