Post B0XCko6CaDdLlVsCJM by EverydayMoggie@sfba.social
(DIR) More posts by EverydayMoggie@sfba.social
(DIR) Post #B0XB6Jlbq1j49dN23c by futurebird@sauropods.win
2025-11-23T10:22:50Z
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Is there a name for when someone thinks they are really bad at something (for example math) and they have learned not to trust their own intuition at all so they make really wild errors by second guessing themselves?Here is a question:Which angles are equal?To me this is an "easy" question even if you don't know about isosceles triangles or anything. The symmetry of the figure suggests that 3 and 2 are congruent.I have a student who is struggling with this kind of thing.
(DIR) Post #B0XBTJ52YaykgYQAgS by futurebird@sauropods.win
2025-11-23T10:26:57Z
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She's good at algebra. It's dealing with figures, orienting them, seeing symmetry that seems to be the problem OR maybe she's just not trusting any of her instincts since most of math seems so counter intuitive. But sometimes the answer is obvious, and the obvious answer is right?
(DIR) Post #B0XBbTRBvtM17mg0Se by TheOtterDragon@eldritch.cafe
2025-11-23T10:28:25Z
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@futurebird I think that's the concept of learned helplessness ?
(DIR) Post #B0XC1VeoIpG5XPSflg by GustavinoBevilacqua@mastodon.cisti.org
2025-11-23T10:33:08Z
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@futurebird This remembers me the Meno dialogue by Plato, where Socrates demonstrates the "inborn knowledge".https://en.wikipedia.org/wiki/Meno#Dialogue_with_Meno's_slave
(DIR) Post #B0XC7qsuID336w4yno by futurebird@sauropods.win
2025-11-23T10:34:19Z
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One of the harder things to accept as a teacher is that some kids will just never like math. That's fine though. I can cope. What everyone can like at least is getting the right answer and knowing it's right. Knowing that yourself not needing anyone to tell you. So I'm hoping we can get to that stage at least.
(DIR) Post #B0XCezMhmbKoy9omPo by temporal_spider@masto.ai
2025-11-23T10:40:13Z
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@futurebird I wish you had been my math teacher instead of the badly misnamed Ms. Paramour. I always thought I was just being too sensitive about the way she seemed to dislike me in particular, until another student asked me why she always picked on me. I still don't know, but I really checked out that year, and never checked back in. Rather a shame.
(DIR) Post #B0XCkKA3tItaunRrA8 by oblomov@sociale.network
2025-11-23T10:41:07Z
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@futurebird it is possible that she just doesn't good spatial “awareness” (I'm not sure that's the right term?) rather than lack of trust, although this doesn't make it any easier to tell how much of it is nature and how much is (lack of) nurture. She wouldn't be the first person I know of with excellent abstract reasoning skill and no spatial intuition anyway.(That being said, verifying the intuition even when the answer is obvious is a Good Habit™ for a mathematician 8-D)
(DIR) Post #B0XCko6CaDdLlVsCJM by EverydayMoggie@sfba.social
2025-11-23T10:41:13Z
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Maybe it's not any of those things; it could be that she just can't see the symmetry. Brains can have all kinds of weird gaps in visual-spatial understanding.@futurebird
(DIR) Post #B0XD5lZt9UDu1kkkQi by toerror@mastodon.gamedev.place
2025-11-23T10:45:05Z
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@futurebird I think the long delay between doing the work, which might be a big list of questions, and getting the answers in a classroom format doesn't help. Particularly if you are struggling, you're trying to do the work and freezing because of the inevitability of flaiure looming over you.In a software version, you could try things until you get it right in a tight feedback loop, which would also remove the negative interaction with a human thing.
(DIR) Post #B0XD7dDvBTZohDMqIK by futurebird@sauropods.win
2025-11-23T10:45:24Z
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@oblomov To be honest I don't really know. I've known her for only a few months and she's working very hard, possibly too hard to keep up. I'm worried she has some horrible complex system to either compensate or avoid dealing with the spatial reasoning. I have the students work with compasses and it helps some of them. The compass is her mortal enemy. Every time she places it, it's just a guess ...
(DIR) Post #B0XD99eQ6actYcUKeG by gimulnautti@mastodon.green
2025-11-23T10:45:44Z
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@futurebird the ”i’m bad at math” fallacy is incredibly common.My ex kept saying to so much to my kid, I have had to keep fixing that assumption all her life, with no end in sight.
(DIR) Post #B0XDHrEtvd4X3qhZqK by futurebird@sauropods.win
2025-11-23T10:47:20Z
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@gimulnautti Very very few people are really "bad at math" in any real sense of the phrase. It's possible... but most of the time it's more like "had bad experiences being wrong and now avoid it" or "it's tedious and I have other things to do"
(DIR) Post #B0XDMa4PBtlvG92pf6 by gimulnautti@mastodon.green
2025-11-23T10:48:10Z
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@futurebird one bad teacher might be all they need
(DIR) Post #B0XDRGaL3xd2HADQhM by futurebird@sauropods.win
2025-11-23T10:49:02Z
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@gimulnautti Sometimes you can learn a LOT from a bad teacher. But that tends to come later in ones education.(thinking of my analysis teacher in college. good lord. )
(DIR) Post #B0XDgO3pYCy5nyDiFs by gimulnautti@mastodon.green
2025-11-23T10:51:44Z
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@futurebird But no, I don’t know the name of this specific phenomenon, other that it’s a form of cognitive bias.
