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(Kalid from betterexplained here) Thanks for the comment, totally agree with moderation. My goal is to ask "Is the structure I'm providing helpful right now?".
by kalid 11y ago
(Kalid from betterexplained here)
Thanks for the comment, totally agree with moderation. My goal is to ask "Is the structure I'm providing helpful right now?".
There's an implicit assumption that "more structure is better" (especially in technical subjects that can be structured) because it seems official and defensible. It reminds me of many Wikipedia articles -- they grow in length (why not?) and become more precise (why not?) and you're left with a description inscrutable to a beginner.
Calculus, for example, gets my goat because we spend weeks on limits, continuity, L'Hospital's Rule, etc. so students can "properly" understand derivatives. (Never mind that Newton and Leibniz never used them and seemed to do ok.) Showing a circle non-rigorously transform into a triangle to measure its area (Archimedes) gets closer to the meaning of Calculus than a page of epsilons, deltas and tangent lines. One you have the idea, you put in the rigorous skeleton by showing how the formal rules describe the same result.
Appreciate the comment!
- TeMPOraL 11y agoI also agree that you need a mix for optimal learning. I noticed myself that when trying to really grok something, most of the work happens after I both know the formal description and the intuitive idea behind it - it's figuring out how exactly the two fit together that leads to actual understanding.
- kalid 11y agoExactly. Terry Tao calls this having a "post-rigorous" understanding (https://terrytao.wordpress.com/career-advice/there’s-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/there’s-more-to...). We can't think the formal rules are sufficient. (And in the case of adjectives, it seems explicit knowledge of the formal rules aren't even necessary for fluency.)
- adrianN 11y agoYou probably like this http://cr.yp.to/papers/calculus.pdf http://cr.yp.to/papers/calculus.pdf It develops calculus in just 12 pages without being hand-wavy.
- kalid 11y agoThanks!