Post Ao6qed2GH2GaasF5ZA by GinevraCat@toot.community
(DIR) More posts by GinevraCat@toot.community
(DIR) Post #Ao6Pd9qUcMlj0koOhc by futurebird@sauropods.win
2024-11-16T14:03:13Z
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I teach at a very academically rigorous school. But, there are a few things this school does that might surprise people:1. Many teachers teach a wide range of grade levels. So you could have a teacher who *could* teach Linear Algebra teaching you in 4th grade math.2. The school makes time for creative math and CS in addition to the regular class. So I get to work with students without pressure to get them past any particular test or goal posts.
(DIR) Post #Ao6PneJ0DvnCNP9LNo by steve@discuss.systems
2024-11-16T14:05:05Z
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@futurebird I really love (1)
(DIR) Post #Ao6Ps4TQsAwQh68XgG by futurebird@sauropods.win
2024-11-16T14:05:54Z
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In most other teaching contexts I've always been trapped teaching the most advanced topics since I was one of a few people who *could* ... having teachers with deep math experience from a young age makes a big difference. And when I'm working with them outside of their regular class I can work on teaching something that doesn't fit well into a "standard" ... how to *play* at mathematics. And the students really do need it.
(DIR) Post #Ao6Qgh9nK7N79C5gNE by whknott@mastodon.social
2024-11-16T14:14:52Z
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@futurebird Yabbut do you teach physics with calculus or without?
(DIR) Post #Ao6RJBdOSQlefwI0lk by PizzaDemon@mastodon.online
2024-11-16T14:22:00Z
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@futurebird this is pretty fantastic. When I was in 5th grade at a magnet school, I got tossed from the special math class for behavior. The teacher and I had a heated exchange. I could be a little snot.After my mom got pulled in to hear about what happened she debriefed me at home. "Yes, you were rude and out of line but, reading between the lines of what the vice principal said, the response was so severe because you asked questions she didn't know the answers to and you wouldn't let it go"
(DIR) Post #Ao6RbLvOw8DnnrNIAK by futurebird@sauropods.win
2024-11-16T14:25:18Z
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@PizzaDemon I don't know if avoiding that as a teacher is as much about knowing a lot about the subject as it is about being comfortable modeling what to do when you don't know something. My students stump me all the time. Then we find the answer together, if one exists.
(DIR) Post #Ao6SPFUn79KwLIijFA by emjonaitis@mathstodon.xyz
2024-11-16T14:34:17Z
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@futurebird I would love to hear more about where you teach. I’m a board member at a small private school that is similar in this way and am very curious about peer institutions. (I agree with you about the importance of having strong math teachers in the early grades, BTW.)
(DIR) Post #Ao6SdI04bDIYAG2zmy by TeflonTrout@beige.party
2024-11-16T14:36:50Z
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@futurebird @PizzaDemon Beige bless you for this. Actually? All joking aside.That's incredibly important, I wish I could have been your student. After high school, which solidified by belief that I inherently suck at math, I did online college. I was kind of terrified of college algebra, but I eventually realized that this stuff is kind of amazing, beautiful, and occasionally fun. Thank you for preventing that sort of anxiety, it's just frigging miserable to walk up to that classroom door feeling like that. :chef_kiss:
(DIR) Post #Ao6St9ZVhgj4epBg00 by Lichtenbergian@mastodon.sdf.org
2024-11-16T14:39:37Z
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@futurebird @PizzaDemon That was my advice to teachers new to the Georgia Governor's Honors Program (summer experience for gifted high schoolers) who were freaking about content matter: You don't have to know it for them to learn it.
(DIR) Post #Ao6TyQ8ncwh9Rpljwe by leon_p_smith@ioc.exchange
2024-11-16T14:51:51Z
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@futurebird Of course, I'm one of those oddballs who believes that we should thinking about how to best prepare 4th graders for Linear Algebra...Honestly I do think that an introduction to linear transformations, with an emphasis on their geometric interpretation, should be part of the elementary curriculum. And my philosophy of math education reflects that: I cannot think of a simpler or more ideal situation for introducing, motivating, and understanding matrix multiplication than studying the Symmetry Group of the Square D_4, as it has a particularly simple action on the Cartesian coordinate plane.So my idea is to start by emphasizing an intuitive understanding of D_4, via this manipulative and these worksheets:https://github.com/constructive-symmetry/constructive-symmetry/tree/master/D002_Book_of_AlgebraLater, my idea is to revisit D_4 and learn how to compute its arithmetic without the help of the manipulative. The canonical representation of D_4 is the eight 2x2 matrixes with a single 0 and a single ±1 in every row and column. The determinant of these matrices is ±1, with the sign corresponding to the orientation.Then almost by magic, the Stern-Brocot tree SL(2,N) is all those 2x2 matrices with natural-number entries and determinant 1, which also happens to hint at the result I mentioned before, that the modular group GL(2,Z) is equivalent to D_4 * SL(2,Z) * D_4, where * is Minkowski multiplication.So discussing any kind of algebraic module, let alone a module over a monoid, is usually reserved for second or third year Linear Algebra, but honestly I feel like a very concrete instantiation of this concept should be an Elementary/Middle School topic.
(DIR) Post #Ao6ZUHpsXZquj9vvCC by epicdemiologist@wandering.shop
2024-11-16T14:53:10Z
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@futurebird @PizzaDemon When my youngest was in 1st grade the teacher asked the kids to name parts of a plant. My kid said "Chloroplasts!" (thank you, Magic School Bus!) The teacher blinked, paused, and said "I don't know what that is, but I'll find out!" and she did. TEACHERS, PLEASE DO THIS! (Said kid now works for NASA as a planetary scientist & lab manager)
(DIR) Post #Ao6iog9cjZ1zWqy2aW by futurebird@sauropods.win
2024-11-16T17:38:12Z
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@whknott They know a little calc before they get into physics. And they often tell me about how they used it in my calc class.But, what I wish we could do is stop treating Statistics like it's... the math class for "weak" students who couldn't do calculus. Part of the problem is there is still a tendency to classify kids as "math people" and "not math people" although I'm breaking my peers of this notion every chance I get. Part of it is this snobbishness pure math people have about stats.
