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.

It’s almost certain that you once had a test go badly. Whether that means you failed, or that you got a much lower score than you are used to depends on who you are and what your expectations are during a test. However, I would argue that the reason you had a bad test largely stems from the problem of not knowing where to start.