This is not about “where I’m coming from”. Are you unfamiliar with the findings of Project Follow Through, the largest and most expensive educational comparative study in history?
The Moore method is developed for advanced students of mathematics in a small-class setting. It is intended for those who have already mastered the foundations and display some expertise in their field. Moore himself did not advocate for its use with general students and certainly did not consider this an appropriate way to teach students at an elementary school level.
I have direct experience with the Moore method and I can confirm that it is effective in its intended context. You are a PhD candidate — the Moore method is more than appropriate for students like you; in fact that’s precisely it’s purpose.
As for discovery learning (which is considerably more relevant for this discussion than the Moore method, which is not strictly “discovery learning” as practiced in public schools today): Every PhD in mathematics is required to build upon an established base of knowledge and produce original research. That is “discovery learning” as it is intended, and in its most effective context. In contrast, large-scale experiments at the elementary school level prove it to be a disaster, and those who advocate for this are doing the world of mathematics no favour.
Those with no personal base of expertise in a subject simply cannot be expected to “pull themselves up by the bootstraps”. If that were the case the most effective way to teach students would be to blow up schools, fire all the teachers and put kids out on the street to figure things out themselves from scratch. But you know as well as I do that this would only lead back to the stone age. Kids’ brains today are no different than those of our ancestors 10,000 years ago. The difference you see comes from education — the ability of students to advance to a modern PhD level in mathematics, where their ancestors could not … is having a heritage of established foundational knowledge passed on to them from previous generations. Or, again as in the Newton quote: “standing on the shoulders of giants”. Discovery learning applied to novices (as opposed to experts) cheats them of that birthright.
Have you ever heard of the expertise reversal effect? Look it up. I’ll suggest you stop mixing home-brewed philosophy about pedagogy-du-jour and consider the robust findings of cognitive science as pertains to how mathematics is shown to be best learned. Or … if you’re so convinced … cite us some RCTs and I’ll do the same.