(DIR) Post #Ao6iytxUGU2DEoAIgy by futurebird@sauropods.win
2024-11-16T17:40:03Z
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@whknott And where has treating statistics like "the lesser math" gotten us? I blame the messy way LLMs and other tools are being slathered around on everything on the general neglect of statistics by "serious math people"It's an unsupervised area and it has fallen into chaos. And they have the powerful tools that claim to do the magic that the people want.
(DIR) Post #Ao6jVk63x2eMCzptj6 by Jirikiha@mastodon.cloud
2024-11-16T17:45:58Z
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@futurebird @whknott having taken both Calc and Stats, I'd say statistics was harder for me.But then, I'm no mathematician. Math is a tool to accomplish a goal, not something to play with.I've met people with the opposite opinion, and that's fine. We just need to realize that those opposing philosophies can complement each other or fight each other. It's up to us to decide which it is.
(DIR) Post #Ao6kQ1sF2lI7YmD8iW by futurebird@sauropods.win
2024-11-16T17:56:09Z
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@DaleHagglund @Jirikiha @whknott All that and combinatorics and probability too. It's exceedingly nontrivial. My graduate advisor said "in combinatorics the questions are all easy to understand and impossible to answer"So then why is there is notion that statistics is for "lightweights" ? Part of it is all of the barebones rough and ready recipe based stats courses for business and social science majors... but there are calc classes like that too so why does it stick only to stats?
(DIR) Post #Ao6kY8vqgY3Blclcfo by futurebird@sauropods.win
2024-11-16T17:57:37Z
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@drdrowland @Jirikiha @whknott I found out that our HS stats class didn't even cover the central limit theorem and I almost started crying on the spot. I hope they let me teach in next year. I'm going to fix it.
(DIR) Post #Ao6kcgK0U9L8TvENqC by emjonaitis@mathstodon.xyz
2024-11-16T17:58:25Z
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@futurebird @whknott When I was dipping my toe into the water of a stats degree, I came to understand that there's the way that it's taught to people in other disciplines -- which maps well onto the "lesser math" reputation -- and the way that it's taught in stats degree programs -- which leans heavily not just on intro calculus but also Real Analysis (which, coming to the field late, I did not have). The gap here is vast and I think is part of the reason that statistics as a field has not been successful in guild behaviors like naming constructs or policing who can practice it.
(DIR) Post #Ao6kdyqN6elODSzMOW by YakyuNightOwl@mastodon.world
2024-11-16T17:58:22Z
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@Jirikiha @futurebird @whknott Thanks for this discussion. Stats shouldn't be considered lesser when it's the first taste a whole lot of us had of advanced math problems. Calculating batting average and winning percentage were good lessons taught early.
(DIR) Post #Ao6lZyZiGO7OB8qpg8 by karchie@freeradical.zone
2024-11-16T18:08:50Z
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@emjonaitis @futurebird @whknott statistics has the sad fate that some of its results turn out to be super useful to other fields that mostly don’t require much math. So “statistics” classes tend to be full of recipes that the students learn to use but not really understand and so misuse; while “mathematical statistics” classes are the point in grad school (after plenty of calculus as an undergrad) where I stopped feeling like I had a talent for math
(DIR) Post #Ao6lrFRanWzZQ6HyDI by futurebird@sauropods.win
2024-11-16T18:12:16Z
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@karchie @emjonaitis @whknott I miss teaching Into to Math Stats SO MUCH. The students, all math majors would get so excited when we finally *proved* the foundations for all these mysterious recipes they had been using for years in other courses. And not everyone needs that total foundation to ... you know take an average or whatever.... but at least the people who teach it could know. Hell... I might ask if they'll let me teach it again in the summer. They might.
(DIR) Post #Ao6mXEm9fn65Veve9Q by trochee@dair-community.social
2024-11-16T18:19:49Z
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@futurebird @whknott I was "good at math" all the way up to multivariate calculus in collegeI bailed because I couldn't relate the next steps (linear algebra) to anything I cared about. Ironically I finally came back to MV calculus & linear algebra which I studied bc I cared abt machine learning which I studied bc i cared abt statistics and discrete mathwhich I studied bc I cared abt computational linguisticsBut I wish that stats & discrete math had been an obvious direction in HS
(DIR) Post #Ao6nn5WRwbeZOlhlKK by AbyssalRook@mstdn.social
2024-11-16T18:33:54Z
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@futurebird That mentality drives me up the wall as a "math person" myself, even when it comes from people I know who say they aren't. This isn't to say discalculia or related conditions aren't a thing, but our education systems, even on a global level, are so incapable of teaching mathematics that it's instilled in probably tens of millions of people that there's something intrinsically wrong with them for not "getting it" immediately from the specific way it's taught.
(DIR) Post #Ao6npMVblBlAezOa5g by mkb@mastodon.social
2024-11-16T18:34:12Z
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@futurebird @whknott What’s frustrating to me is in the adult life school was preparing me for, I have needed calculus zero times since completing my AP math exam in 1986. That’s even working in a technical field. Meanwhile, statistics has come up nearly every day. In some hypothetical future society where we start improving education rather than burning books, I’d like to see statistics as ongoing, required curriculum, staring with some rudiments when kids are very young.
