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.
It’s about a 30min read so thank you in advance if you really take the time to read it, but I think it’s worth it if you joined such discussions in the past, but I’m probably biased because I wrote it :)
So you think it’s ok to teach contradictory stuff to them in Maths? 🤣 Ok sure, fine, go ahead and find me a Maths textbook which has “weak juxtaposition” in it. I’ll wait.
You haven’t provided a textbook that has strong juxtaposition.
So you’re telling me you can’t see the Maths textbook screenshots/photo’s?
That’s not a source, that’s a screenshot. You can’t look up the screenshot, you can’t identify authors, you can’t check for bias. At best I can search the title of the file you’re in that you also happened to screenshot and hope that I find the right text. The fact that you think this is somehow sufficient makes me question your claims of an academic background, but that’s neither here nor there. What does matter is that I shouldn’t have to go treasure hunting for your sources.
And, to blatantly examine the photo, this specific text appears to be signifying brackets as their own syntactic item with differing rules. However, I want to note that the whole issue is that people don’t agree so you will find cases on both sides, textbook or no.
Lennes was complaining that literally no textbooks he mentioned were following “weak juxtaposition”, and you think that’s not relevant to establishing that no textbooks used “weak juxtaposition” 100 years ago?
You are welcome to cite the specific wording he uses to state this. As far as I can tell, at least in the excerpt linked, there is no such complaint.
You haven’t provided a textbook that has strong juxtaposition
I told you, in my thread - multiple ones. You haven’t provided any textbooks at all that have “weak juxtaposition”. 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 you’re in that you also happened to screenshot and hope that I find the right text
I didn’t “just happen” to include the name of the textbook and page number - that was quite deliberate. Not sure why you don’t want to believe a screenshot, especially since you can’t quote any that have “weak juxtaposition” in the first place.
BTW I just tried Googling it and it was the first hit. You’re welcome.
What does matter is that I shouldn’t have to go treasure hunting for your sources.
You don’t - the screenshots of the relevant pages are right there. You’re 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 what’s 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 don’t agree
People who aren’t 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? That’s like saying “I don’t remember what I did at Xmas, so therefore it’s ambiguous whether Xmas ever happened at all, and anyone who says it definitely did is wrong”.
no such complaint.
So what do you think he is complaining about?
I told you, in my thread - multiple ones. You haven’t provided any textbooks at all that have “weak juxtaposition”. i.e. you keep asking me for more evidence whilst never producing any of your own.
You seem to have missed the point. I’m 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 didn’t “just happen” to include the name of the textbook and page number - that was quite deliberate. Not sure why you don’t want to believe a screenshot, especially since you can’t quote any that have “weak juxtaposition” in the first place. BTW I just tried Googling it and it was the first hit. You’re welcome.
You seem to have missed the point. You’re providing a bad source and expecting the person you’re arguing against to do legwork. I never said I couldn’t find the source. I’m saying I shouldn’t have to go looking.
You don’t - the screenshots of the relevant pages are right there. You’re the one choosing not to believe what is there in black and white, in multiple textbooks.
You’ve 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 here’s an article from someone who writes textbooks speaking on the ambiguity. Again, the ambiguity exists and your claim that it doesn’t 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 aren’t relevant (and aren’t as set in stone as you imagine) but that’s not entirely relevant. What is relevant is there is an argument and it’s not just uneducated folk mistaking the ‘truth’.
People who aren’t 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? That’s like saying “I don’t remember what I did at Xmas, so therefore it’s ambiguous whether Xmas ever happened at all, and anyone who says it definitely did is wrong”.
You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isn’t at the high school level.
But wait, there’s more. Here’s another source from another mathematics professor. This one ‘supports’ weak juxtaposition but really mostly just points at the ambiguity. Which again, is what I’m going for, that the ambiguity exists and one side is not immediately justified/‘correct’.
So what do you think he is complaining about?
That’s 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 it’s all in my thread. Where’s yours?
I’m saying I shouldn’t have to go looking
You didn’t have to go looking - you could’ve just accepted it at face-value like other people do.
You’ve provided a single textbook,
No, multiple textbooks. If you haven’t seen the others yet then keep reading. On the other hand you haven’t provided any textbooks.
the argument is that both sides are valid and accepted
But they’re not. The other side is contradicting the rules of Maths. In a Maths test it would be marked as wrong. You can’t go into a Maths test and write “this is ambiguous” as an answer to a question.
here’s 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 “It is not clear what the textbook had intended with the 3y”. 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 Lennes’ 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 “I don’t know what this means - it must be ambiguous”.
Not only that, but he also didn’t know how to handle x/x/x, which shows he doesn’t remember left associativity either. BTW it’s equal to x/x² (which is equal to 1/x).
the ambiguity exists
…amongst 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 it’s written in an ambiguous way. No it isn’t! It’s written in the standard mathematical way, as per what is taught from textbooks). It’s like saying “I’ve forgotten the combination to my safe, and I’ve been unable to work it out, therefore the combination must be ambiguous”.
You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isn’t 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! It’s taught by high school teachers (I’ve taught this topic many times - I’m tutoring a student in it right now). Paradoxically, the first Youtube I saw to get it correct (in fact still the only one I’ve seen get it correct) was by a gamer! 😂 He took the algebra approach. i.e. rewrite this as 6/2a where a=1+2 (which I’ve also used before too. In fact I did an algebraic proof of it).
the ambiguity exists and one side is not immediately justified/‘correct’
The side which obeys the rules of Maths is correct and the side which disobeys the rules of Maths is incorrect. That’s why the rules of Maths exist in the first place - only 1 answer can be correct (“ambiguity” people also keep claiming “both answers are correct”. Nope, one is correct and one is wrong).
That’s a leading question and is completely unhelpful to the discussion.
Twice I said things about it and you said you didn’t believe my interpretation is correct, so I asked you what you think he’s saying. I’m not going to go round in circles with you just disagreeing with everything I say about it - just say what YOU think he says.
