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 :)
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.
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!
Any calculator which fails to obey The Distributive Law is wrong. It is disobeying a rule of Maths.
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.
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...
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.
I said "In Australia" (not in Australian high school), so I mean all of Australia.
Definitely is. I have never seen anyone here ever use a colon to mean divide. It's only ever used for a ratio.
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?