(DIR) Post #Ao6o2PZTgYY5vGQawK by futurebird@sauropods.win
2024-11-16T18:36:43Z
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@AbyssalRook Math is a core component of being human and the human ways of thinking and reasoning. It is "for" everyone. Yes some will get deeper in and more esoteric than others, but that's just about investing your time and heart in learning more details and depth. Part of that artificial barrier serves to protect the sense that mathematics is a secret priesthood and it's just a way of hoarding power which disgusts me.
(DIR) Post #Ao6onShTrxBHEnbftY by AbyssalRook@mstdn.social
2024-11-16T18:45:11Z
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@futurebird Very true! And that baffles me, too. Why would people want to keep, of all things, MATHEMATICS as some kind of secret club?Do you have any idea how much I want to talk to my friends about cool stuff you can do with math?And also looking down on Statistics?? Some of my favorite stuff to DO with math is counting things, and statistics is just finding the most insane ways to count things and then making those results fight each other for dominance.
(DIR) Post #Ao6or8yN9qANDDGNsW by davew@mastodon.online
2024-11-16T18:45:51Z
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@futurebird @whknott So much of the real problem is that there are “math teachers” and “not math teachers”. Knowing a subject does not mean one is a good teacher. My daughter suffered as a not math person for years until she finally got a teacher who knew how to teach instead of simply regurgitating the content in the text. Thank heaven for good caring teachers.
(DIR) Post #Ao6prtQCYtnTE0CXK4 by Scmbradley@mathstodon.xyz
2024-11-16T18:57:10Z
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@futurebird @whknott I wonder if part of the reason stats gets this rep is that there's lots of programs at the university level where the most useful part of maths is stats (parts of biology, psychology, etc) and this maybe feeds into this perception that stats is maths for people who don't do maths.
(DIR) Post #Ao6pwdQNSycx3gXpPk by mansr@society.oftrolls.com
2024-11-16T18:57:58Z
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@futurebird That's fantastic.
(DIR) Post #Ao6qed2GH2GaasF5ZA by GinevraCat@toot.community
2024-11-16T19:05:58Z
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@futurebird I love teaching without a fixed end point. I got to teach yr 9 maths a while back and we got to do so many fun riddles that really led to some interesting mathematics.
(DIR) Post #Ao6sLrPYnhLlaNJodk by BashStKid@mastodon.online
2024-11-16T19:25:02Z
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@futurebird @whknott It’s annoyingly backwards, for sure. Everything is statistical, it’s so much more useful than the tiny number of deterministic, fully defined, abstracts. You don’t have to be Schrödinger to see that.
(DIR) Post #Ao6tdBaF9a5L1g8n56 by marc_w@union.place
2024-11-16T19:39:16Z
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@futurebird @whknott The closer we look, the more the universe seems to be fundamentally stochastic. Probability distributions on the small scale and statistics on the large are as important as calculus in understanding where we are.
(DIR) Post #Ao6uxdhQQfI5yIoi00 by pdcawley@mendeddrum.org
2024-11-16T19:54:15Z
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@futurebird @whknott I mean… I have a problem with stats because so many of the people who founded the field seem to have been awful people trying to come up with rigorous seeming ways to support their outright racism.
(DIR) Post #Ao6v3P5XfJhmOTqVea by futurebird@sauropods.win
2024-11-16T19:55:19Z
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@pdcawley @whknott But then you also have this:https://www.tableau.com/blog/how-web-du-bois-used-data-visualization-confront-prejudice-early-20th-century
(DIR) Post #Ao6v5r8IMsDtx2Ir32 by marc_w@union.place
2024-11-16T19:55:46Z
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@futurebird "Many teachers teach a wide range of grade levels. So you could have a teacher who *could* teach Linear Algebra teaching you in 4th grade math."This is really important. I taught 8th grade math at a 6-8 middle school. There were two of us among the 18 teacher who taught math who had degrees in math, and how much they'd learned in earlier grades was wrong was frightening. An unholy number of elementary school teachers never liked math and do a poor job teaching it.
(DIR) Post #Ao6vKrHg5UJmlRqTmy by futurebird@sauropods.win
2024-11-16T19:58:28Z
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@marc_w They are generally not paid enough to demand as much. Nor offered the time and financial support for professional development. Any school teacher should be able to take additional certain university courses for free, and if they are taking say, two courses they should get a slightly reduced schedule. To be a teacher is to spend your whole life as a student, and some of that in independent work but I think it's literal too.
(DIR) Post #Ao6vTd8G4c1DTlcddI by futurebird@sauropods.win
2024-11-16T20:00:02Z
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@marc_w It's not like the best teachers spring fully formed from programs handing out masters in education. That is only the beginning. And a single teacher is ideally a part of a community of teachers who support each other and make each other better.But too often it's just everyone trying to survive.
(DIR) Post #Ao6vrMO3yzhgUlKWzg by pdcawley@mendeddrum.org
2024-11-16T20:04:19Z
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@futurebird @whknott oooh, those are brilliant. That spiral chart, in particular… I'd not come across it before, but it's a real gut punch, isn't it?I'm not sure that overtly polemic data visualisation belongs in the same subject as the eugenicist statisticians trying to paint their prejudices as somehow objective though. DuBois is absolutely honest about his subjectivity, Galton and co weren't.
(DIR) Post #Ao6x39KMSq7xQ7mftQ by Jackiemauro@fosstodon.org
2024-11-16T20:16:50Z
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@hrefna @futurebird @DaleHagglund @Jirikiha @whknott As a stats phd I just want to say I love you all, thank you for the validation. Really helps counter the person who when I told them I got into my program they said “what is there even to study?”
(DIR) Post #Ao6x3BNcpfvVmpKJG4 by futurebird@sauropods.win
2024-11-16T20:17:40Z
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@Jackiemauro @hrefna @DaleHagglund @Jirikiha @whknott Jesus.
