Post Anu2MOS0Qy2QXgsOUC by OWOP@mastodon.world
(DIR) More posts by OWOP@mastodon.world
(DIR) Post #Antunj2pAvjabAcUc4 by futurebird@sauropods.win
2024-11-10T13:21:14Z
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#3GoodThings 1. Teaching everything from 5th grade programming to 12th grade statistics and calculus is so rewarding. I'm loving my job.2. I've started keeping physical notebooks again in the past two months. The key is to just have a notebook for each project or thing and pick it up and write today's date. Then it's easy to get going. Even if I just write one sentence. 3. I've been learning more about boats and sailing for my long term goals.
(DIR) Post #AntwArkF5sYmCFWh3g by semitones@tiny.tilde.website
2024-11-10T13:36:37Z
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@futurebird What do you do with the notebooks you finish?
(DIR) Post #AntwJNTV0StYvDkmGW by futurebird@sauropods.win
2024-11-10T13:38:10Z
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@semitones Put them on my bookshelf of full notebooks for future reference. They are very useful when planning lessons, revisiting problems, writing stories and just for the memories...Looking at my old drawings can make me wince a little but it also lets me know I'm getting better. Really those are what I'd grab first if there were a fire.
(DIR) Post #AntxPFKSIzytLjsyO0 by futurebird@sauropods.win
2024-11-10T13:50:25Z
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@semitones I also have a whole bookshelf of lovely blank books to fill up in the future. But in 2020 I started using the iPad for lecture notes and it broke my whole notebooks system down... and I got lazy about writing the date and just fell out of the habit of keeping good notebooks.It feels SO GOOD to be back!
(DIR) Post #AntySbbw1BafHLE9Bo by leon_p_smith@ioc.exchange
2024-11-10T14:02:12Z
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@futurebird 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
(DIR) Post #AntynDMtLYvGAm1BAm by futurebird@sauropods.win
2024-11-10T14:05:58Z
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@leon_p_smith You will be happy to know my 5th graders are proficient in binary. And can mostly write decent for loops. Though some still need to work on this.
(DIR) Post #Anu0xN9i0omtKdp6S8 by leon_p_smith@ioc.exchange
2024-11-10T14:30:10Z
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@futurebird Actually the Stern-Brocot Tree provides a very elegant bridge between binary numbers and Cantor's equivalence of the rationals and the integers.You want to find out what the google-th fraction is in this particular bijection? All you have to do is convert 10^100 to binary, follow that path on the Stern-Brocot Tree, and then read off the result.
(DIR) Post #Anu10esOaE9TA1I9my by futurebird@sauropods.win
2024-11-10T14:30:49Z
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@leon_p_smith Stern-Brocot Tree? I will check it out, thanks!
(DIR) Post #Anu1Pdga9A5ghwg5vk by futurebird@sauropods.win
2024-11-10T14:35:19Z
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@leon_p_smith Ah Stern-Brocot Tree. I *have* seen that before. I do an activity with the 5th graders with a square of paper. We cut it in half, then cut one of the halves in half and so on writing the fractional value on each one. I challenge them to see how tiny they can go. We puzzle them together showing the infinite sum is 1. I hope when they are older this will make infinite sums with finite value less mysterious. That the denominators are the binary place values is a lovely bonus.
(DIR) Post #Anu2MOS0Qy2QXgsOUC by OWOP@mastodon.world
2024-11-10T14:45:56Z
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@futurebird TWW: Language is the stories that we tell. *“Believe me, my young friend, there is nothing–absolutely nothing–half so much worth doing as simply messing about in boats.” **Yup, it’s true, the sound, the smell, the feel of the helm. One lifetime is not enough. OWOP
(DIR) Post #AnuQPBUJU2Zu6joqwa by futurebird@sauropods.win
2024-11-10T19:15:20Z
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@PrinceOfDenmark This isn't a bug of the hobby... it's a feature!
(DIR) Post #AnuWdeaUghjG8bzchM by leon_p_smith@ioc.exchange
2024-11-10T20:25:09Z
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@futurebird Yeah, you have the positive integers n down the right spine of the Stern-Brocot Tree, and all the unit fractions 1/n down the left spine. My idea is to use the unit fractions in an analogy to units of measurement to teach how to add fractions the right way, by adding like units.This contrasts nicely with the mediant operation at the heart of the Stern-Brocot Tree, also known as "adding fractions the wrong way", which I hope will help students remember which operation is which.Moreover, the mediant is not a well-defined function of fractions, which sets up a very nice future lesson, as fully owning and utilizing well-definedness is kind of the key to mastering modular arithmetic.In addition, the Stern-Brocot tree is intimately connected to the extended Euclidean Algorithm, and as such it encompasses like, 85% of the algorithmic content of elementary number theory, and all of the trickiest bits. Want to compute a modular multiplicative inverse, or the trickier direction of the chinese remainder theorem? The Stern-Brocot tree can do it! Kevin Bacon and the Stern-Brocot Tree mentions a lot of connections such as these, though I honestly I've come across several more connections that need to be elaborated upon, including Christoffel Words, Knot Theory, Rational Tangles, the 3-strand braid group, the moduli space of isosceles triangles, elliptic curve cryptography, and modular forms.It's the gift that keeps on giving, and while there are a number of concepts in math that are this way, I don't think anything is as well-connected to cutting-edge research mathematics, *and* also approachable by children.In terms of an undergraduate math curriculum, the Stern-Brocot Tree is highly relevant to Discrete Math, Abstract Algebra, and Number Theory, and seems well worth mentioning in Linear Algebra, Real Analysis, Complex Analysis, and Numerical Analysis.
(DIR) Post #AnuazBn2pw9V0lO6pU by MichaelTBacon@social.coop
2024-11-10T21:13:54Z
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@futurebird +1 on the physical notebooks. About every 3-4 years I think this is outdated, I should have some kind of organization app, and then after missing important deadlines and losing important notes, I go back to the physical notebooks.I've been on one big consolidated one for a while now, but I think I'm about to go back to project notebooks.