(DIR) Post #B0XDpSUsQUX8AbCFRA by Divorytaur@mastodon.social
2025-11-23T10:53:22Z
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@futurebird Paranoid?
(DIR) Post #B0XDxvpxE0L5U05zg8 by klefstadmyr@social.vivaldi.net
2025-11-23T10:54:54Z
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@futurebird Maybe the expression should be "reverse Dunning-Krüger"?
(DIR) Post #B0XEqYQtwTnMp7QJMW by lkundrak@metalhead.club
2025-11-23T11:04:45Z
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@futurebird *takes the bong from the student*
(DIR) Post #B0XF9Oqpn6XobmXVwW by futurebird@sauropods.win
2025-11-23T11:08:06Z
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@jetlagjen We use the numbers consistently because I find using three letters is more confusing for most students. eg ∠ABC = ∠BCAvs. ∠3 = ∠2Which do you find less confusing?We could also do ∠B = ∠C but naming angles by single letter is a bad habit since there can be multiple angles at a vertex.
(DIR) Post #B0XGDH9qR8ONrOqMZk by futurebird@sauropods.win
2025-11-23T11:20:01Z
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@pthane I'm trying to understand this. If I flip a board "l-r" will the result be different than "r-l" ?The way I'm picturing this the answer would be "no" right?
(DIR) Post #B0XGQImjhK0UfiFJjc by 3TomatoesShort@disabled.social
2025-11-23T10:54:08Z
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@EverydayMoggieI was thinking this - I can see it, but it's not *super* obvious to me. I think if I was a young'un just starting out in math, I would want to cut it out and fold it in half to check 😅 (Ooh though I remember now we had little mirror thingies to check, too?)@futurebird
(DIR) Post #B0XGQJke6ZvffWHA7E by Bumblefish@mastodon.scot
2025-11-23T10:57:39Z
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@3TomatoesShort @EverydayMoggie @futurebird I was going to suggest paper modeling. I can’t calculate anything to save my life, but give me a concrete thing I can shape with my hands and things start to make sense. You mentioned compasses. Nobody has reliably convinced me they can do anything except make circles. The whole thing where you use them to make angles is deep magic that only wizards can perform.
(DIR) Post #B0XGQOltRMtjEptjFo by Bumblefish@mastodon.scot
2025-11-23T10:59:35Z
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@3TomatoesShort @EverydayMoggie @futurebird Get her to start quilting. Then planning her quilt designs. That’ll help.
(DIR) Post #B0XGRrTyBBdCZbDCS0 by DrorBedrack@mastodon.social
2025-11-23T11:22:44Z
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@futurebird turn around the page? we learn about these type of triangles with the not-equal side parallel to the bottom of the page, some people may have a problem turning it in their heads and "seeing" it's the same thing
(DIR) Post #B0XGgnAUVAGNXLDieO by agathos@mastodon.babb.no
2025-11-23T11:25:21Z
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@futurebird i was a kid like that, and i later got diagnosed with dyscalculia. The reason i didnt get diagnosed as a kid, was because i have very strong memory so i just memorized everything. So i could really struggle if a triangle was a little rotated, because it didnt fit the example i memorized.
(DIR) Post #B0XHFnLroMjsF1ERea by futurebird@sauropods.win
2025-11-23T11:31:47Z
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@Bumblefish @3TomatoesShort @EverydayMoggie "The whole thing where you use them to make angles is deep magic that only wizards can perform."I've noticed that the angle construction is harder for students. Not just this one who's having extra difficulty, but all of them are a little mystified when I say "now we'll copy and angle" but there is some good intuitive geometry in this construction. A compass isn't just for making circles. It's a fixed distance you can put wherever you want.
(DIR) Post #B0XHNdyIZQFlSwx01w by futurebird@sauropods.win
2025-11-23T11:33:10Z
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@wakame @jetlagjen I've never seen it done that way before. But I do think it's more clear than using three letters since the vertex is repeated and stands out a bit more.
(DIR) Post #B0XHYs1CgW80DVf9Bg by Cheeseness@mastodon.social
2025-11-23T11:35:11Z
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@futurebird It's tough when things seem like arbitrary unpredictable magic. I can only speak for my own journey, but it was only as an adult when I was able to set problems for myself and find joy and a sense of discovery in exploring them that I was able to build a better relationship with maths.At least with your example triangle there, you can print it out a few times to fold/cut up/otherwise compare to prove/consider/discuss that there are fundamental rules at work.
