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Hey! Good questions. I'll try to clarify: 1. First want to clarify that the learner is first introduced to the topics through mastery learning (i.e., not given a topic until they've seen and mastered the prereqs). So, they would explicitly learn A before learning B, and explicitly learn B before learning C. It's only in the review phase when we do all this stuff with "knocking out" repetitions implicitly. 2. When you say "then you can assume that you also know B and A to at least some part," I want to emphasize that if C encompasses B and B encompasses A in the sense of a full encompassing that would account for a full repetition, then doing C fully exercises B and A as component skills. Not just exercises them "to some part." For instance, topic C might be solving equations of the form "ax+b=cx+d," topic B might be solving equations "ax+b=c," and topic A might be solving equations "ax=b." 3. This scenario should never happen: "you are shown C, but don't know B anymore, and thus cannot answer and have to repeat C." There are both theoretical and practical safeguards. 3a-- Theoretical: if you are at risk of forgetting B in the near future, then you'll have a repetition due on B right now, which means you're going to review it right now (by "knocking it out" with some more advanced topic if possible, but if that's not possible, we're going to give you an explicit review of B itself. In general, if a repetition is due, we're not going to wait for an "implicit knock-out" opportunity to open up and let you forget it while we wait. We'll just say "okay, guess we can't knock this one out implicitly, so we'll give it to you explicitly." 3b-- Practical: suppose that for whatever reason, the review timing is a little miscalibrated and a student ends up having forgotten more of B than we'd like when they're shown C. Even then, they haven't forgotten B completely, and they can refresh on B pretty easily. Often, that refresher is within C itself: for instance, if you're learning to solve equations of the form "ax+b=cx+d," then the explanation is going to include a thorough reminder of how to solve "ax+b=c." And even in other cases where that reminder might not be as thorough, if you're too fuzzy on B to follow the explanation in C, then you can just refer back to the content where you learned B and freshen up: "Huh, that thing in C is familiar but it involves B and I forgot how you do some part of B... okay, look back at B's lesson... ah yeah, that's right, that's how you do it. Okay, back to C." And then the act of solving problems in C solidifies your refreshed memory on B. Anyway, I think I've clarified all your questions? But please do let me know if you have any follow-up questions or I've misinterpreted anything about what you're asking. Happy to discuss further. |
I guess math is uniquely suited for this kind of strategy, but would you say it translates to learning concepts in other domains too?
I was thinking about whether something like "what is X?" -> "What field is X used in?", which seems to form a hierarchy for me, would benefit of this technique? Personally, I found that for something like the preceding example, I could answer the second question without thinking about what X is at all, just by rote memorization of the wording. Happened to me quite a lot when I was using Anki. And actually, I guess this is even acceptable in some way, since the question is not about activating "what X is", but "what X is used in". What I am trying to express: I feel like I would not necessarily activate a parent concept by answering a child concept, and I think that might be true for a lot of questions outside math problems, although they form a hierarchy. So I am wondering what you think about the general applicability of this technique...
Please don't take all of this questioning wrong, I think you are doing pretty cool stuff, and I am grateful for everyone trying to push the boundaries of current SRS approaches :-)!