(DIR) Post #Ao6zyOJVcNH4JWoA9Q by macbraughton@infosec.exchange
2024-11-16T20:50:25Z
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@futurebird @AbyssalRook the part that really gets me is that they gatekeep and then get a sense of superiority about their knowledge, which ends up blinding them to ways that they may be (and probably are) wrong or missing things! Formal mathematics is ultimately just another way of thinking, and when you get deep enough into theory, specifically Gödel’s incompleteness theorem, one should be humble about the limitations inherent within it as a discipline (not mention prodigies like Ramanujan who defy all categories of what somebody who is supposed to be good at it look like)
(DIR) Post #Ao71S8xDOAkHJp8BjU by Jackiemauro@fosstodon.org
2024-11-16T21:06:08Z
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@martinvermeer @hrefna @futurebird @DaleHagglund @Jirikiha @whknott Yea I mean I think somewhat ironically part of the reason we as a discipline got sort of sidelined w ML is cause we got soooo wrapped around the axle on some of this Mathy stuff that in the end maybe didn’t matter so much. But does it converge????? Maybe sometimes who cares. Maybe it was our own insecurities, come to haunt us haha.
(DIR) Post #Ao723yPf1rrDd7TW8e by dymaxion@infosec.exchange
2024-11-16T21:13:50Z
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@futurebirdI work in tech, not physics or more classical engineering, but I can say that the number of times I've wished staff knew calculus when they didn't? Zero in twenty years. The number of times I've wished they knew basic statistics when they didn't? At least once a month, for twenty years.@whknott
(DIR) Post #Ao7304mZVOQgBFtfvs by futurebird@sauropods.win
2024-11-16T21:24:21Z
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@dymaxion @whknott When you've wished you knew more about stats what was it that you wanted to do, find out, or know?
(DIR) Post #Ao75FMSeG5qvGIzhr6 by belehaa@wandering.shop
2024-11-16T19:31:22Z
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@futurebird @karchie @emjonaitis @whknott That's the stats class I wish I had in college. I wanted to know how and why stats stuff worked. Instead I got about 10 weeks of rote "mean median mode" and a sprinkling of combinations and permutations. Just the most basic "what," no "why" 😭
(DIR) Post #Ao76aF5GytesPya6OO by Jackiemauro@fosstodon.org
2024-11-16T20:30:48Z
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@hrefna @futurebird @DaleHagglund @Jirikiha @whknott Totally agree. It’s fun stuff but it’s ~weird~.
(DIR) Post #Ao76aGbZKJ5P8QhPN2 by whknott@mastodon.social
2024-11-16T21:51:36Z
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@Jackiemauro @hrefna @futurebird @DaleHagglund @Jirikiha As a ME student, I did great with calculus, loved Diffeqs, was fine with vector matrices and multi-variable, partials... but stats was more akin to bio. So much memorizing and none of the math I already knew was at all useful. Easy As in everything else, struggled to maintain a C in stats.
(DIR) Post #Ao7B9Zwpnjud4ujueO by trachelipus@masto.ai
2024-11-16T22:55:42Z
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@futurebird One of the things that finally made Algebra click for me was when my 8th grade Earth Science instructor used it in the intro chemistry section of the class: "You know how to do this already; you studied it last semester in your math class." Imagine if we taught basketball the same way we teach math, by making kids do eight years of conditioning drills before letting them play their first game.
(DIR) Post #Ao7SDdrisOCBbis7FI by MichaelPhillips@dice.camp
2024-11-17T02:06:55Z
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@futurebird @AbyssalRook I mean specifically, statistics is a core way of being superhuman. Like humans have assorted natural insights and tendencies toward a bunch of parts of mathematics. But the way our brains are wired. Are inherently bad at statistics. It's a thing we have to actively learn and fight against our insights. Because statistics are fighting with the sort of natural heuristics that our brain use to minimize effort in our traditional social groups, which are very small universes.
(DIR) Post #Ao8C4icERRwpcoJE9I by dymaxion@infosec.exchange
2024-11-17T10:40:44Z
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@futurebirdHmm. Often, really just basic statistical numeracy so they could understand data they seeing in papers, etc. Sometimes, more the ability to reason about what is and isn't good data for quantitative decision-making — folks really love to make up meaningless numbers to let them avoid qualitative deveined when quant data isn't there. Sometimes data analysis to understand things like perf impact from log data for edge cases. So in some ways, not really statistics itself, but all things that I find that folks who made it through at least one real stats course are likely to be better at, if that makes sense?@whknott
(DIR) Post #Ao8FkWgVUVbKe8w4iO by futurebird@sauropods.win
2024-11-17T11:21:56Z
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@dymaxion @whknott So, more experience with the creation of data visualizations and summary statistics (where do they come from?) Methods to access their quality and predictive value?I ask because I've had many people say something along these lines "why did I learn so much calculus, everything I need to do with math is statistics?" This can confuse me a little because understanding distributions is so much easier if you know calculus. (To find maximums and areas under curves.)
