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Indeed. I think the point about allowing people to understand the subject at various stages in their lives very apt. We apply pedagogical simplification to almo
by hderms 10y ago
Indeed. I think the point about allowing people to understand the subject at various stages in their lives very apt. We apply pedagogical simplification to almost everything we teach children anyways, but it's quite possible that we could be much more far reaching in our attempts. It would be interesting to see a world where children are taught basic abstractions of group theory.
Mathematics is one of those fields where it is difficult to simplify. Period. But in addition, the practitioners often actively resist this simplification. Mathematics is firmly rooted in proof, but not all mathematics education needs to be firmly rooted in proofs, and for that matter, not all mathematics education must be rooted in mechanistic repetition of solution techniques. There is perhaps a way to endow people with these concepts when they couldn't otherwise arrive at them through rigorous proving.
- catnaroek 10y ago> not all mathematics education must be rooted in mechanistic repetition of solution techniques. Actually, coming up with proofs often requires creativity. If anything, the emphasis on memorizing formulas and solution procedures comes from an aversion to teaching proofs.
- tmptmp 10y ago>> There is perhaps a way to endow people with these concepts when they couldn't otherwise arrive at them through rigorous proving. Indeed it would be great if there is such a way. But sadly, without proofs, these concepts are half baked and are thus harmful as they give a false sense of understanding and thence the more harmful overconfidence. I remember the great thought that applies to entire math education (and also to education in general) - "There is no royal road to geometry." [1] [1] https://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2.80.9CRoyal_Road.E2.80.9D_in_famous_quotations https://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2....