Right. The conceptual roadmap I have works for me. But it doesn't work for my students because they don't have the detailed foundations for it that I have. Trying to give them _my_ roadmap can be wildly counterproductive.
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Replying to @ProfJayDaigle @St_Rev and
The trick to teaching is to find the roadmap that works for that student at that point in their learning. And this is a little different for every student because every student has a slightly different background.
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Replying to @ProfJayDaigle @St_Rev and
This is why office hours and supervised small group work are so invaluable. But there are still better and worse choices of roadmap to present in class. Finding the good choices there is one of the hardest and most important problems in education.
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Replying to @ProfJayDaigle @Meaningness and
I would argue the opposite TBH. The 'optimal roadmap' might shave 10% off learning time, at a cost of multiplying instructor labor costs by 10 or so. (This is what office hours amount to.)
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Replying to @St_Rev @Meaningness and
I wrote a piece on radically reforming education a few years ago (https://medium.com/@revspace/nintendo-school-for-gabrielduquette-57f1b3c92f59 … for a nicely formatted version) and part of the core concept was: replace lectures completely with student-matched video lectures, turn instructors into tutors.
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But that would require a way to meaningfully a) filter for the 'best' teachers and b) understand learning well enough to match lectures to students. And *we have no idea how to do this*.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.