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 :)
I’m not sure if I’d call it the “scientific” one. I’d actually say that the weak juxtaposition is just the simple one schools use because they don’t want to confuse everyone. Scientist actually use both and make sure to prevent ambiguity. IMHO the main takeaway is that there is no consensus and one has to be careful to not write ambiguous expressions.
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.
I mean the blog post says
“If you are a student at university, a scientist, engineer, or mathematician you should really try to ask the original author what they meant because strong juxtaposition is pretty common in academic circles, especially if variables are involved like in $a/bc$ instead of numbers.”
It doesn’t say scientific but…
I’m a scientist and I’ve only ever encountered strong juxtaposition in quick scribbles where everyone knows the equation already. Normally we’re very careful to use fraction notation (or parentheses) when there’s any possibility of ambiguity. I read the equation and was shocked that anyone would get an answer other than 9.
As a Maths teacher, I’m shocked whenever anyone ever gets an answer other than 1. I’m not sure how you came up with 9 when you previously said you’ve only ever seen strong juxtaposition? You can only get 9 with so-called “weak juxtaposition” (which is wrong).
My comment was directed to the blog post and the claims contained in it.
The blog post claims it is popular in academy, if that is a deserved label, then I don’t understand how the author of the post lands on “there is no good or bad way, they are all valid”. I am in favor of strong juxtaposition but that is not the case that I am making here. Sorry for the confusion.
The blog post also completely ignores what is actually taught in high school - as found in Year 7-8 Maths textbooks - which indicates how much credibility you should attach to the blog post - none.
So I shouldn’t use text written by the author to understand the pov of the author and critic his pov because it is “only” a blog post, noted.
Not sure how you came up with that conclusion. I never said anything about it being “just a blog post”.
You said…
And I’m pointing out he arrived at that by ignoring what’s taught in high school, which is where it’s taught (not in academia). It’s like saying “It’s ambiguous if there’s such a thing as rain” if you present weather evidence which has omitted every single rainy day that has happened. i.e. cherry-picking. Every single blog which says it’s ambiguous has done the exact same thing. You can find what actually is taught in high school here
I am sorry, misunderstanding on my end. It read to me as if you were expressing that I shouldn’t be using the blog as source. I had a huge jet lag, idk maybe there is the reason. My bad sorry
That’s cool. I’m not sure what you mean about not using it as a source though, because that was also my point! If you want sources for how this should actually be done (and what actually is taught at school), then see my thread - contains actual textbook references (where there’s a screenshot of a textbook, the place it’s come from is in the top-left of the screenshot), actual historical documents (Lennes and Cajori), worked examples, proofs, etc. You said you believe in “strong juxtaposition”, so we’re kinda in agreement - I’m just pointing out that the actual rules are Terms and The Distributive Law (i.e. 2 different rules have been lumped together as one under the “strong juxtaposition” banner), neither of which is discussed anywhere in the blog (and when I, and others, have pointed this out, the OP has ignored us and downvoted our comments). I also made 5 fact check posts rebutting the false/misleading claims made in the blog - just sort the comments here by “new” and you’ll see them (no prizes for guessing who downvoted them).
In other words, I wasn’t saying “don’t pay attention to any blog posts” (which I think is what you thought I meant?), I was saying “don’t pay attention to this blog post” (for multiple reasons that I’ve posted in many places in here).