(DIR) Post #B0XHZvng6qWcEfqHGi by DrorBedrack@mastodon.social
2025-11-23T11:35:22Z
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@futurebird oh, no. This isn't obvious at all.
(DIR) Post #B0XHbCPdpZEq30ChGq by futurebird@sauropods.win
2025-11-23T11:35:19Z
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@jetlagjen How do you name the vertices?We could go with greek letters rather than numbers but I have tried this and students find it more confusing than the numbers. I don't really think the issue this student has is due to labeling.
(DIR) Post #B0XHyltG5k1ujwITlw by willyyam@mastodon.social
2025-11-23T11:39:49Z
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@futurebird @jetlagjen I think your approach makes sense; with computers+clip art you have other choices too! "Which two Pokemon are the same angle?" etc...
(DIR) Post #B0XI0dUoGxOlHhkalk by pikesley@mastodon.me.uk
2025-11-23T11:40:11Z
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@futurebird @Bumblefish @3TomatoesShort @EverydayMoggie I expect you're already familiar with this game, but if not, you'll love ithttps://www.euclidea.xyz/
(DIR) Post #B0XIGkApDG06d15Eoa by th@social.v.st
2025-11-23T11:42:43Z
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@futurebird @jetlagjen numbers are fine for me although I find the uppercase versus lowercase used in some trig identities like the Law of Cosine confusing.
(DIR) Post #B0XJZbtUJvMcPDXBuS by twigpi@mastodon.social
2025-11-23T11:57:38Z
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@futurebird Wild errors come from unclear presentations. The diagram shows contradictory layout. It's obvious from the lines that B and C are where the equal angles are at, but because someone put 2 and 3 in the spaces where the angles are, as if they where measurements, almost anyone who looks at this problem who isn't used to bad illustrations will likely experience unnecessary anxiety and confusion about the solution.
(DIR) Post #B0XK6D2ZkITYseKU9w by Tattie@eldritch.cafe
2025-11-23T12:03:36Z
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@futurebird it sounds like it might be in the region of learned helplessness? Like a learned incompetence? "I can't do math so whatever I think is the answer of probably wrong."
(DIR) Post #B0XK8sHrMZk3NpkWOG by futurebird@sauropods.win
2025-11-23T12:04:04Z
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@agathos This is interesting. The student happens to be really good at memorizing things. And thinking back when a problem is rotated it really throws her.Maybe we can work on doing things like first rotating the paper to a familiar position.
(DIR) Post #B0XKlG2DWBNq2WjdR2 by Bumblefish@mastodon.scot
2025-11-23T12:11:00Z
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@futurebird @3TomatoesShort @EverydayMoggie 🤣intuitive…you keep using that word. I do not think it means what you think it means (to paraphrase the immortal Inigo Montoya🤣)
(DIR) Post #B0XKljgdGzwY0GroxM by futurebird@sauropods.win
2025-11-23T12:11:05Z
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@DrorBedrack If anyone has ideas to make the idea of copying an angle more obvious I would love it. I've tried pointing out that it's basically copying a triangle too. You are duplicating the length of all three sides and thus you get the angle for free. It's "Side Angle Side" ... but that seems maybe more confusing than just doing it a few times and feeling how well it works.
(DIR) Post #B0XKwEq2J5HJVxH1Um by futurebird@sauropods.win
2025-11-23T12:13:04Z
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@Bumblefish @3TomatoesShort @EverydayMoggie OK let me try this one:How would you use a compass to make a very pointy isosceles triangle like a wizard's hat? For a quilt or something.
(DIR) Post #B0XKyuJr3KAckDUfNg by Bumblefish@mastodon.scot
2025-11-23T12:13:32Z
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@futurebird @3TomatoesShort @EverydayMoggie I wouldn’t. I’d use two rulers as god intended.
(DIR) Post #B0XL0KxFVZyDdsbN0C by futurebird@sauropods.win
2025-11-23T12:13:49Z
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@Bumblefish @3TomatoesShort @EverydayMoggie Ok but try.
(DIR) Post #B0XL3v53eK7oYNxjzk by Bumblefish@mastodon.scot
2025-11-23T12:14:26Z
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@futurebird @3TomatoesShort @EverydayMoggie I got a circle.
(DIR) Post #B0XL7f4j6Bi64Xakgi by futurebird@sauropods.win
2025-11-23T12:15:08Z
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@Bumblefish @3TomatoesShort @EverydayMoggie Great use the center and the circle to make a pointy triangle.
(DIR) Post #B0XLGABLKR8YrfjyfQ by Bumblefish@mastodon.scot
2025-11-23T12:16:36Z
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@futurebird @3TomatoesShort @EverydayMoggie Ok so where I’m holding the compass is a pointy triangle.
(DIR) Post #B0XLT4saM34aBS7o8W by Bumblefish@mastodon.scot
2025-11-23T12:15:56Z
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@futurebird @3TomatoesShort @EverydayMoggie Oh wait if I lie it down and trace around it I got a…wait wait *that’s* got an angle . What’s going on here?
