I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
Itâs about a 30min read so thank you in advance if you really take the time to read it, but I think itâs worth it if you joined such discussions in the past, but Iâm probably biased because I wrote it :)
You havenât provided a textbook that has strong juxtaposition
I told you, in my thread - multiple ones. You havenât provided any textbooks at all that have âweak juxtapositionâ. i.e. you keep asking me for more evidence whilst never producing any of your own.
At best I can search the title of the file youâre in that you also happened to screenshot and hope that I find the right text
I didnât âjust happenâ to include the name of the textbook and page number - that was quite deliberate. Not sure why you donât want to believe a screenshot, especially since you canât quote any that have âweak juxtapositionâ in the first place.
BTW I just tried Googling it and it was the first hit. Youâre welcome.
What does matter is that I shouldnât have to go treasure hunting for your sources.
You donât - the screenshots of the relevant pages are right there. Youâre the one choosing not to believe what is there in black and white, in multiple textbooks.
with differing rules
Yeah, I wrote about inconsistency in textbooks here (also includes another textbook saying you have to expand brackets first), but also elsewhere in the thread is an example where they have been consistent throughout. Regardless of when they remove brackets, in every single case they multiply the coefficient over whatâs inside the brackets as the first step (as per BEDMAS, and as per the screenshot in question which literally says you must do it before you remove brackets).
people donât agree
People who arenât high school Maths teachers (the ones who actually teach this topic). Did you notice that neither The Distributive Law nor Terms are mentioned at any point whatsoever? Thatâs like saying âI donât remember what I did at Xmas, so therefore itâs ambiguous whether Xmas ever happened at all, and anyone who says it definitely did is wrongâ.
no such complaint.
So what do you think he is complaining about?
I told you, in my thread - multiple ones. You havenât provided any textbooks at all that have âweak juxtapositionâ. i.e. you keep asking me for more evidence whilst never producing any of your own.
You seem to have missed the point. Iâm holding you to your own standard, as you are the one that used evidence as an excuse for dismissal first without providing evidence for your own position.
I didnât âjust happenâ to include the name of the textbook and page number - that was quite deliberate. Not sure why you donât want to believe a screenshot, especially since you canât quote any that have âweak juxtapositionâ in the first place. BTW I just tried Googling it and it was the first hit. Youâre welcome.
You seem to have missed the point. Youâre providing a bad source and expecting the person youâre arguing against to do legwork. I never said I couldnât find the source. Iâm saying I shouldnât have to go looking.
You donât - the screenshots of the relevant pages are right there. Youâre the one choosing not to believe what is there in black and white, in multiple textbooks.
Youâve provided a single textbook, first of all. Second of all, the argument is that both sides are valid and accepted depending on who you ask, even amongst educated echelons. The fact there exists textbooks that support strong juxtaposition does nothing to that argument.
But you want some evidence, so hereâs an article from someone who writes textbooks speaking on the ambiguity. Again, the ambiguity exists and your claim that it doesnât according to educated professors is unsubstantiated. There are of course professors who support strong juxtaposition, but there are also professors who support weak juxtaposition and professors that merely acknowledge the ambiguity exist. The rules of mathematics you claim are set in stone arenât relevant (and arenât as set in stone as you imagine) but thatâs not entirely relevant. What is relevant is there is an argument and itâs not just uneducated folk mistaking the âtruthâ.
People who arenât high school Maths teachers (the ones who actually teach this topic). Did you notice that neither The Distributive Law nor Terms are mentioned at any point whatsoever? Thatâs like saying âI donât remember what I did at Xmas, so therefore itâs ambiguous whether Xmas ever happened at all, and anyone who says it definitely did is wrongâ.
You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isnât at the high school level.
But wait, thereâs more. Hereâs another source from another mathematics professor. This one âsupportsâ weak juxtaposition but really mostly just points at the ambiguity. Which again, is what Iâm going for, that the ambiguity exists and one side is not immediately justified/âcorrectâ.
So what do you think he is complaining about?
Thatâs a leading question and is completely unhelpful to the discussion. I asked you to point out where exactly, and with what wording, your position is supported in the provided text. Please do that.
without providing evidence for your own position
You know full well itâs all in my thread. Whereâs yours?
Iâm saying I shouldnât have to go looking
You didnât have to go looking - you couldâve just accepted it at face-value like other people do.
Youâve provided a single textbook,
No, multiple textbooks. If you havenât seen the others yet then keep reading. On the other hand you havenât provided any textbooks.
the argument is that both sides are valid and accepted
But theyâre not. The other side is contradicting the rules of Maths. In a Maths test it would be marked as wrong. You canât go into a Maths test and write âthis is ambiguousâ as an answer to a question.
hereâs an article from someone who writes textbooks
Not high school textbooks! Talk about appeal to authority.
Yep, seen it before. Note that he starts out with âIt is not clear what the textbook had intended with the 3yâ. How on Earth can he not know what that means? If he just picked up any old high school Maths textbook, or read Cajori, or read Lennesâ letter, or even just asked a high school teacher(!), he would find that every single Maths textbook means exactly the same thing - ab=(axb). Instead he decided to write a long blog saying âI donât know what this means - it must be ambiguousâ.
