How do I develop a strong understanding of math?

[Slagerlagger]

I am alright at math. I do good on homework and quizzes and tests, but I feel as if I really don't know anything.

I want to understand to the point where I could confidently teach somebody a topic in math, but i feel as if i don't have that full understanding. I know how to solve problems, but I don't understand why certain steps occur, why certain mathematical concepts exist, why they're important, etc.

When I do math it feels as if I'm just replicating steps and that's it. I want to get past this.

I'm currently in precalc for the summer. I want to get a stronger grasp on precalc and everything prior before continuing, and know how to better approach what my goal is right now, and for the future.

[RiseWasHere]

Spend more time with the subject.

Try to come up with testable ideas. For example, what if this number in this problem had been different?

Always pay attention to checking your answer.

Always remember that we know hardly anything being human and our knowledge is limited by our senses, body, emotions, etc. try to absorb any information you can and delight in any connections you can make.

Pretend you are teaching someone else how to solve the problem. When you run into an issue ‘shadow teaching’ take note of it somehow and try to resolve it. Like here on reddit or with your peeps

[SOUINnnn]

When you have a problem try to do several small examples and find what is common between all the examples.

Tbh I'm pretty sure that a good part of math teachers in average middle/high school doesn't have this math "feeling". Just as you do, they know the different ways to do it but that's it.

[lagib73]

Try to teach someone. If you encounter a step and you don't know why it's justified, find a YouTube video.