(DIR) Post #B0XLT5tgZRXzL9eCUS by futurebird@sauropods.win
2025-11-23T12:18:59Z
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@Bumblefish @3TomatoesShort @EverydayMoggie OK now I'm confused what you have done. This is what I was expecting. But, people always surprise me.
(DIR) Post #B0XLXXJkZ2nRXcxOnQ by Bumblefish@mastodon.scot
2025-11-23T12:19:47Z
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@futurebird @3TomatoesShort @EverydayMoggie No that would not occur to me in a million years.
(DIR) Post #B0XLaGTrcUIsBvzMWW by futurebird@sauropods.win
2025-11-23T12:20:18Z
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@Bumblefish @3TomatoesShort @EverydayMoggie EXACTLY!The legs of the compass are the same length (roughly) so it makes an isosceles triangle.
(DIR) Post #B0XLcWWAxrL2Ve9BZ2 by DrorBedrack@mastodon.social
2025-11-23T12:20:40Z
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@futurebird The explanation is awesoeme, I just think it's a hard concept to grasp, even with the best explanation. Especially in a busy classroomAnd... yes, doing it for yourself a few times seems to be the best way to learn, no matter how good the theory and explanations are...damn human limitiations
(DIR) Post #B0XMYb7C1y0PYx9a4G by Bumblefish@mastodon.scot
2025-11-23T12:21:20Z
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@futurebird @3TomatoesShort @EverydayMoggie However if you had asked me to cut it like a pizza we’d have been fine.
(DIR) Post #B0XMYcNBM0ODSpdrd2 by futurebird@sauropods.win
2025-11-23T12:31:12Z
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@Bumblefish @3TomatoesShort @EverydayMoggie OK pizza good to know. Anyway. Connecting the center of a circle to two points like that is a great way to create an angle. When you copy an angle you are just cutting two pizza slices that are the same. If the pizzas are the same size, and the distance between the points on the circle is the same. The angle at the top (center) is the same.
(DIR) Post #B0XMers4e235Gi4V0a by dahukanna@mastodon.social
2025-11-23T12:29:12Z
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@Bumblefish @3TomatoesShort @EverydayMoggie @futurebird Using a compass to draw an isosceles triangle is a step too far for me.I’d start with physical paper, then model different scales in a digital tool and then translate that to angle degrees + line proportions.I’ve repeated this process enough that I can “tear” a flattened 3-D cube out of a sheet of paper in capital T or lower-case t configurations.
(DIR) Post #B0XMesx4cvdscVQ0RM by futurebird@sauropods.win
2025-11-23T12:32:19Z
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@dahukanna @Bumblefish @3TomatoesShort @EverydayMoggie That sounds like so much work to me. If you want someone with two parts that are the same length that start at the same point they have to be on a circle. No need to measure anything.
(DIR) Post #B0XNNFLGk2zwntt9wu by reqa@digitalcourage.social
2025-11-23T12:40:17Z
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@futurebird could be a perspective/3D interpretation issue? My brain tends to see 2 closer to me and thus vaguely feeling like it might be a smaller angle than 3. Only the equal double tic marks make me reason that they must be equal. But then, could also intentionally be a misleading drawing, so unless I take measures myself, my assessment depends on trusting the tic marks.
(DIR) Post #B0XNn3TlTEUBXaAXKK by futurebird@sauropods.win
2025-11-23T12:44:57Z
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@pthane I think focusing on the results might help? If they go top/bottom the text will be upside down. So "flip it so the edge with the text is *still* near you but the lighter side of the board is on top" maybe?The "left right" makes me think of rotating since with 90 degree turns left and right matter?
(DIR) Post #B0XNnUq1kZKwORnCHA by dahukanna@mastodon.social
2025-11-23T12:45:04Z
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@futurebird I‘be no cognitive intuition for geometry, never been able to tell left from right, am a visual learner & can imagine an Apple+smell it+hear crunch when I bite into it, …So validating a flat planer isosceles triangle needs deliberate cognitive effort, else i’m guessing based on “way wind blows” or my mood.As a digital Designer, developed systems that enable expressing visual scene by literally, mentally mathematically raytracing scene. POV ray was “heaven”- camera, lights, action!
(DIR) Post #B0XOQOWFB6gE5Z5SJE by mattmcirvin@mathstodon.xyz
2025-11-23T12:52:04Z
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@futurebird My experience as a tutor and a teaching assistant in math-heavy subjects was that, while it's not everyone, there are a lot of kids who basically get the material but who need someone to occasionally encourage them that they're on the right track when they seize up and second-guess themselves.The second-guessing can be useful in more advanced study if it's targeted appropriately. If I didn't know for sure that that diagram was supposed to represent Euclidean geometry, I *couldn't* actually say that the congruent angles followed from the symmetry of the triangle without further assumptions. (Maybe the metric space it's in doesn't share that symmetry!) Then, that student's suspicion of intuition would be warranted. It's just misfiring in situations where it's not.
