Honestly that’s my pet peeve about this category of content. Over the years I’ve seen (at least) hundreds of these check-out-how-bad-at-math-everyone-is posts and it’s nearly always order of operations related. Apparently, a bunch of people forgot (or just never learned) PEMDAS.
Now, having an agreed-upon convention absolutely matters for arriving at expected computational outcomes, but we call it a convention for a reason: it’s not a “correct” vs “incorrect” principle of mathematics. It’s just a rule we agreed upon to allow consistent results.
So any good math educator will be clear on this. If you know the PEMDAS convention already, that’s good, since it’s by far the most common today. But if you don’t yet, don’t worry. It doesn’t mean you’re too dumb to math. With a bit of practice, you won’t even have to remember the acronym.
Most actual math people never have to think about pemdas here because no one would ever write a problem like this. The trick here is “when was the last time I saw an X to mean multiplication” so I would already be off about it
1 + 1/2 in my brain is clearly 1.5, but 1+1÷2 doesn’t even register in my brain properly.
Right, and that clue IMO unravels the more troubling aspect of why this content spreads so quickly:
It’s deliberately aimed at people with a rudimentary math education who can be made to feel far superior to others who, in spite of having roughly the same level of proficiency, are missing/forgetting a single fact that has a disproportionate effect on the result they expect.
That is, it’s blue-dress-level contentious engagement bait for anyone with low math skills, whether or not they remember PEMDAS.
“No one” in this context meant “no one who actually does maths professionally.”
In a Maths textbook
Right, and I have decades of maths experience outside of textbooks. So it’s probably been 20 years since I had a meaningful interaction with the × multiplication symbol.
You don’t know that the obelus means divide??
I clearly know what the symbol means, I demonstrated a use of it. But again, haven’t had a meaningful interaction with the symbol in 20 years, and yet I deal with / for division daily.
When I see 1+½ i can instantly say “one and a half”, but when I see 1 + 1 ÷ 2 i actually have to pause for a moment to think about order of operations. Same with 1+2x vs 1 + 2 × x … one I recognize the structure of the problem immediately, and one feels foreign.
The point is that people who do maths for a living, and are probably above average in maths, tend to write things differently than people who are stopped their maths education in high school (or lower), and these types of memes are designed around making people who know high school maths feel smart. People who actually know maths don’t need memes to justify being better at maths than the rest of the public.
I’m not sure what motivates you to so generously offer your various dyadic tokens of knowledge on this subject without qualification while ignoring my larger point, but will assume in good faith that your thirst for knowledge rivals that of your devotion to The Rules.
First, a question: what are conventions if not agreed upon rules? Second, here is a history of how we actually came to agree upon the aforementioned rules which you may find interesting:
I’m a Maths teacher with a Masters - thanks for asking - how about you?
while ignoring my larger point
You mean your invalid point, that I debunked?
what are conventions if not agreed upon rules?
Conventions are optional, rules aren’t.
here is a history of how we actually came to agree upon the aforementioned rules which you may find interesting
He’s well-known to be wrong about his “history”, and if you read through the comments you’ll find plenty of people telling him that, including references. Cajori wrote the definitive books about the history of Maths (notation). They’re available for free on the Internet Archive - no need to believe some random crank and his blog.
By qualification I meant explanation. My doctorate is irrelevant to the truth.
Since you asked, my larger point was about the unhelpful nature of this content, which makes students of math feel inordinately inferior or superior hinged entirely on a single point of familiarity. I don’t handle early math education, but many of my students arrive with baggage from it that hinders their progress, leading me to suspect that early math education sometimes discourages students unnecessarily. In particular, these gotcha-style math memes IMO deepen students’ belief that they’re just bad at math. Hence my dislike of them.
Re: Dave Peterson, I’ll need to read more about this debate regarding the history of notation and I’ll search for the “proven rules” you mentioned (proofs mean something very specific to me and I can’t yet imagine what that looks like WRT order of operations).
If what riled you up was my use of the word “conventions” I can use another, but note that conventions aren’t necessarily “optional” when being understood is essential. Where one places a comma in writing can radically change the meaning of a sentence, for example. My greater point however has nothing to do with that. Here I am only concerned about the next generation of maths student and how viral content like this can discourage them unnecessarily.
It sure is. I’ve seen a PhD who didn’t read the only textbook he had referenced in his thesis, which proved his idea that teachers were doing it wrong and he wasn’t, was wrong. 😂 Should’ve listened to the people who teach it (or actually read the textbook he referenced 🙄 ).
which makes students of math feel inordinately inferior
They don’t. All students get this correct. It’s only adults who have forgotten the rules that get it wrong.
these gotcha-style math memes IMO deepen students’ belief that they’re just bad at math
Nope. Students never get these wrong.
proofs mean something very specific to me and I can’t yet imagine what that looks like WRT order of operations
All you have to do is see which way gives wrong answers for 2+3x4 and you’ve proven which ways don’t work 😂
note that conventions aren’t necessarily “optional”
Yes they are.
when being understood is essential
You don’t understand how to do 2+3x4-5 without knowing which conventions people use for the order of the plus and minus?
Here I am only concerned about the next generation of maths student and how viral content like this can discourage them unnecessarily
Honestly that’s my pet peeve about this category of content. Over the years I’ve seen (at least) hundreds of these check-out-how-bad-at-math-everyone-is posts and it’s nearly always order of operations related. Apparently, a bunch of people forgot (or just never learned) PEMDAS.
