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by bitL
3574 days ago
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And this is the problem - you don't teach students how Euler or Aristotle came up with the idea that they would understand, instead you force an abstraction on them right from the start without them grasping any connection to any part of reality they are immersed in. Some of us are capable of connecting the dots right away, some aren't, though would be if we saw how people came up with those ideas. Also, I was absolutely furious when I attended mathematical olympiad as a 10-year old and the problem formulation required familiarity with University math level language. You mathematicians are shooting yourself into feet. |
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Surely because that's history, we don't teach it that way because then you lose the links that have [much] later been found with other areas of maths -- isn't it the linking in to different areas that provides all the power? We want current students to understand a far wider curriculum and realise the links that come out of those abstraction, no?
I guess it's like whether you teach grammar to language students or hope that through language use they'll derive their own abstractions that allow them to understand the grammar sufficient to say things that they've never heard before.
From a history perspective we probably don't know how they came up with the idea, even if their journals (!) had a specific derivation of a proof then that wouldn't mean that was their initial direction of travel necessarily.