> 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.

> 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.