if someone receives explanation E_1 of a concept C, and they're paying attention, and they still don't intuitively grok C, then they need at least one more different explanation E_2.
That sounds about right to me. I'm not an expert on pedagogy, but from my own experience self-learning as an adult (a couple of languages to vary levels of fluency, math concepts that I never learned in school, a moderate amount of various fields) your hypothesis is correct. Being exposed to a concept from multiple angles or in multiple forms reduces the chance that someone won't be able to understand it.
I'd be willing to bet money that people who actually study the psychology of learning have a name for this concept, but I don't know what it is.
Yeah, we'd hope there's a good bit of existing pedagogy that applies to this. Not much stood out to me, but maybe I haven't looked hard enough at the field.
Why just math? This may seem like an obvious question, but your hypothesis applies to any type of learning: how to be a better parent, how to self-regulate emotions, moral philosophy, systems thinking or statistical thinking, physics, and so on.
Maybe! I'm most interested in math because of its utility for AI alignment and because math (especially advanced math) is notoriously considered "hard" or "impenetrable" by many people (even people who otherwise consider themselves smart/competent). Part of that is probably lack of good math-intuitions (grokking-by-playing-with-concept, maths-is-about-abstract-objects, law-thinking, etc.).
That sounds about right to me. I'm not an expert on pedagogy, but from my own experience self-learning as an adult (a couple of languages to vary levels of fluency, math concepts that I never learned in school, a moderate amount of various fields) your hypothesis is correct. Being exposed to a concept from multiple angles or in multiple forms reduces the chance that someone won't be able to understand it.
I'd be willing to bet money that people who actually study the psychology of learning have a name for this concept, but I don't know what it is.
Yeah, we'd hope there's a good bit of existing pedagogy that applies to this. Not much stood out to me, but maybe I haven't looked hard enough at the field.
Why just math? This may seem like an obvious question, but your hypothesis applies to any type of learning: how to be a better parent, how to self-regulate emotions, moral philosophy, systems thinking or statistical thinking, physics, and so on.
Maybe! I'm most interested in math because of its utility for AI alignment and because math (especially advanced math) is notoriously considered "hard" or "impenetrable" by many people (even people who otherwise consider themselves smart/competent). Part of that is probably lack of good math-intuitions (grokking-by-playing-with-concept, maths-is-about-abstract-objects, law-thinking, etc.).