(DIR) Post #B0XOisYgEPYuSz2aDA by futurebird@sauropods.win
2025-11-23T12:55:28Z
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@dahukanna That's interesting. I *also* have no sense of left or right. "you injured your left leg which one still hurts?"But, this has always been a secret advantage in mathematics since seeing patterns backwards happens as fast as forwards. I don't mind doing measurements but here is another shot at avoiding it:An isosceles triangle is a pendulum. The distances are the same because it's the same string. If a pendulum could swing all the way around it would make a circle.
(DIR) Post #B0XOmZ80PlIDMZK0vY by semitones@tiny.tilde.website
2025-11-23T12:56:02Z
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@futurebird @jetlagjen I like the system where you have one arc in one angle then two arcs, etc., and an equal number of arcs for angles that are the same size. But I guess if you are asking the student which angles have the same size, you can't use arcs in the problem.Using letters to represent the line segments is the standard? I agree, naming angles by the combination of letters was confusing.What if you use the dot of color to identify each angle? I guess that wouldn't photocopy well..
(DIR) Post #B0XOq5qBFM9zghfN32 by futurebird@sauropods.win
2025-11-23T12:56:46Z
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@mattmcirvin That is too much second guessing. I mean... it's correct. I didn't say what kind of geometry or if this is on a plane. But ... that's too much.
(DIR) Post #B0XOy3ym3EYoEPUD1k by futurebird@sauropods.win
2025-11-23T12:58:11Z
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@semitones @jetlagjen Using color to identify angles means you can't use it to show which ones are the same. Which is a great use for color if you don't have color blind students. (I don't at the moment but it's always in the back of my mind. )
(DIR) Post #B0XPIp62a25O9dmgXA by dahukanna@mastodon.social
2025-11-23T13:01:52Z
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@futurebird
(DIR) Post #B0XPO6LFtDYP5WPx9E by semitones@tiny.tilde.website
2025-11-23T13:02:52Z
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@futurebird @jetlagjen if I remember correctly, there are some combinations of colors that are more colorblind-safe than others, but I agree it is an important consideration.The rock climbing gym I work at uses this knowledge to decide which colors of holds go on the wall next to each other.Maybe when art classes teach color theory they should include a topic about colorblind-safe colors. Reference: https://davidmathlogic.com/colorblind/
(DIR) Post #B0XQQfBPQDBrgBb73Y by phpete@mastodon.coffee
2025-11-23T13:14:33Z
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@futurebirdSkimming through is showing me that clearly I'm in the minority of your sample, but nonetheless:The three letter structure is what I grew up with, (but also/and so) was the easiest way to teach one of my kids. Line segments were intuitive to her, meaning the three letter system gave her all the angles on a figure without 'extra' labels. "Just follow the lines".As a tangent to the thread, kudos once again to the effort you expend on your students.@jetlagjen
(DIR) Post #B0XQW2BxIqUSUJPkdk by futurebird@sauropods.win
2025-11-23T13:15:33Z
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@dahukanna 1 and 2 are totally correct. An equilateral triangle is kind of isosceles triangle. One that works in three ways. A line is a degenerate isosceles triangle with two right angles and a zero angle at the vertex OR two zero angels at the base and a 180 angle at the vertex. Probably better to call it a line. Both of these are not always called isosceles but they are the natural extremes.
(DIR) Post #B0XQl0PWCwjzJ6tgcS by futurebird@sauropods.win
2025-11-23T13:18:16Z
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@phpete @jetlagjen The three letters eg ∠ABC where B is the vertex are also what I learned and I hated the numbers when I first saw them. But, from experience I find they just work better. My little grumble about "but numbers are for measuring" and also "that's not how I learned it" are something I've gotten past. I go with what helps the most students get it. Hence I don't use greek letters with ninth graders. Learning the new symbols at the same time was too much for some.
(DIR) Post #B0XR5iPELNRNY2daQy by futurebird@sauropods.win
2025-11-23T13:22:01Z
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@phpete @jetlagjen Also different populations of students have different needs. So, maybe I would switch if I thought it would work better with a new group. I make a big deal about introducing the Greek letters in the spring when we start trig. This gives them time to learn how to write them. So they do learn them by the end of the year? New symbols are a big deal and deserve space. Don't just spring them on people. I do find the numbers a little "janky" from a pure maths lens.
(DIR) Post #B0XRDhqIK4D47K6gqG by dahukanna@mastodon.social
2025-11-23T13:17:54Z
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@futurebird I interpreted “pendulum could swing all the way around it would make a circle.” On z-axis, not y-axis
(DIR) Post #B0XRDizC4SvFfDHJLs by futurebird@sauropods.win
2025-11-23T13:23:26Z
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@dahukanna Well then you are making triangles in a different plane or triangular prisms maybe.