(DIR) Post #Ao8GawJVRqIPBxAb4q by dymaxion@infosec.exchange
2024-11-17T11:31:22Z
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@futurebirdYeah, largely in that kind of space. Also rigor around what it means to measure something, etc. Like, obviously calculus is useful — if nothing else, not having the conceptual tools of first and second derivatives makes looking at a line on a graph or the area under it less intuitively useful — but I think it's more about the things that you learn along the way.@whknott
(DIR) Post #Ao8HC7B21O6jb9vsNk by futurebird@sauropods.win
2024-11-17T11:38:07Z
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@dymaxion @whknott I realize that mathematicians can make everyone very tired because we are more interested in the foundations and shape of the containers than their contents. We teach students how to complete the square to solve quadratics ... mostly so they can prove the quadratic formula for themselves. But often these students don't even really understand that if a*b=0 that means a, b or both must be 0 or how that is at all relevant to "finding x" 1/
(DIR) Post #Ao8HTZ1XjxQIt3oZoO by futurebird@sauropods.win
2024-11-17T11:41:15Z
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@dymaxion @whknott Because what mathematics really is are the *proofs* not the solutions, not the algorithms, but that unbroken chain from a minimal set of assumptions to the solution. Over and over we work to demonstrate this unbroken chain, though in most undergrad statistics courses this is just something we give up on in favor of getting the students competent enough with the algorithms to mostly apply them correctly. And that's part of why such courses aren't seen as "real math." 2/
(DIR) Post #Ao8KQCZP4BR8F1k07E by louisffourie@c.im
2024-11-17T12:14:16Z
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@futurebird @dymaxion @whknott I didn't do any statistics courses as an undergrad. Many years later I did a graduate course in Geostatistics (spatial statistics) where the lecturer went from absolute basics to advanced concepts step by step, seamlessly, and we were spellbound. In a statistics course. It was amazing.
(DIR) Post #Ao8KbSn16R47jNTjF2 by futurebird@sauropods.win
2024-11-17T12:16:19Z
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@louisffourie @dymaxion @whknott I hope you have your notes. Do you remember what book or books you used?Such treatments are kind of rare. Statistics is not as well formed as a "course" as calculus and other mathematics.
(DIR) Post #Ao8KhCGjRIlmEL6yLQ by futurebird@sauropods.win
2024-11-17T12:17:21Z
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@JorgeStolfi @dymaxion @whknott This is what it is supposed to be, but it's VERY easy to loose the plot.And that produces people alienated from mathematics. "Why did I have to learn all of that???"
(DIR) Post #Ao8KvFrirctLRI7JQW by RogerBW@discordian.social
2024-11-17T12:19:51Z
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@futurebird A problem I noticed at school that seemed worse with maths than with other subjects: one bad teacher, or a teacher who's having to read one chapter ahead of the class while juggling a bunch of other jobs, can destroy the spirit of enquiry and experimentation for life.
(DIR) Post #Ao8L9Yvcmk3KcFlS9g by tuban_muzuru@ohai.social
2024-11-17T12:22:27Z
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@futurebird @JorgeStolfi @dymaxion @whknott I am going to write The Old Man's Math Book. Starting with Sirius and the stars rotating in the night sky, Babylonians, Hipparchus, the math of the ancients.Then algebra,taught properly, calculating the payout for everyone involved in the spice trade, shares of a commodity with a yet-unknown price."The train leaves the station at 10 mph."No it doesn't. Takes five minutes to accelerate the train to 10 mph.Real world math
(DIR) Post #Ao8LW5vam56FKhUeYa by louisffourie@c.im
2024-11-17T12:26:32Z
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@futurebird @dymaxion @whknott He had meticulous notes and only gave textbook references. He was a textbook author himself. He also interspersed the theory with real examples as well as anecdotes. The course was geared to industry professionals.And yes, I do have the notes!
(DIR) Post #Ao8MUzKbul9QXTER9c by futurebird@sauropods.win
2024-11-17T12:37:32Z
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@JorgeStolfi @dymaxion @whknott The foundations of set theory are a mess? This is news to me. There have always been mathematicians interested in pipe dreams like universal axioms or more minimal sets of axioms. But if you need to get things done you *can* ... you just need to be honest about what you are assuming, and it might not be as minimal as some want. Different assumptions create different mathematics that have their own uses. Maybe I'm not understanding what you are saying.
(DIR) Post #Ao8MlgF48qh8Fzb7ho by silvermoon82@wandering.shop
2024-11-17T12:28:50Z
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@RogerBW @futurebird In my last couple years of high school I had a terrible physics teacher then a terrible calculus teacher. Took the joy out of learning the cool stuff, the math I'd been waiting *years* to start learning at school. My uncle noticed and started slipping me his college math textbooks. Had to teach myself trig and statistics and what calculus I worked out.
(DIR) Post #Ao8NGC5EJx1JhNXz3A by futurebird@sauropods.win
2024-11-17T12:46:03Z
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@JorgeStolfi @dymaxion @whknott I think this is analogous to the "foundational problems in animal taxonomy and speciation" there are huge unaddressed problems and questions there (siphonophorae, lichens...) but these questions are exciting and good and don't make the process of classifying animals in clades by last common ancestor any less useful or revolutionary. The exceptions don't break the system they help to further define it. It's similar with these paradoxes at the heart of math.
(DIR) Post #Ao8NjbMHQaqyUAXqDo by futurebird@sauropods.win
2024-11-17T12:51:23Z
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@JorgeStolfi @dymaxion @whknott At the base of every axiomatic system are terms that cannot be defined using the system itself. Terms that require consensus and should be recognized as such. And these are always worth re-examining and removing, changing to see what other systems we may develop. It is still a human endeavor, based on language. And I think that's a feature not a bug.
(DIR) Post #Ao8OFC3v0vAZIW1L4y by Mcdyer@masto.ai
2024-11-17T12:57:06Z
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@futurebird @whknott This. It's disparaging the weapon that will be used against you.
(DIR) Post #Ao8PFYTRmshQlDhJbc by futurebird@sauropods.win
2024-11-17T13:08:22Z
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@JorgeStolfi @dymaxion @whknott Part of understanding these systems and their tremendous power is recognizing that there are undefined terms and knowing exactly what you have assumed through the consensus of language and conventions of meaning. Do you want to purge subjectivity from mathematics? Good luck with that. But I think it's also worth asking WHY so much of the mathematics of a century ago was focused on this goal? Why did otherwise brilliant people burn up so much time chasing it?
