[noelwelsh]

What you describe is entirely normal in my experience learning lots of stuff and teaching many others. It might help you to let go of the idea that learning is a linear process where you master one topic and move on to the next. As I learn more I'm continually getting a deeper understanding of basic material I "mastered" decades ago. I often tell my students I don't think their understanding is complete but it is sufficient to move on, and the later material will help them get a better understanding. And it does!

[mlyle]

> that learning is a linear process where you master one topic and move on to the next.

It's closer to true in mathematics than most other places, but not very close to true.

It's amazing the "layer cake model" of mathematics learning is such a strong idea even among many mathematics teachers.

On the other hand, sometimes a missing concept like cancellation in fractions or just poor proficiency in arithmetic rears its head and makes doing later stuff very hard. Once a student gets used to being and staying confused, it's often game over.

[RealityVoid]

> Once a student gets used to being and staying confused, it's often game over.

I think this is a very good insight, that somehow eluded me. Many many people are OK being confused about things, and I never considered that it's something they learn, but it makes so much sense.