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 :)
What’s especially wild to me is that even the position of “it’s ambiguous” gets almost as much pushback as trying to argue that one of them is universally correct.
Last time this came up it was my position that it was ambiguous and needed clarification and had someone accuse me of taking a prescriptive stance and imposing rules contrary to how things were actually being done. How asking a person what they mean or seeking clarification could possibly be prescriptive is beyond me.
Bonus points, the guy telling me I was being prescriptive was arguing vehemently that implicit multiplication having precedence was correct and to do otherwise was wrong, full stop.
👍 That was actually one of the reasons why I wrote this blog post. I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts.
That probably won’t convince everybody but if that won’t probably nothing will.
And I wrote a bunch of fact checks pointing out there is consensus amongst the actual experts - high school Maths teachers and textbook authors, the 2 groups who you completely ignored in your blog post.
When I went to college, I was given a reverse Polish notation calculator. I think there is some (albeit small) advantage of becoming fluent in both PEMDAS and RPN to see the arbitrariness. This kind of arguement is like trying to argue linguistics in a single language.
Btw, I’m not claiming that RPN has any bearing on the meme at hand. Just that there are different standards.
This comment is left by the HP50g crew.
It would be better if we just taught math with prefix or postfix notation, as it removes the ambiguity.
Ambiguity is fine. It would tedious to the point of distraction to enforce writing math without ambiguity. You make note of conventions and you are meant to realize that is just a convention. I’m amazed at the people who are planting their feet to fight for something that what they were taught in third grade as if the world stopped there.
You’re right though. We should definitely teach different conventions. But then what would facebook do for engagement?
It already is written without ambiguity.
This is actually taught in Year 7 - the people who only remember the 3rd Grade version of the rules are the ones getting it wrong.
There isn’t ambiguity to begin with - just people who have forgotten the rules of Maths.
Without any additional parentheses, the division sign is assumed to separate numerators and denominators within a complete expression, in which case you would reduce each separately. It’s very, very marginally ambiguous at best.
You are correct with your definition - Terms are separated by operators and joined by grouping symbols - and it’s consequently not ambiguous at all (using so-called “weak juxtaposition” breaks that rule).
Assumed by whom? Clearly not everyone.
It’s what is actually taught in high school, so there are those who remember and those who don’t.
That’s because following the rules of Maths is universally correct.
He was using the wrong words, but he was correct - the actual rules are The Distributive Law and Terms (“implicit multiplication” is a rule made up by those who have forgotten these 2 rules).