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adamzerner comments on Rethinking Education - Less Wrong
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Maybe, but probably at level 1, maybe level 2, but surely not level 3.
I don't see anyone else emphasizing the importance of the dependency tree and of making sure that at a small enough level, students know the prerequisite information.
At a small enough level, yes. But I don't think we'll really be able to understand this level well enough to use it. So I think that the idea is just something to keep in mind when thinking about how to motivate students.
Not at all! If I thought that this could be done with 10 volunteers I'd be trying to do it right now. I think that this would need hundreds, probably thousands of people. Consequently, I think that the best thing I could be doing is making enough money to (help) pay for all of this, so I'm starting a startup: http://www.collegeinsideview.com/.
When I was a student, teaching other students privately math, I automatically started explaining any topic by testing whether they understand the prerequisites. -- I started one step before the new topic, and if they failed the test, I backtracked another step before the failed test. I didn't have a complete map in my mind, but at each moment I simply thought: "what are the immediate prerequisities for this?".
I doubt I was the first person to think about this. Does the fact that I don't remember anyone explaining this to me explicitly (before I came to university) make it somewhere between the levels 2 and 3?
You know what all teachers do in summer, before the school year starts? They prepare the sequence in which they will explain the topics during the year. (At least if they teach for the first time, because later they usually reuse the stuff from the previous year.)
As I said, they probably don't think about this as a "directed acyclic graph", but rather as a "linear sequence where some parts can be reordered" (because most of them are not computer science people). The idea that the topics have some prerequisites, and you need to explain them in the proper order, is out there at least for decades.