Comment by mncharity
6 years ago
Incoming tech seems about to change the texts-and-tutoring constraint and opportunity space. I wonder if it's time to start thinking and exploring ahead?
Consider an art project, where you sit in a booth, and watch an interesting video drama. But why is it interesting? The video is a graph of segments, like an old "choose your own adventure" story. And there's an eye tracker watching you. So if you're interested in characters A and B, the story mutates to emphasize them.
Consider a one-on-one tutor on a good day. Noticing a student engaged and enthused, they might reorder content on the fly to leverage that. Might emphasize different aspects, and alter presentation, based on observed interests and weaknesses. Or consider working with a young child, watching them read word by word, noticing their where they hesitate and frown, probing for their thoughts, adjusting difficulty, providing a path of development.
What if that was math content rather than a drama or children's book? What if we could do this at scale? Eye tracking is just one tech coming in on the coattails of VR/AR. A setting for personalization AI is another.
What if saying "the best way to organize and present this topic in a textbook", becomes like saying "the Capital mandates, that every teacher of this grade, will today all teach the following lesson, by saying the following words, regardless of local context"? While not on a national level, that is a real thing.
What might it take to start encoding an adventure graph for linear algebra? The "oh, if you like this perspective on this topic, you might like this similar perspective on this other topic"?
Or if we don't have the tooling for that yet, can we start thinking about the tooling? Or fruitfully do something else now, in preparation for opportunity? Perhaps Kahn academy problems in more flavors, in a richer graph? ML-based textbook aggregation, synthesis and retheming? Perhaps it's all not ripe yet. But something else, maybe?
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.
I think your idea can be developed today by selecting online forums centered on topics. The main problem is moderation and how to plan the journey.