(DIR) Post #B0XRSU5Xk4g7nsHnma by phpete@mastodon.coffee
2025-11-23T13:26:06Z
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@futurebirdSolid thinking across the board, it sounds like you're the kind of teacher we'd all like to have. I'm curious, has your class size ever affected your decision to introduce 'one more thing', (read: Greek letters in this example)A 15:1 classroom is a different environment than a 30:1. @jetlagjen
(DIR) Post #B0XRngqRVcwvRqKoJU by futurebird@sauropods.win
2025-11-23T13:29:57Z
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@phpete @jetlagjen Absolutely. If I had 30 students I would not do the compass work. And that would be a big loss, but I would not be able to go around the room and help enough of them to hold it correctly, and keeping that many compasses sharp and ready to go is too much work. Likewise teaching them to sharpen the lead on the compass is too much of a class time-sink. (although it's a very cool skill to have, so it make me sad)I bring only working compasses with sharp lead to class.
(DIR) Post #B0XS1zFDtdDWZGk6wi by Bumblefish@mastodon.scot
2025-11-23T13:32:32Z
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@futurebird @3TomatoesShort @EverydayMoggie But why use a compass to do that? Why not a ruler through the middle?
(DIR) Post #B0XS9mjOIxL44hZWWe by semitones@tiny.tilde.website
2025-11-23T13:33:53Z
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@futurebird @jetlagjen ps this is the system of arcs I was talking about, to identify which angles are the same size. It works pretty well until you have a more complicated shape with many angles. Is there a name for this system?
(DIR) Post #B0XSBVBkUz0QFLefRY by futurebird@sauropods.win
2025-11-23T13:34:17Z
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@Bumblefish @3TomatoesShort @EverydayMoggie Rulers are less precise than a compass. You could use a ruler if you wanted. But it will only be as precise as the markings you have made on the ruler.
(DIR) Post #B0XSGOENnI9M7GDY7E by Bumblefish@mastodon.scot
2025-11-23T13:35:08Z
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@futurebird @3TomatoesShort @EverydayMoggie Not measuring anything, just using it to get a straight line. Could use any straight edge.
(DIR) Post #B0XSKg17bjawRA3iNM by futurebird@sauropods.win
2025-11-23T13:35:55Z
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@Bumblefish @3TomatoesShort @EverydayMoggie This is a very deep mathematical question in a way. Why do we do geometric constructions with a "straight edge" and compass and not a ruler and compass?
(DIR) Post #B0XSVctpXUDDxArymO by futurebird@sauropods.win
2025-11-23T13:37:54Z
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@semitones @jetlagjen We use this system, but asking which angles are the same when they are marked like this isn't testing the concept I'm getting at. It's called "decoration" or "tic marks" and the little marks on the sides of the original triangle I posted are a part of the same system. I would expect a student to mark the angles like this based on the way the sides are marked. My struggling student would make the wrong two the same.
(DIR) Post #B0XShjnlhcaupqoF60 by Bumblefish@mastodon.scot
2025-11-23T13:40:04Z
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@futurebird I don’t think I need a compass at all because I can draw crosshairs at and then join the bottom.
(DIR) Post #B0XSpcDrlVQne6lyWe by dahukanna@mastodon.social
2025-11-23T13:41:27Z
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@futurebird You know how some people have “musical perfect pitch” and can reproduce a note intuitively?I need sheet music and the appropriate pitch fork and then I can work out the rest of the associated melody differential Lu.Some people have “maths perfect pitch”. I don’t. I’ve done a lot of deliberate practice and training so that it looks like it’s intuitive but it’s informed memorization, with rapid recap.
(DIR) Post #B0XSro8wPqIhCDVxjM by jmax@mastodon.social
2025-11-23T13:41:53Z
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@futurebird @phpete @jetlagjen I survived a physics degree, and as a side effect, found to my amusement that I had memorized every letter of the Greek alphabet, but had only a hazy idea of their order.
(DIR) Post #B0XT03Xl2emLHA3UrA by phpete@mastodon.coffee
2025-11-23T13:43:22Z
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@futurebirdWell I hope you're never stuck in that position. It'd be a loss to everyone involved. Thanks for the lovely chat, but my coffee is done, signaling the start of yet another "day" where there are "things to do" and all that. Be well!@jetlagjen
(DIR) Post #B0XT5MlyyUdwMYF0Cm by futurebird@sauropods.win
2025-11-23T13:44:21Z
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@Bumblefish @3TomatoesShort @EverydayMoggie But how would you get the angle at the center exactly the same with just ruler?
(DIR) Post #B0XTAuPtJdN49eYDWy by Bumblefish@mastodon.scot
2025-11-23T13:45:21Z
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@futurebird @3TomatoesShort @EverydayMoggie Wherever the cross happens is the peak of the triangle.
