💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

What is your answer to 18÷3x2=? Boosts appreciated No, this isn't a trick question. An oft-cited blog has made the claim that "most humans" will get the wrong answer, which I think is a completely ridiculous claim, so I want hard data on the split. Unlike some other polls I've run, I want #teachers and #students to answer also, since you all come under "most humans" :-) #Mathematics #Maths #Math #arithmetic #OrderOfOperations #poll #education #school

@_elena@mastodon.social Reminds me of a time on here when someone claimed that Mastodon was a ghost town, because no-one was replying to his posts... but he wasn't replying to other people's posts! Just magically expected the engagement to happen just from posting. 😂 And then the kicker is, when I pointed out he needed to post more and ENGAGE MORE if he wanted to get engagement, he called me a spammer and blocked me! Gee, I wonder why he gets no engagement?! 😂

@ApostateEnglishman@mastodon.world @simon@bne.social "It's called the order of operations, which is indeed a notational convention" - they're rules, the order of operations rules "Is it (18÷3)x2 or 18÷(3x2)?" - neither, it's what I wrote in the poll, the way it was always written before we started using brackets in Maths, when Euler started using them in the 18th Century "both have a universally correct answer" - as does the expression I wrote, and has done for many centuries

@ApostateEnglishman@mastodon.world @simon@bne.social "I hate these things because it's social convention where you mentally place the brackets" - there AREN'T any brackets. "Some folks like to imagine math(s) is some Platonic thing" - it's a universal truth actually https://dotnet.social/@SmartmanApps/112019943359120289 "syntax is a human construction" - notation depends on culture, the rules don't

@JenMsft@mastodon.social @Axolotl1@gaygeek.social "I guess it's probably harder to notice over on mastodon" - this is the first post I've seen about it. Was news to me! 😂

@rzeta0@mathstodon.xyz I don't know, but textbooks usually have the answers in the back, so I'd be surprised if you could find enough without answers to make a book out of it

@JenMsft@mastodon.social To err is human... but to really screw up takes a computer 😂

@medus@social.medusmedia.com @JenMsft@mastodon.social It used to be, then they changed it, a couple of years ago

@aral@mastodon.ar.al From your local government franchise 😂

@bitflipped@mastodon.world It's probably the same people who claim that I, a Maths teacher, doesn't know the rules of Maths 😂

@TechDesk@flipboard.social "some coders would prefer just to leave them cracked open" - well that makes them easier to spot than putting a mark on their forehead then 😂

@mojo@aus.social @josh@masto.byrd.ws "the usual “tax is theft” crowd will scream blue murder" - well, hopefully they will practise what they preach and not scream blue murder in any public spaces, which are funded by the proceeds of this "theft", or drive on any public roads to get there, which were built with the proceeds of this "theft", or drink water out of a tap... 😂

@jenniferplusplus@hachyderm.io "You can't put the genie back in the bottle" - spoiler alert: it wasn't Jeannie anyway, but her evil sister!

4/x Products are Terms

6/x Expanding Brackets is the reverse of Factorising (hence why solving brackets is first in order of operations)

@404mediaco@mastodon.social "reign in" - rein in

@rzeta0@mathstodon.xyz OMG, there's nothing worse than having a poorly-educated American put a red underline for my correctly-spelt English word. Oh wait, yes there is. The e-calculator written by a poorly-educated American that doesn't obey the order of operations rules 🙄 https://dotnet.social/@SmartmanApps/111164851485070719

@bemmesr@mathstodon.xyz More often than not the teacher explains the proof rather than the textbook (which is more an aid to teachers than to be used stand-alone), but I have a few explanations here https://dotnet.social/@SmartmanApps/110968910722113903 such as a proof of Pythagoras, amongst other things. Is there anything you wanted further explaining about in high school Maths?

