TI calcs give the wrong answer, and it's in their manual why - they only follow the Primary School rule ("inside the brackets"), not the High School rule which supersedes it (The Distributive Law).

I’d actually say that the weak juxtaposition is just the simple one schools use

Schools don't teach "weak juxtaposition" - they teach the actual rules of Maths! As per what's in Maths textbooks. It's adults who've forgotten the rules who make up the "weak juxtaposition" rule. See Lennes.

No, it doesn't. It never talks about Terms, nor The Distributive Law (which isn't the same thing as the Distributive Property). These are the 2 rules of Maths which make this 100% not ambiguous.

somewhere

You know EXACTLY where I said those things, and you've been avoiding addressing them ever since because you know they prove the point that #MathsIsNeverAmbiguous See ya.

Sources are important not just for what they say but how they say it, where they say it, and why they say it.

None of which you've addressed since I gave you the source. Remember when you said this...

you can’t identify authors, you can’t check for bias

So, did you do that once I gave you the link? And/or are you maybe going to address "what they say but how they say it, where they say it, and why they say it" in regards to the link I gave you?

You keep reiterating your point as if it is established fact,

What they teach in Maths textbooks aren't facts? Do go on. 😂

tell me how it supports you

I did, and you've apparently refused to read the relevant part.

in comparison to a Phd

You know not all university lecturers do a Ph.D. right? In which case they haven't done any more study at all. But I know you really wanna hang on to this "appeal to authority" argument, since it's all you've got.

I have no interest in continuing this discussion

Yeah I saw that coming once I gave you the link to the textbook.

including the ‘highschool’ math

...when they were in high school.

teach the same (or similar) curriculum each and every year

There you go. Welcome to why high school teachers are the expert in this field.

math textbooks as the ultimate solution and so, so many of them are written by professors

So wait, NOW you're saying textbooks ARE valid in what they say? 😂

I want to point out that your only two sources

All that points out is that you didn't even read THIS thread properly, never mind the other one. Which two are they BTW? And I'll point out which ones you've missed.

I assume you accepted that seeing as you did not respond to that point

Well, I'll use your own logic then to take that as a concession, given how many of my points you didn't respond to (like the textbook that I gave you the link to, and the Cajori ab=(ab) one, etc.).

I’ve given 3 sources,

3 articles you mean.

all of which you dismiss simply because

...all of them have forgotten about The Distributive Law and Terms., which make the expression totally unambiguous. Perhaps you'd like to find an article that DOES talk about those and ALSO asserts that the expression is "ambiguous"? 😂 Spoiler alert: every article, as soon as I see the word "ambiguous" I search the text for "distributive" and "expand" and "terms" - can you guess what I find? 😂 Hint: Venn diagram with little or no overlap.

I could probably find some highschool textbooks that support weak juxtaposition if I searched,

Do you wanna bet on that? 😂

without ever providing a source that explains these rules

They're in my thread, if you'd bothered to read any further. By your own standards, 😂I'll take it that you concede all of my points that you haven't responded to.

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

You know some things are true by definition, right, and therefore don't have a proof? 1+1=2 is the classic example. Or do you challenge that too?

So do YOU have a hypothesis then? How "weak juxtaposition" could EVER work given "strong juxtaposition" is the only type ever used in any of the rules of Maths? I'll wait for your proof...

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?

Ok so you’re saying it never happened, but then in the very next sentence you acknowledge that you know it is happening with TI today

You asked me what I do if my students show me 2 different answers what do I tell them, and I told you that has never happened. None of my students have ever had one of the calculators which does it wrong.

that both behaviors are intentional and documented

Correct. I already noted earlier (maybe with someone else) that the TI calculator manual says that they obey the Primary School order of operations, which doesn't work with High School order of operations. i.e. when the brackets have a coefficient. The TI calculator will give a correct answer for 6/(1+2) and 6/2x(1+2), but gives a wrong answer for 6/2(1+2), and it's in their manual why. I saw one Youtuber who was showing the manual scroll right past it! It was right there on screen why it does it wrong and she just scrolled down from there without even looking at it!

none of these calculators is “wrong”.

Any calculator which fails to obey The Distributive Law is wrong. It is disobeying a rule of Maths.

there is no ambiguity where there actually is.

