Leon P Smith on Nostr: npub1zdp33…2vqv8 by the way, have you ever taken a look at my philosophy of math ...
npub1zdp33shl69xr0uq3x8n5gsjykq9upycwh6nqm02c3f6x0frrn0dq42vqv8 (npub1zdp…vqv8) by the way, have you ever taken a look at my philosophy of math education? It centers around computer programming, the Stern-Brocot Tree, Pascal's Triangle, and the Symmetry Group of the Square.
This is New Math 2.0, more or less. I've worked almost my entire life on it.
I've long been under the opinion that some of the examples the original New Math effort weren't... the best motivated, such as drilling arithmetic in alternative bases.
I've also long been under the opinion that computer programming needed to be one of those focuses in the math curriculum.
And I've long been frustrated by the lack of coverage of the Euclidean Algorithm, which is bordering on absurd given how much time we spent talking about reducing fractions in elementary school.
So at some point I realized modular arithmetic would be a much better thing to repeatedly emphasize, relative to arithmetic in alternative bases. For starters, you actually end up somewhere new and interesting, instead of the relatively pendantic ability to do the same thing in another notation.
Then I realized the Symmetry Group of the Square D_4 lead all over the place, including modular arithmetic.
Then I stumbled across the Stern-Brocot Tree SL(2,N), and realized it was the most important partial answer to the question "how to teach math?" I'd ever found, as it roped in the Euclidean Algorithm, implicated damn near everything, and certain things I'd struggled with as an undergrad suddenly started to make sense.
Eventually I started thinking about it all, trying to come up with the best answer as to why this is all interesting, and while writing Kevin Bacon and the Stern-Brocot Tree, realized that the modular group GL(2,Z) is the Minkowski product D_4 * SL(2,N) * D_4.
https://github.com/constructive-symmetry/constructive-symmetry
This is New Math 2.0, more or less. I've worked almost my entire life on it.
I've long been under the opinion that some of the examples the original New Math effort weren't... the best motivated, such as drilling arithmetic in alternative bases.
I've also long been under the opinion that computer programming needed to be one of those focuses in the math curriculum.
And I've long been frustrated by the lack of coverage of the Euclidean Algorithm, which is bordering on absurd given how much time we spent talking about reducing fractions in elementary school.
So at some point I realized modular arithmetic would be a much better thing to repeatedly emphasize, relative to arithmetic in alternative bases. For starters, you actually end up somewhere new and interesting, instead of the relatively pendantic ability to do the same thing in another notation.
Then I realized the Symmetry Group of the Square D_4 lead all over the place, including modular arithmetic.
Then I stumbled across the Stern-Brocot Tree SL(2,N), and realized it was the most important partial answer to the question "how to teach math?" I'd ever found, as it roped in the Euclidean Algorithm, implicated damn near everything, and certain things I'd struggled with as an undergrad suddenly started to make sense.
Eventually I started thinking about it all, trying to come up with the best answer as to why this is all interesting, and while writing Kevin Bacon and the Stern-Brocot Tree, realized that the modular group GL(2,Z) is the Minkowski product D_4 * SL(2,N) * D_4.
https://github.com/constructive-symmetry/constructive-symmetry