@dpnash@c.im "something annoying like “6➗️2x” in it" - which is ALSO unambiguous https://dotnet.social/@SmartmanApps/110846452267056791 ab=(axb) BY DEFINITION "*ordered sequence* of operations" - there's only one operator - there IS only one order in which you can do it! "which is unambiguously “six divided by the result of multiplying x by two”" - as is the original expression you wrote "not the same as the ordered sequence" - yes it is "nobody writes expressions like these the first way" - I do, as does everyone else here

@caten@mathstodon.xyz "I have lost a lot of faith in Wikipedia recently" - you only have to look at several of their Maths pages to know any faith is misplaced. The edits are mostly done by people who have no idea what they're talking about (see the page about 0.(9)=1), who never reference any Maths textbooks, despite many of them being freely available on the Internet Archive. Meanwhile edits by actual Maths professors (such as Rick Norwood) get backed out by the admins 🙄

@rhelune@todon.eu The AI even SAYS the correct thing to do - distribute INSIDE THE BRACKETS - but then fails to do it, same as in several other cases where it says the right thing to do but then fails to do it

@rhelune@todon.eu "I tried, but, although my prefix calculator can evaluate infix expressions, it complains about the lack of the explicit operator" - no, that's an e-calc, programmed by a programmer who has forgotten about the Distributive Law 🙄 https://dotnet.social/@SmartmanApps/110819283738912144 Watch the video in my previously linked thread, and you'll see a Sharp calculator has no issue with it at all. Same goes for my Casio calc. "with actual mathematicians" - no, there's none of them on here, only Gaslighters

@bemmesr@mathstodon.xyz "If so, could you provide an example of such a proof?" - yep, just grab some Cuisenaire Rods and prove it the same way it's proven to young kids

@bemmesr@mathstodon.xyz "I'd suggest you read https://math.berkeley.edu/~wu/order5.pdf as it essentially makes the same argument I'm making" - and is contradicted by Maths textbooks and proofs. 🙄 Note the complete lack of textbook references "perhaps with more clarity and conviction" - #LoudlyNotUnderstandingThings "It's not an uncommon idea" - the idea of Earth being flat used to not be an uncommon idea "this has turned out to be somewhat of a research task" - you could've just read my thread in the first place 🙄

5/x a(b+c) is a single Term

@rhelune@todon.eu "I thought it was about cultural differences" - there aren't any. Maths is universal https://dotnet.social/@SmartmanApps/112019943359120289 "so I asked both Wolfram Alpha and good old GNOME calculator" - both of which give the WRONG answer. 🙄 Pick up a calculator instead https://dotnet.social/@SmartmanApps/111164851485070719

@dpnash@c.im "clearly the correct answer, period" - except some aren't following it correctly, and end up with a wrong answer. "which nicely sidesteps most of the notational ambiguities" - there aren't any ambiguities

@bemmesr@mathstodon.xyz "division operators are just more ambiguous" - division symbols aren't the problem, it's people forgetting what Terms are which is the problem. 1÷ab=1÷(axb), not 1÷axb <== Lennes was infamously making this mistake more than 100 years ago https://dotnet.social/@SmartmanApps/110965810374299599 "Fractions make things much clearer for everyone" - can't be written on one line except by using brackets, (1÷2), in which case you can still use any symbol for the division operator

@TimWardCam@c.im @ColinTheMathmo@mathstodon.xyz @solderandchaos@mastodon.me.uk "Nobody would write "18÷3x2" professionally" - Maths textbook authors do, all the time, as do Maths teachers "put the brackets in" - no brackets needed, just obey the rules of Maths

7/7 So when people say "Cajori said there was no agreement about whether to do 2(4) first or not"...