There actually isn't. We use decimal points (not commas like some European countries), the obelus (not colon like some European countries), etc., so no, there is never any ambiguity. And the expression in question here follows those same notations (it has an obelus, not a colon), so still no ambiguity.

i recommend reading this one instead: The PEMDAS Paradox

Yes, I've read that one before. Makes the exact same mistakes. Claims it's ambiguous while at the same time completely ignoring The Distributive Law and Terms. I'll even point out a specific thing (of many) where they miss the point...

So the disagreement distills down to this: Does it feel like a(b) should always be interchangeable with axb? Or does it feel like a(b) should always be interchangeable with (ab)? You can't say both.

ab=(axb) by definition. It's in Cajori, it's in today's Maths textbooks. So a(b) isn't interchangeable with axb, it's only interchangeable with (axb) (or (ab) or ab). That's one of the most common mistakes I see. You can't remove brackets if there's still more than 1 term left inside, but many people do and end up with a wrong answer.

By “we” do you mean high school teachers, or Australian society beyond high school?

I said "In Australia" (not in Australian high school), so I mean all of Australia.

Because, I’m pretty sure the latter isn’t true

Definitely is. I have never seen anyone here ever use a colon to mean divide. It's only ever used for a ratio.

Do you have textbooks where the fraction bar is used concurrently with the obelus (÷) division symbol?

All my textbooks use both. Did you read my thread? If you use a fraction bar then that is a single term. If you use an obelus (or colon if you're in a country which uses colon for division) then that is 2 terms. I covered all of that in my thread.

EDITED TO ADD: If you don't use both then how do you write to divide by a fraction?

I have never encountered strong juxtaposition

There's "strong juxtaposition" in both Terms and The Distributive Law - you've never encountered either of those?

Noted that you were unable to tell me what The Distributive Law relates to (given your claim it's not brackets).

did you stop after realizing that it was saying something you found disagreeable

I stopped when he said it was ambiguous (it's not, as per the rules of Maths), then scanned the rest to see if there were any Maths textbook references, and there wasn't (as expected). Just another wrong blog.

What will you tell your students if they show you two different models of calculator, from the same company

Has literally never happened. Texas Instruments is the only brand who continues to do it wrong (and it's right there in their manual why) - all the other brands who were doing it wrong have reverted back to doing it correctly (there's a Youtube video about this somewhere). I have a Sharp calculator (who have literally always done it correctly) and most of my students have Casio, so it's never been an issue.

trust me on this

I don't ask them to trust me - I'm a Maths teacher, I teach them the rules of Maths. From there they can see for themselves which calculators are wrong and why. Our job as teachers is for our students to eventually not need us anymore and work things out for themselves.

The truth is that there are many different math notations which often do lead to ambiguities

Not within any region there isn't. e.g. European countries who use a comma instead of a decimal point. If you're in one of those countries it's a comma, if you're not then it's a decimal point.

people don’t often encounter the obelus notation for division at all

In Australia it's the only thing we ever use, and from what I've seen also the U.K. (every U.K. textbook I've seen uses it).

Check out some of the other things which the “÷” symbol can mean in math!

Go back and read it again and you'll see all of those examples are worded in the past tense, except for ISO, and all ISO has said is "don't use it", for reasons which haven't been specified, and in any case everyone in a Maths-related position is clearly ignoring them anyway (as you would. I've seen them over-reach in Computer Science as well, where they also get ignored by people in the industry).

"The obelus is treated differently,” Church said. "It could mean ratios, division or numerator and denominator, and these all tweak the meaning of the symbol.”

This is the only symbols I've ever seen used (but feel free to provide a reference if you know of any where it isn't - the article hasn't provided any references)...

Ratio is only ever colon.

Division is obelus (textbooks/computers) or slash (computers, though if it's text you can use a Unicode obelus).

Fraction is fraction bar (textbooks) or obelus/slash inside brackets (computers). i.e. (a/b).

The first step in order of operations is solve brackets. The first step in solving unexpanded brackets is to expand them. i.e. The Distributive Law. i.e. the ONLY time The Distributive Law ISN'T part of order of operations is when there's no unexpanded brackets in the expression.