(DIR) Post #B0XTIcEkn6Tu5X14XA by futurebird@sauropods.win
2025-11-23T13:46:44Z
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@Bumblefish @3TomatoesShort @EverydayMoggie The peak is the angle at the center, right? I don't see a "cross"
(DIR) Post #B0XTVvOWsHV9Gkw1oG by Bumblefish@mastodon.scot
2025-11-23T13:49:05Z
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@futurebird @3TomatoesShort @EverydayMoggie That’s because you haven’t drawn one and for the life of me I don’t know why. You need the cross to cut the pizza.
(DIR) Post #B0XTnUk8hcqtp8QABU by futurebird@sauropods.win
2025-11-23T13:52:18Z
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@Bumblefish @3TomatoesShort @EverydayMoggie OK great. I still don't see how to cut two slices that are the same size from the identical circles without measuring with the ruler or using the compass again.
(DIR) Post #B0XTypWdm6lTSqVoFE by Bumblefish@mastodon.scot
2025-11-23T13:54:20Z
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@futurebird @3TomatoesShort @EverydayMoggie Infinite spiral of isosceles triangles, just eyeballed
(DIR) Post #B0XU1G8lnAOMaXVNVA by Bumblefish@mastodon.scot
2025-11-23T13:54:49Z
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@futurebird @3TomatoesShort @EverydayMoggie The opposite one will always be the same size.
(DIR) Post #B0XU4zUNdxw06SOOky by futurebird@sauropods.win
2025-11-23T13:55:30Z
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@Bumblefish @3TomatoesShort @EverydayMoggie Absolutely. But if you want to copy an angle to a new location that won't help.
(DIR) Post #B0XU7UhAafGNT0ZIi8 by Bumblefish@mastodon.scot
2025-11-23T13:55:56Z
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@futurebird @3TomatoesShort @EverydayMoggie Tracing paper FTW!
(DIR) Post #B0XU9KxlkIHHrVDAPY by semitones@tiny.tilde.website
2025-11-23T13:56:13Z
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@futurebird @jetlagjen okay, now I'm really into brainstorming territory, and this may be way more overcomplicating it, but what if you put the triangle on the Cartesian grid and then ask them which angles were the same, identifying them by their Cartesian coordinates? Or for students like me who were confused by symbols in general and wanted to use more words in math, what if you labeled them like this?I'm not sure this is a big problem though, so might be just wasting time here lol
(DIR) Post #B0XUIsePreYMwui4R6 by futurebird@sauropods.win
2025-11-23T13:58:00Z
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@Bumblefish @3TomatoesShort @EverydayMoggie Tracing paper isn't really making a copy. It's just the same figure again. As I see it anyways. But my point here is that it take two "measurements" with these tools. I'm going to use some of this I think. Very cool stuff.
(DIR) Post #B0XVBTz1HPLGN3Np0S by Bumblefish@mastodon.scot
2025-11-23T14:07:50Z
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@futurebird @3TomatoesShort @EverydayMoggie Copy/paste works too…but this is basically how every conversation I have with math teachers goes, and I feel bad because I don’t get it, and it must be annoying for them all. In high school my last teacher just said I don’t actually need to know it and put me in a basic class where we learned to calculate rent on a low salary. Now that was easy to understand!
(DIR) Post #B0XX5cgsC2DHXyEGBc by agathos@mastodon.babb.no
2025-11-23T14:29:11Z
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@futurebird i never learned how to do any calculations, everything had to be memorized. Multiplication got memorized by making a little song to the sequence. So if i needed to know 6*4, i had to check the 4 "song" and very quickly "sing" in my head 4,8,12,16,20, 24. This did work really really well for many years, but i never learned any understanding. I also cant tell time, and i still use my fingers to count. So it seemed like i "got it" in algebra since i was able to memorize a lot of it.
(DIR) Post #B0XZDvssumttIfwBGq by futurebird@sauropods.win
2025-11-23T14:53:01Z
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@undead The things that are the same are what we are really trying to talk about.
(DIR) Post #B0XZUhalJ4LztdSOPY by futurebird@sauropods.win
2025-11-23T14:56:08Z
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@undead I didn't mean that you were off base. (Nor do I think you have anything to apologize for. )It's fine to prefer a certain notation ... but the notation isn't really what it's about. I'm just suggesting that as a thread to pull to get past what isn't as important here. I'm very particular about notation because I know it can be confusing as I explain here:https://sauropods.win/@futurebird/115598693916804903
(DIR) Post #B0XgYT1S7JPXXzgRd2 by billseitz@toolsforthought.social
2025-11-23T16:15:13Z
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@futurebird I don't think you want to encourage "seeing" the symmetry because that's subjective/risky (and some tests "trick" you by making segments same/similar in length but not having the symbols to prove it)
(DIR) Post #B0XpyB76DvOP7WexrU by Kitbuckley@urbanists.social
2025-11-23T18:00:43Z
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@futurebird @Bumblefish @3TomatoesShort @EverydayMoggie
(DIR) Post #B0Xr4blAANxhSC1rFI by hitsuyonai@mastodon.online
2025-11-23T17:11:08Z
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@jetlagjen @futurebird A, B, C for vertices, α, β, γ for angles? But what would I know? It's all Greek to me! 😉 Someone posted a link to this a while back; interesting in the context of the presentation discussion:[#AltTextForMe - help!]I thought it was obvious, but I'd seen in a Primary Maths Challenge (aimed at 9/10, 10/11 year old UK kids) … How many different isosceles triangles with whole number sides can you make from a loop of string 21 units long?https://www.theguardian.com/science/2025/feb/17/can-you-solve-it-the-simple-geometry-question-that-fools-almost-everyone:
(DIR) Post #B0XrPyfICTYeZgTNYG by futurebird@sauropods.win
2025-11-23T18:16:57Z
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@hitsuyonai @jetlagjen "drawing is NOT to scale"the nerve.
