You should look up "direct instruction" or mastery based learning. I was in agreement with you, mostly, but self-discovery has limits. I recently think this isn't the "optimal" way to teach, sometimes it's counterproductive. There might not _be_ an optimal way to teach and it might all be situational.

> People do not, as a general rule, "learn" stuff by people telling them stuff.

Yes. Recalling stuff and applying stuff is how we learn.

I strongly suggest you look into Math Academy and just bowse Justin Skycak's books on their method. I think they are right in many many aspects perhaps except the behavioral motivation ones. I think kids going through school need to either build self motivation or have someone build it for them, and I feel that is the gap in MA.