Here’s one article which shows a different view on this:
FWIW, my experience is that I learn better going up and down the different layers, rather than exhausting and completely “automating” the lower layers before attempting to go to the advanced material on the upper layers.
Plus, some experience with something what you’re learning is useful for is a great motivator and can help focus.
I guess the failure to avoid is the conclusion “I have already done this successfully once, no need to pay attention to this ever again, because I am already good at it”.
Practicing it is one option, doing something related and then revisiting it later seems like even better option, because it can give you a different perspective.
By the way, in the linked article, I can confirm that this little known thing is true for most teachers. It may sound weird if you had good math education, but that is an exception, not the rule:
the people who teach in elementary schools are not mathematicians. Most of them are math-phobic, just like most people in the larger culture.
I wish that instead of giving up on math, we could find a way to teach the teachers. Technically it should not be difficult (we only need to teach them the elementary school math, but in a way they will understand), the main problem would probably be admitting that “teachning elementary school math to elementary school math teachers” is a thing that needs to be done (to avoid the situation where the teachers are ashamed to participate, because that would mean admitting that they actually suck at their jobs). Perhaps redesigning the math curriculum, and then teaching math to math teachers under the pretense that we are “preparing them for the new curriculum” could be a solution.
I can confirm that my maths teachers at primary school were terrible: if you stepped a little bit outside what’s in the book, they were absolutely lost.
They were a lot better in secondary school, possibly because they had a much stronger mathematical education (secondary school teachers usually have a university degree in the subject they teach or in a closely related field, at least in my country).
I also absolutely agree with what you say about overconfidence and the need to revisit a subject / layer instead of thinking “it’s over for good”.