Not only that, but he also didnât know how to handle x/x/x, which shows he doesnât remember left associativity either. BTW itâs equal to x/xÂČ (which is equal to 1/x).
the ambiguity exists
âŠamongst people who have forgotten the rules of Maths. The Maths itself is never ambiguous (which is the claim many of them are making - that the Maths expression itself is ambiguous. In fact the article under discussion here makes that exact claim - that itâs written in an ambiguous way. No it isnât! Itâs written in the standard mathematical way, as per what is taught from textbooks). Itâs like saying âIâve forgotten the combination to my safe, and Iâve been unable to work it out, therefore the combination must be ambiguousâ.
You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isnât at the high school level.
Thank you. I just commented to someone else last night, who had noticed the same thing, I am so tired of people quoting University people - this topic is NOT TAUGHT at university! Itâs taught by high school teachers (Iâve taught this topic many times - Iâm tutoring a student in it right now). Paradoxically, the first Youtube I saw to get it correct (in fact still the only one Iâve seen get it correct) was by a gamer! đ He took the algebra approach. i.e. rewrite this as 6/2a where a=1+2 (which Iâve also used before too. In fact I did an algebraic proof of it).
the ambiguity exists and one side is not immediately justified/âcorrectâ
The side which obeys the rules of Maths is correct and the side which disobeys the rules of Maths is incorrect. Thatâs why the rules of Maths exist in the first place - only 1 answer can be correct (âambiguityâ people also keep claiming âboth answers are correctâ. Nope, one is correct and one is wrong).
Thatâs a leading question and is completely unhelpful to the discussion.
Twice I said things about it and you said you didnât believe my interpretation is correct, so I asked you what you think heâs saying. Iâm not going to go round in circles with you just disagreeing with everything I say about it - just say what YOU think he says.
You didnât have to go looking - you couldâve just accepted it at face-value like other people do.
I could also walk off a cliff, doesnât mean I should. Sources are important not just for what they say but how they say it, where they say it, and why they say it.
But theyâre not. The other side is contradicting the rules of Maths. In a Maths test it would be marked as wrong. You canât go into a Maths test and write âthis is ambiguousâ as an answer to a question.
âŠamongst people who have forgotten the rules of Maths. The Maths itself is never ambiguous (which is the claim many of them are making - that the Maths expression itself is ambiguous. In fact the article under discussion here makes that exact claim - that itâs written in an ambiguous way. No it isnât! Itâs written in the standard mathematical way, as per what is taught from textbooks). Itâs like saying âIâve forgotten the combination to my safe, and Iâve been unable to work it out, therefore the combination must be ambiguousâ.
The side which obeys the rules of Maths is correct and the side which disobeys the rules of Maths is incorrect. Thatâs why the rules of Maths exist in the first place - only 1 answer can be correct (âambiguityâ people also keep claiming âboth answers are correctâ. Nope, one is correct and one is wrong).
Yes, that is your claim which you have yet to prove. You keep reiterating your point as if it is established fact, but you havenât established it. Thatâs the whole argument.
Twice I said things about it and you said you didnât believe my interpretation is correct, so I asked you what you think heâs saying. Iâm not going to go round in circles with you just disagreeing with everything I say about it - just say what YOU think he says.
Literally just give me a direct quote. If youâre using it as supporting evidence, tell me how it supports you. If you canât even do that, itâs not supporting evidence. I donât know why you want me to analyze it, youâre the one who presented it as evidence. My analysis is irrelevant.
Thank you. I just commented to someone else last night, who had noticed the same thing, I am so tired of people quoting University people - this topic is NOT TAUGHT at university! Itâs taught by high school teachers (Iâve taught this topic many times - Iâm tutoring a student in it right now). Paradoxically, the first Youtube I saw to get it correct (in fact still the only one Iâve seen get it correct) was by a gamer! đ He took the algebra approach. i.e. rewrite this as 6/2a where a=1+2 (which Iâve also used before too. In fact I did an algebraic proof of it).
I was being sarcastic. If you truly think highschool teachers who require almost no training in comparison to a Phd are more qualified⊠I have no interest in continuing this discussion. Thatâs simply absurd, professors study every part of mathematics (in aggregate), including the âhighschoolâ math, and are far more qualified than any highschool teacher who is not a Phd. This is true of any discipline taught in highschool, a physics professor is much better at understanding and detailing the minutiae of physics than a highschool physics teacher. To say a teacher knows more than someone who has literally spent years of their life studying and expanding the field when all the teacher has to do is teach the same (or similar) curriculum each and every year is⊠insaneâespecially when youâve been holding up math textbooks as the ultimate solution and so, so many of them are written by professors.
I want to point out that your only two sources, both a screenshot of a textbook, (yes, those are your only sources. Youâve given 4, but one Iâve repeatedly asked about and youâve refused to point out a direct quote that provides support for your argument, another I dismissed earlier and I assume you accepted that seeing as you did not respond to that point) does not state the reasoning behind its conclusion. To me thatâs far worse than a professor who at least says why theyâve done something.
Iâve given 3 sources, all of which you dismiss simply because theyâre not highschool textbooks⊠yâknow, textbooks notorious for over-simplifying things and not giving the logic behind the answer. I could probably find some highschool textbooks that support weak juxtaposition if I searched, but again thatâs a waste of money and time. You donât seem keen on acknowledging any sort of ambiguity here and constantly state it goes against the rules of math, without ever providing a source that explains these rules and how they work so as to prove only strong juxtaposition makes sense/works. If youâre really so confident in strong juxtaposition being the only way mathematically, I expect you to have a mathematical proof for why weak juxtaposition would never work, one that has no flaws. Otherwise, at best you have a hypothesis.
