Teaching a skill directly is known to be more a more efficient way of learning rather than force students to try to discover it on their own.
The studies you refer to are demonstrating that active/unguided is superior to passive/direct.
But the full picture is that active/direct > active/unguided > passive/direct. (I didn't include passive/unguided here because I'm not sure it's possible to create such a combination.)
Other studies -- that only manipulate one variable at a time -- support this big picture.
Its possible, we call the end result LLM. It isn't very effective though as we can see from the result and how much learning it took.
To me though the more interesting result isn’t really about pedagogy, it’s that people’s (undergrad physics students, in the case of the specific study I’m thinking of) subjective impressions of the effectiveness of instruction are unreliable.
Yes, common finding in studies that explore subjective vs objective measurements of learning under conditions involving "desirable difficulties":
My undergraduate math professor was like that, and he was pretty brutal, but by the end of the 2nd semester it was pretty clear who was going to end up majoring in something to do with math and who wasn't. From a pure selection standpoint, this makes sense to me. On the other hand, for those who "won't" it can make the experience pretty miserable.
I'm probably confusing people with my use of the word "will" in this context, since it can mean several things in English. What I'm really saying is that those who have the actual aptitude "will derive complex concepts on their own, and will be likely to pursue further their math education". It's already difficult to identify those people when they're young enough, and even harder if you teach math in a "lowest common denominator" approach, which is essentially what the American strategy is (with notable exceptions that probably just prove the rule).
At what point would you say they've actually acquired the skill?