Now, having an agreed-upon convention absolutely matters for arriving at expected computational outcomes, but we call it a convention for a reason: it’s not a “correct” vs “incorrect” principle of mathematics. It’s just a rule we agreed upon to allow consistent results.
So any good math educator will be clear on this. If you know the PEMDAS convention already, that’s good, since it’s by far the most common today. But if you don’t yet, don’t worry. It doesn’t mean you’re too dumb to math. With a bit of practice, you won’t even have to remember the acronym.
Most actual math people never have to think about pemdas here because no one would ever write a problem like this. The trick here is “when was the last time I saw an X to mean multiplication” so I would already be off about it
1 + 1/2 in my brain is clearly 1.5, but 1+1÷2 doesn’t even register in my brain properly.
Right, and that clue IMO unravels the more troubling aspect of why this content spreads so quickly:
It’s deliberately aimed at people with a rudimentary math education who can be made to feel far superior to others who, in spite of having roughly the same level of proficiency, are missing/forgetting a single fact that has a disproportionate effect on the result they expect.
That is, it’s blue-dress-level contentious engagement bait for anyone with low math skills, whether or not they remember PEMDAS.
Blue-dress-level?
Old internet thing. Hotly debated at the time.
https://en.wikipedia.org/wiki/The_dress
I’ll add the contextual link above for others, since it’s been awhile.
And yet Maths textbooks do! 😂
In a Maths textbook
You don’t know that the obelus means divide??
“No one” in this context meant “no one who actually does maths professionally.”
Right, and I have decades of maths experience outside of textbooks. So it’s probably been 20 years since I had a meaningful interaction with the × multiplication symbol.
I clearly know what the symbol means, I demonstrated a use of it. But again, haven’t had a meaningful interaction with the symbol in 20 years, and yet I deal with
/for division daily.When I see
1+½i can instantly say “one and a half”, but when I see1 + 1 ÷ 2i actually have to pause for a moment to think about order of operations. Same with1+2xvs1 + 2 × x… one I recognize the structure of the problem immediately, and one feels foreign.The point is that people who do maths for a living, and are probably above average in maths, tend to write things differently than people who are stopped their maths education in high school (or lower), and these types of memes are designed around making people who know high school maths feel smart. People who actually know maths don’t need memes to justify being better at maths than the rest of the public.
No it doesn’t. Everyone who does Maths professionally does it the same way as in Maths textbooks 🙄
And that would be wrong. It’s 1 plus one half. 1½ is one and a half.
You don’t know to Divide before Adding??
Says person with “decades of maths experience outside of textbooks” 🙄
That would be me
Nope. We all write it the same way as we were taught, even those who have done Maths at University (also me).
No, they’re designed around getting those who have forgotten the rules to argue about it. i.e. engagement bait
I learned BEDMAS. Doesn’t really change your comment other than effectively “spelling” of a single term
Proven rules actually
No we don’t - the order of operations rules
The rules most definitely are
proven rules which are true whether you agree to it or not! 😂
Yep
No it isn’t.
As long as you know the rules then that’s all that matters
Dear Mr Rules,
I’m not sure what motivates you to so generously offer your various dyadic tokens of knowledge on this subject without qualification while ignoring my larger point, but will assume in good faith that your thirst for knowledge rivals that of your devotion to The Rules.
First, a question: what are conventions if not agreed upon rules? Second, here is a history of how we actually came to agree upon the aforementioned rules which you may find interesting:
https://www.themathdoctors.org/order-of-operations-historical-caveats/
Happy ruling to you.
I’m a Maths teacher with a Masters - thanks for asking - how about you?
You mean your invalid point, that I debunked?
Conventions are optional, rules aren’t.
He’s well-known to be wrong about his “history”, and if you read through the comments you’ll find plenty of people telling him that, including references. Cajori wrote the definitive books about the history of Maths (notation). They’re available for free on the Internet Archive - no need to believe some random crank and his blog.
Dear colleague,
By qualification I meant explanation. My doctorate is irrelevant to the truth.
Since you asked, my larger point was about the unhelpful nature of this content, which makes students of math feel inordinately inferior or superior hinged entirely on a single point of familiarity. I don’t handle early math education, but many of my students arrive with baggage from it that hinders their progress, leading me to suspect that early math education sometimes discourages students unnecessarily. In particular, these gotcha-style math memes IMO deepen students’ belief that they’re just bad at math. Hence my dislike of them.
Re: Dave Peterson, I’ll need to read more about this debate regarding the history of notation and I’ll search for the “proven rules” you mentioned (proofs mean something very specific to me and I can’t yet imagine what that looks like WRT order of operations).
If what riled you up was my use of the word “conventions” I can use another, but note that conventions aren’t necessarily “optional” when being understood is essential. Where one places a comma in writing can radically change the meaning of a sentence, for example. My greater point however has nothing to do with that. Here I am only concerned about the next generation of maths student and how viral content like this can discourage them unnecessarily.
It sure is. I’ve seen a PhD who didn’t read the only textbook he had referenced in his thesis, which proved his idea that teachers were doing it wrong and he wasn’t, was wrong. 😂 Should’ve listened to the people who teach it (or actually read the textbook he referenced 🙄 ).
They don’t. All students get this correct. It’s only adults who have forgotten the rules that get it wrong.
Nope. Students never get these wrong.
All you have to do is see which way gives wrong answers for 2+3x4 and you’ve proven which ways don’t work 😂
Yes they are.
You don’t understand how to do 2+3x4-5 without knowing which conventions people use for the order of the plus and minus?
It doesn’t. None of them get it wrong. 🙄