1. No, he didn't. He was talking about literal multiplication, with a multiply sign

2. he uses a/bc and a/(bc) as equivalent expressions on page 272, as every textbook (then and now) does (except for those using Lennes' made up wrong rule), because that's ALWAYS been the rule, ab=(a X b), as, even before Brackets started being used in Maths, aa was already the notation for a Product

@camwilson@mastodon.social If you ever need evidence to present to someone who is under the illusion that AI answers are factual, here is my (ongoing) thread of AI's horribly wrong Maths answers... https://dotnet.social/@SmartmanApps/116000100388648367

@PetraSchwer@mathstodon.xyz Missing do the exercises, check your answers, for textbooks

@rhelune@todon.eu P.S. "with actual mathematicians" - I'm an actual Maths teacher, hence all the Maths textbooks (and calculators) in my threads

3/x Terms - ab==(axb)

@james@bne.social @camwilson@mastodon.social

@rhelune@todon.eu "This one is correct, though" - no it isn't. "does multiplication have a higher priority than division in the US?" - brackets have priority over everything everywhere https://dotnet.social/@SmartmanApps/110819283738912144

@bemmesr@mathstodon.xyz "so I'll at least give you that there are not *many* textbooks published in the last 150 years which differ on the order of operations" - there aren't ANY which differ on the order of operations "of course we have no reason to believe this to be the case" - we have EVERY reason to believe it's the case - proofs 🙄 "arithmetic is essentially just an axiomatic system" - nope. Literally proven, but feel free to try and find an example of 1+1=3. I'll wait

@shadow53@floss.social I don't think I've saved any links, but there's certainly been several studies in education which show people (students in this case) lose skills/knowledge when they delegate it to AI instead of doing it themselves (think students getting dumber instead of smarter, because AI did their homeworrk/essay)

1/x #MathsMonday I'm coming back to #Mathematics order of operations (hopefully) one last time, just to flesh it out with some more #Maths textbook references, for those who want it (having only initially given one in each case). Not going overboard, just 4 #Math textbook screenshots per post (since Mastodon only allows 4 pics per post, that's a good number to finish it off with). I may come back in future, if some particularly good ones come along, hence unknown post count for now...

@claudius@darmstadt.social @cmconseils@mastodon.social Don't mention 67 round me - some of the kids are STILL going on about it 🙄

7/x Expand Brackets first, until no Brackets remain

@bemmesr@mathstodon.xyz "I just think it's generally an error to use the division symbol instead of a fraction" - It's not being used instead of a fraction. It's being used as an operator - different precedence to a fraction

@rhelune@todon.eu " so I am not going to waste any more time" - using e-calcs is a waste of time. The only one I've ever seen consistently give the right answer is MathGPT.

@bemmesr@mathstodon.xyz P.S. the order of operations rules pre-date the use of brackets in Maths by centuries, hence why they're rock-solid and don't need any brackets

@rhelune@todon.eu P.S. the issues with Wolfram are well-known https://dotnet.social/@SmartmanApps/113304148810366402

@bemmesr@mathstodon.xyz "depends entirely on your definitions" - all of which can be found in Maths textbooks 🙄 "we don't have a global standard for these definitions" - yes we do! In Maths textbooks 😂 "people would still be confused about 1÷ab" - people who aren't using Maths. People on socials getting confused doesn't matter 1 iota "the source of confusion go away" - doesn't make people stop forgetting you mean "their scope is entirely unambiguous" - as are operators, the rule of Left Associativity

2/x The rule of Left Associativity (note: I'll come back and add alt text to them all later - part of the reason for posting these to begin with - put it in once and done)

@bemmesr@mathstodon.xyz "we need to indicate its scope by relying on brackets" - no we don't. Term on the left divided by the term on the right "suggest that we use the form ‘((φ)÷(ψ))’" - and of course, you are suggesting using that with + and - as well, for the exact same reason (equal precedence). Good luck getting ANYONE to agree with you about writing 10 times as many brackets for simple calculations 😂 "the brackets leave no room for confusion" - the RULES OF MATHS already leave no room for confusion 🙄

6/7 Where we can clearly see Cajori using a:(bc) and a:bc as equivalent expressions, which is precisely because bc=(b X c) BY DEFINITION, as already discussed at https://dotnet.social/@SmartmanApps/110846452267056791 This was what Lennes failed to understand - he kept calling Products "Multiplication", even though it's IN BRACKETS, and thus done in the BRACKETS step, as he observed every textbook doing. He said it was an "exception to the rule", whereas in fact it's the ACTUAL rule, ab=(a X b), as per Cajori page 272...