Being taught the material by someone who understands it well beyond the level covered by the class text/curriculum seems pretty crucial to me, too.

I think the fact that many primary teachers (and a few secondary ones) don't have a good grip on the underlying math themselves is probably a huge part of this problem.

I'm not really surprised by that observation, incidentally. My own mom was a terrible person to be teaching math beyond basic operations. Luckily, she taught K-2, so it was okay. But I had plenty of experience socially with her friends who were no more capable, and some of them were teaching 3-6. tired

Schrödinger's cat walks into a bar. And doesn't.