Comment by mncharity

Hmm, I hope the "centralized planning" story wasn't distasteful. I was thinking of the stark contrast between say my writing a learning progression for category theory, versus say pointing out to a toddler that their observation about a game piece on a path, generalizes to any finite loop, including time of day, or a simple parking lot.

So let's see, possible contributions from interactive visualization to teaching linear algebra? Very not my field. And it's been decades for me. And my exposure to math education research is limited. So I don't recall what challenges, misconceptions, and failure modes are faced there. So, all I can offer is a handwave: perhaps a hands-on version of some 3Blue1Brown video?

Apropos "this is how everyone I know of already learns", at least for science education, this describes very very few K-13 students. Even among freshmen at a first-tier university. I'd be surprised if math was significantly different. Surprised but very interested.

Apropos "Many textbooks already have", yes... progress is often not something startlingly novel, but doing something we've already recognized as desirable, but doing it faster, better, more thoroughly, more cheaply, more consistently, for more people, etc.

Perhaps it might be more useful to think of tutoring others, rather than learning oneself? Dropping on someone a pile of texts, and telling them "find the corresponding sections yourself, work past the differences of notation, when you you think you might have a misconception, try googling the math education research primary literature to find how to deal with it, ...", well, hmm. What are the learning experiences we would ideally wish for each student, and can we use incoming tech to deploy less ghastly approximations of that.