(DIR) Post #Ao8PGlm9ojEIIy1ogK by MishaVanMollusq@sfba.social
2024-11-17T13:08:29Z
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@futurebird @JorgeStolfi @dymaxion @whknott “The Wake of Poseidon”
(DIR) Post #Ao8PaSWn5dR0OtEHkO by futurebird@sauropods.win
2024-11-17T13:12:08Z
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@JorgeStolfi @dymaxion @whknott And isn't it amazing that we can isolate this "obvious" thing as an assumption and then ask: what happens if we do not assume it's true?Sometimes that is fruitful, sometimes it just breaks everything. To me that's very powerful.
(DIR) Post #Ao8Q0J9qYAYWrvp62K by jmax@mastodon.social
2024-11-17T13:16:48Z
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@futurebird @JorgeStolfi @dymaxion @whknott Because it was the last hope for those who wanted fundamental certainty in their worldview. Religion struck out, physics was finding fundamental limits. If you yearned for completeness and certainty, it was distressing.
(DIR) Post #Ao8Qm9jAulA1WPABt2 by mattmcirvin@mathstodon.xyz
2024-11-17T13:25:26Z
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@futurebird @JorgeStolfi @dymaxion @whknott I think that all the way back to at least Leibniz there was this idea that you might be able to automate the general search for truth by reducing it to turn-the-crank derivations. It's the same impulse that leads people to treat ChatGPT as an oracle.
(DIR) Post #Ao8Qob3cH4EWrWt9DE by plinth@infosec.exchange
2024-11-17T13:25:54Z
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@futurebird @JorgeStolfi @dymaxion @whknott This is tangential to your current discussion, but I thought you might be interested. Raymond Smullyan in The Tao is Silent has an essay where via a Socratic argument discusses whether or not systems of morals are finitely axiomatizable. The conclusion one the the speakers draws is that not only are systems of morals finitely axiomatizable, but that they can be reduced to precisely one axiom: "everyone has the right to do as they please."At any rate, it's a delightful book and the irony of a logician examining the Tao (which is illogical) is entertaining. I found it after reading "The Mind's I" where it had been excerpted.End of sidebar.
(DIR) Post #Ao8R35RQ6Wql9OvpzM by mattmcirvin@mathstodon.xyz
2024-11-17T13:17:45Z
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@dymaxion @futurebird @whknott Where I wish people understood calculus is in *political* discussions, particularly involving economics. Not any of the techniques, just the basic idea of a function, its derivative and its integral being different things.And maybe the idea that if you have a function of multiple variables, its rate of change is going to depend on which specific things you're holding constant.But that last one is a HARD idea. It doesn't even really show up in AP Calculus, it's a later class. It trips people up when they're studying college-level thermodynamics.
(DIR) Post #Ao8SHecCE33QFTTyKm by pbloem@sigmoid.social
2024-11-17T13:31:37Z
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@JorgeStolfi @futurebird @dymaxion @whknott This sounds like a grounding problem. The axioms are perfectly consistent (or automated proof checking wouldn't work) but their relation to reality is what's messy.Probability theory shows this very clearly. The same set of axioms is accepted by frequentists and Bayesians alike with very different interpretations.So long as you treat the whole thing as an ungrounded string rewriting exercise with no relation to reality, there is no mess.
(DIR) Post #Ao8ToDtGhxP0sFYtQu by guyjantic@infosec.exchange
2024-11-17T13:59:28Z
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@futurebird @whknott As a "not math person" who teaches stats to people who Do Not Want To Learn Stats, full agreement.Perhaps it's the cognitive dissonance effects, but I have formed an opinion that "math people" looking down on stats are reacting to their difficulty with/distaste for having to interface with the "real world." Some approaches to stats are purely theoretical, but it is a field inherently pointed toward application. The history of academia is partly the history of "pure" academics denigrating any application of their pure knowledge. I think that's partly because interfacing theory with reality is messy and difficult in ways some of the pure-math people find especially challenging.
(DIR) Post #Ao8UAbJoHdlRuDeAro by guyjantic@infosec.exchange
2024-11-17T14:03:29Z
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@futurebird @dymaxion @whknott My stats courses (intro, for psychology students) are definitely not "real math." We do zero proofs, zero calculus, etc. I've thought of renaming the course from "statistics" to "applied data analysis with a little theory". This fits our students' needs, and since we don't have a functioning university any more (i.e., we are structurally prevented from requiring, say, another couple of math courses for our majors), it's what we can do. I find it immensely valuable but I often wish we could require and therefore teach a more rigorous sequence of actual-statistics courses.
(DIR) Post #Ao8VdjLxaccDB26fdQ by guyjantic@infosec.exchange
2024-11-17T14:19:41Z
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@Jirikiha @futurebird @whknott I don't know how to test this claim, but my first stats teacher said, "There have been any number of child prodigies in mathematics but there has never been a child prodigy in statistics." I think about that, sometimes.
(DIR) Post #Ao8VerAi0RCxiPNfoe by AlliFlowers@talkedabout.social
2024-11-17T14:19:30Z
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@guyjantic Reminds me of when I met my quantitative analysis prof. He asked how I was feeling and I said I was terrified cause I’m not a math person. He laughed and replied “not to worry. Stats isn’t math.” @futurebird @whknott
(DIR) Post #Ao8VvBWK7NoJSVHE0W by guyjantic@infosec.exchange
2024-11-17T14:23:07Z
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@futurebird @DaleHagglund @Jirikiha @whknott I'm reminded that the first generation of psychologists in 19th century (e.g., Titchener et al.) insisted that they, like physicists or mathematicians, were discovering basic principles ("the atoms of the mind"), and absolutely not applying any knowledge to anything. Titchener, IIRC, railed against *any* application of psychological knowledge (how much "knowledge he actually generated is debatable). He used terms like "mere" application, stating or implying that any applied endeavor was so far beneath "true" academics that it was worthy of outright scorn.