(DIR) Post #B0XsSYaRiMmuW902tM by futurebird@sauropods.win
2025-11-23T18:28:38Z
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@cinebox @hitsuyonai @jetlagjen It's a troll.
(DIR) Post #B0XswduoT4EJjNs944 by AchillesTang@mastodon.social
2025-11-23T18:34:04Z
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@futurebird Oof, this was me! I was great at algebra but geometry was always incredibly frustrating, and trigonometry? Impossible.
(DIR) Post #B0Xt41kMGI0DfaVGM4 by futurebird@sauropods.win
2025-11-23T18:35:26Z
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@hitsuyonai @jetlagjen
(DIR) Post #B0XtqYNMFcV2lbssl6 by mlohbihler@techhub.social
2025-11-23T18:44:11Z
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@futurebird @hitsuyonai @jetlagjen it took me a minute, but I'm glad to say I got the joke
(DIR) Post #B0XtxsNOHuHipBOJqC by futurebird@sauropods.win
2025-11-23T18:45:33Z
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@Bumblefish @3TomatoesShort @EverydayMoggie The reasoning you did to make this conclusion:https://mastodon.scot/@Bumblefish/115599349455753970... means you can understand geometry and congruent triangles. To know those "slices" are equivalent is "Side Angle Side" I think you just need to learn to like the compass better as a way to deal with lengths. It can be very powerful I'll show you an example. Someone posted a nasty trick question on this thread. Thinking about it with a compass makes the trick vanish.
(DIR) Post #B0Xu5XdnGWdspbicr2 by futurebird@sauropods.win
2025-11-23T18:46:55Z
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@Bumblefish @3TomatoesShort @EverydayMoggie OK here is the trick question in the replies I show how to answer it with a compass. https://mastodon.online/@hitsuyonai/115600121436622666
(DIR) Post #B0XuAxD9cgyjaHq5yq by futurebird@sauropods.win
2025-11-23T18:47:50Z
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@gaditb @hitsuyonai @jetlagjen I think some of the descriptions were fine. Those that mention it's not to scale. Maybe it's an example of when having the description is superior to seeing the image visually.
(DIR) Post #B0XvRgc4gg7Kz22Pya by futurebird@sauropods.win
2025-11-23T19:02:07Z
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@Bumblefish @3TomatoesShort @EverydayMoggie ... are you a spider?
(DIR) Post #B0XxaDdG0USdcCmt7o by ehproque@neopaquita.es
2025-11-23T19:26:00Z
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@futurebird @Bumblefish @3TomatoesShort @EverydayMoggie I wouldn't; I would have started from two arbitrary points, and drawn two circles of equal radius centered on them
(DIR) Post #B0Y3NjWuhTiMVLFYrg by madjohnroberts@mastodon.social
2025-11-23T20:31:00Z
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@futurebird @DrorBedrack the diagram took me a minute to wrap my head around, for me it would have been more immediately obvious what the diagram is doing if it was explained like: we have this angle which is a slice of the full circle. We can draw the same circle around each vertex. To replicate the angle we can find the distance between where the lines intercept the circle, letting us find the 2nd intercept on the 2nd circle, allowing us to draw the angle. Using the _full_ circle helps me
(DIR) Post #B0Y6NfA9ElEwp3G9rs by dr_a@mastodon.social
2025-11-23T21:04:37Z
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@futurebird it sounds you’re dealing with a self-fulfilling prophecy. regardless of how your student got there, they’ll need to overcome the idea that they’re definitely bad at something. i’ve had some success tricking people into doing the thing they think they’re bad at, and then gently pointing out that they’re pretty good at it.
(DIR) Post #B0Zx7ldECCA14Y0MJk by benh@mastodon.scot
2025-11-24T18:30:20Z
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@futurebird Made me wonder about an imagination impairment.Like https://mastodon.scot/@skinnylatte@hachyderm.io
(DIR) Post #B0dOurW0OF4LkJ8nia by PalmAndNeedle@norden.social
2025-11-26T10:25:52Z
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@futurebird @Bumblefish @3TomatoesShort @EverydayMoggie because geometric construction was a thing centuries before precision units were?