Comment by edflsafoiewq
6 years ago
I feel a bit bad for saying this, but I don't think the interactive visualizations here really contribute very much. Yes, you can move the vectors, but the point is already made by the static picture.
Similarly, you can already traverse, not only a single math book in a non-linear order, but any number of different books and other sources concurrently, and this is how everyone I know of already learns. Many textbooks already have a dependency graph in the beginning showing how you can read the chapters! So every person is already traversing their own personalized "adventure graph" for linear algebra and will be throughout their entire education. It is rather the idea of a totalizing tech solution that will be perfect for everyone that smacks of central planning.
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.