(DIR) Post #Ao8WDrDDqaavybFK0O by bug@chitter.xyz
2024-11-17T14:26:09Z
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@JorgeStolfi @futurebird i mean typically we just fix that by only taking complements within a particular superset as the "scope". complements are well-defined within a scope and most of mathematics is about working within defined scopes like the integers and real numbers, etc.
(DIR) Post #Ao8WMr8ZUmQcLlMUE4 by mcc@mastodon.social
2024-11-17T14:28:05Z
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@futurebird @DaleHagglund Anecdata: CS person, almost got a math double major, have *never* been taught a drop of stat in a formal setting. They taught us combinatorics, probability, & recurrence relations (combinatorics with a tophat and monocle) but like, stat is a lot more than that, you need to distributions, you need methods. And this missing knowledge is like a hole in my mind. It's *so* important and I can't do it right. Proper stat only becomes more important to CS every year that passes
(DIR) Post #Ao8WO9RSvN4nPWohma by Chip_Unicorn@im-in.space
2024-11-16T19:30:21Z
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@drdrowland@Jirikiha @futurebird @whknott Statistics and probability are different. Probability is a branch of mathematics. It has axioms, theorems, and proofs. It's an application of measure theory.Statistics is not mathematics. Statistics is attempting to reconstruct original values from incomplete information. Statistics is a set of useful techniques that use probability to estimate how wrong their estimates are.Source: Am a statistician.
(DIR) Post #Ao8XnkPoh9lLH8oZiy by danielittlewood@fosstodon.org
2024-11-17T14:43:41Z
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@JorgeStolfi @futurebird @dymaxion @whknott Are you claiming these are problems in the foundations of set theory right now? My understanding is that the ZF axioms are actually not vulnerable to either - the Russell set simply cannot be defined in the language of ZF, and neither can absolute complements (but relative complements can be defined, and are not problematic).I am pretty certain there aren't any known contradictions implied by ZF. That would be pretty huge news if discovered.
(DIR) Post #Ao8Xpb2OX4MGlnjzgO by TimWardCam@c.im
2024-11-17T14:44:31Z
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@futurebird @DaleHagglund @Jirikiha @whknott I couldn't even get where the "n-1 degrees of freedom" comes from, so essentially I developed no understanding of stats at all[#].I tried going to some stats-for-physicists lectures because I couldn't understand the maths ones, but they were even worse. They didn't even *try* to explain anything, they just said "here's some magic formulae, this is how you use them".[#] Other than, "if you collect some data first, and decide how to analyse it afterwards, you can prove anything you like". As witness the two students I spotted running their data through every test SPSS had to offer in an attempt to find something interesting to write about.
(DIR) Post #Ao8YQ5TCrXqVZzgLWC by mattmcirvin@mathstodon.xyz
2024-11-17T14:51:07Z
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@futurebird @DaleHagglund @Jirikiha @whknott I think it's the orthogenetic focus of the US secondary mathematics curriculum in which classes are thought of as a road leading to calculus as the finish line. (Geometry is already an odd diversion there, since most of it is not directly in the path, but that's a remnant of the 2000-year traditional focus on Euclid as the soul of mathematics.)
(DIR) Post #Ao8ZA86vNRPh5eDMf2 by futurebird@sauropods.win
2024-11-17T14:59:25Z
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@dedicto @danielittlewood @JorgeStolfi @dymaxion @whknott Thanks Douglas. This was a much more clear way to put it than I could have managed at the moment.
(DIR) Post #Ao8jzfIsj2laLX1JBY by jayalane@mastodon.online
2024-11-17T16:59:54Z
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@dymaxion @futurebird @whknott how about a good understanding of dynamic systems and various ways stability can transition into instability? Also doesn’t one need some understanding of integrals and linear algebra to make sense of stats? Like this fuzzy cloud around the mean is a Gaussian and these ten observations are defining a hyperplane in the vector space?
(DIR) Post #Ao8kYwITXIv1BaeMgS by futurebird@sauropods.win
2024-11-17T17:07:10Z
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@jayalane @dymaxion @whknott I think you need to adjust your expectations. A typical undergrad stats course for non-math majors:"If a random variable is normally distributed. Mean 89 and standard deviation of 12 then for a population of 400 how many observations would be greater than 60?"Not even dealing with the distinction between sample and population or the uncertainty. Just can you apply the normal distribution. Some students will struggle with percents.
(DIR) Post #Ao8kicM6X6KaEaxjdo by jayalane@mastodon.online
2024-11-17T17:08:55Z
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@futurebird @dymaxion @whknott it’s just so much harder to understand the basic ideas that way. Like physics without calculus is a lot harder than with. But yeah I couldn’t even get my own kids to take anything past calculus.
(DIR) Post #Ao8kjwWZ21Q94mUFKS by futurebird@sauropods.win
2024-11-17T17:09:06Z
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@jayalane @dymaxion @whknott Most people know a lot less math than people who use math every day suspect. I'd guess something like 1/3 of adults couldn't deal with fractions or percents correctly.
(DIR) Post #Ao8l34CMitxqNa9rVI by jayalane@mastodon.online
2024-11-17T17:12:36Z
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@futurebird @dymaxion @whknott and not just street urchins but serious intellectuals in the humanities. When I first learned Lebesgue integration and measure theory, I thought we should make a measure theory for liberal arts class because the ideas are very interesting. I should know better now.
