What does premature formalization mean and when does it occur? Do you mean formal in the sense of using formulaic, rote manipulations or formal in the sense of proofs and rigor?

As someone who went on to study mathematics at the graduate level, I was bored out of my mind in high school math and most subjects. What's missing from a lot of primary and secondary school education is context, and that's what makes it boring. Math wasn't easy because I was particularly good at it. It was easy because it was just blindly following formulas and basic logic.

Something is very wrong with our educational system because almost all math at the primary and secondary levels is basic logic. So when people with this maximum level of mathematics education say they're "bad at math" or "don't get math", it means that they lack extremely basic logic and reasoning skills.

In my mind, we need to teach mathematics in a contextual way (note that I don't necessarily mean applications) in a way to enrich the reasoning and exploring of it. This should include applications, yes, but not be fully concentrated on applications. Sometimes one needs to just learn and think without being tied to some arbitrary standard of it being applied.