(DIR) Post #Ao8mXkejX0pQhVceSu by mycotropic@beige.party
2024-11-17T17:29:21Z
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@futurebird @whknott I'm a user of statistics and distinctly not a methods person so I get you, they're different classes of math used for different things. I know when my models need a calculus component but in clinical epi I don't usually have signals data, I have slices of things that are in order. This lets me hand off calc stuff to methods people while I pretend like time only matters in survival models!
(DIR) Post #Ao8miXZCXMuZI5BBDs by jmax@mastodon.social
2024-11-17T17:31:19Z
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@futurebird @jayalane @dymaxion @whknott Yeah.
(DIR) Post #Ao8pCnMSZtTss8m3BA by AMS@infosec.exchange
2024-11-17T17:59:11Z
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@futurebird @jayalane @dymaxion @whknott Many even highly educated folks are functionally innumerate, especially in non-quantitative fields, especially when it comes to large numbers and ratios. There is a ton of base level scaffolding that needs to be there to explain some of these things.
(DIR) Post #Ao8pZanFTHUOYPAtbk by AMS@infosec.exchange
2024-11-17T18:03:19Z
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@futurebird @jayalane @dymaxion @whknott Also without looking up my tables 3ish?
(DIR) Post #Ao8qaCiAao2k6oeeeG by dragonfrog@mastodon.sdf.org
2024-11-17T18:14:36Z
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@futurebird @dymaxion @whknott Base Rate Error Rules Everything Around Me (BREREAM)
(DIR) Post #Ao8rxk22yPtQ47juN6 by jmax@mastodon.social
2024-11-17T18:30:04Z
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@futurebird @jayalane @dymaxion @whknott One of my personal annoyances (on the grand scale, this is petty, but it's my petty) is that very few people learn enough math to appreciate the fact that quantum mechanics is one of the great collaborative works of art.
(DIR) Post #Ao8zXRdrWYKX8MOnp2 by ttamttam@fosstodon.org
2024-11-17T19:54:58Z
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@futurebird @dymaxion @whknott A general understanding of stats is essential to fighting disinformation. It doesn't need to go into the continuous domain if that makes calculus a pre req. But people need the tools to reason about things like:What's the expected value of getting this vaccine?What kind of biases might be found in news reporting?How might this graph from a sales team be dishonest?IMO statistical thinking is one of the most important things you can learn/teach
(DIR) Post #Ao9nrguRSuATz70AS0 by KraftTea@mastodon.social
2024-11-18T05:18:49Z
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@futurebird @whknott If statistics is the weak alternative to calculus, then... why is it that so few people have a grasp and natural feel for it, and are incapable of applying it meaningfully in their lives?Statistics is how the Japanese, i.e., did so well at dealing with COVID, while the US popped horse dewormer. Pretty useful, really.
(DIR) Post #Ao9oTWs5EcEXr9wPTs by shuttersparks@qoto.org
2024-11-18T05:25:41Z
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@futurebird @whknott Agreed. Statistics is very important for understanding the world. What made math hard for me when I was young was the preconception that "math is hard". So I expected it to be hard, and it was, until I realized it wasn't.The other roadblock for me may be limited to a few people such as myself. I have a hard / impossible time learning things for which I see no purpose. Algebra was hard because uses for it were not discussed. "Just memorize this algorithm for factoring." Why? "So you pass the class." That doesn't work for me.When I reached calculus it was clear how extremely useful it is. Now I needed algebra. The algebra came to me quick, easy, obvious, because I saw a use for it. I was endlessly puzzled over why two years of algebra in Junior High was so damned hard. And I didn't learn anything in that time.
(DIR) Post #Ao9oZmtaZNyrIBd5hA by Npars01@mstdn.social
2024-11-18T05:25:04Z
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@futurebird @whknott Too many students get sifted out of college early due to a mandatory course on statistics or calculusToo often taught by people who hold the innumerate in contemptToo few realize that high school math does not prepare students well for courses taught by people who are utterly bored with the material or speed talk through complex topicsIt's made clear that an excess failure rate is expected, even desiredIt's a class, not Marine Corps training running a gauntlet
(DIR) Post #AoB6pk1R0tuDLZ14D2 by ballista11@mastodon.social
2024-11-18T19:31:57Z
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@dymaxion @futurebird @whknott I am ashamed to say this but I never took an accounting class. That point made, I had a supervisor who had MBA. He couldn't understand cost and feature comparison for a product I had to develop. Then he would lose it over the physical asset balance sheet. I had some time to kill at test in the University of Nebraska. I read Accounting for Dummies. Turns out I was not the idiot. He got his MBA from the University of Phoenix. 🤦🏻
(DIR) Post #AoB6xTefkYuCty3fN2 by bookwar@nrw.social
2024-11-17T20:46:46Z
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@dymaxion > the ability to reason about what is and isn't good data for quantitative decision-makingThis is not what they teach about in Mathematical Statistics classes unfortunately. So while I get your sentiment, teaching more statistics instead of calculus wouldn't help.@futurebird @whknott
(DIR) Post #AoB6xUbWDlydqTaf5s by dymaxion@infosec.exchange
2024-11-18T01:01:20Z
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@bookwarI have seen in practice that it does. Are they going to actually learn this stuff during the class? No. But when they run into actual problems later, they have a different toolkit of ideas to draw from. That's where the real learning happens.@futurebird @whknott
(DIR) Post #AoB6xW012BAOAk3juq by bookwar@nrw.social
2024-11-18T18:01:25Z
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@dymaxion I think it is more about _how_ you teach, than _what_ you teach.If while teaching Calculus one would highlight that there is not a single notion of integral but rather there are multiple ways to define the sum of infinitely small parts, students would be more open to the concept of - it is important to understand your inputs (definitions and assumptions) before applying your formulas. No matter what exactly is the subject.@futurebird @whknott