If it helps, I saw what you did there, and I exhaled slightly harder out of my nose while smiling wryly. It’s even better the op didn’t get it. So like, well done and stuff 😊
The other choices are people that wanted to awnser ten but could not because it wasn’t a choice. So they took a random number or the one closest to ten
Your obviously is only a convention and not everyone agree with that. Not even all peogramming languages or calculators.
If you wanted obviously, it would have to have different order or parentheses or both. Of course everything in math is convention but I mean more obvious.
2+2*4 is obvious with PEDMAS, but hardy obvious to common people
2+(2*4) is more obvious to common people
2*4+2 is even more obvious to people not good with math. I would say this is the preferred form.
(2*4)+2 doesn’t really add more to it, it just emphasises it more, but unnecessarily.
it would have to have different order or parentheses or both.
Neither. Multiplication is always before Addition, hence “obviously”
Of course everything in math is convention
Nope. The vast majority of it is proven rules
2+(2*4) is more obvious to common people
Weird then how many people were able to get this right without brackets for centuries before we started using brackets in Maths (which we’ve only had for 300 years)
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.
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.
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.
“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.
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.
I feel like people should at least remember math at a 4th grade level and be able to get 10. What is the point of making it obvious the universe will never ever arrange itself in such a fashion. The point is if you remember simple rules you applied for a 10-15 years.
You’ve completely not understood that order of operations is an arbitrary convention. How did you decide to expand the definition of multiplication before evaluating the addition? Convention.
You can’t write 2 + 2 ÷ 2 like this, so how are you gonna decide whether to decide to divide or add first?
How are you gonna write 2 + 2 ÷ 2 with repeated addition?
The definition of Multiplication as being repeated addition
That doesn’t mean it has to be expanded first. You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2) and you are unable to tell me what mathematical law prohibits it.
If this were a universal law, reverse polish notation wouldn’t work as it does. In RPL, 2 2 + 3 × is 12 but 2 3 × 2 + is 8. If you had to expand multiplication first, how would it work? The same can be done with prefix notation, and the same can be done with “pre-school” order of operations.
Different programming languages have different orders of operations, and those languages work just fine.
Your argument amounts to saying that it makes the most sense to do multiplication before addition. Which is true, but that only gives you a convention, not a rule.
PEMDAS isn’t obvious to “common people”? Why not? It doesn’t seem like an arbitrary convention to me…
If “×” means “groups of,” then “2+2×4” means “two plus two groups of four” which only makes sense, to me, to be read as “two plus two groups of four” rather than “two plus two groups of four”
Sure the order of operations could be arbitrarily different, but I feel like we settled on that order because it simply makes more sense intuitively.
I’m aware of the possibility that it only feels natural and intuitive to me because I was taught that way, but I at least don’t think that applies to this specific example
It didn’t occur to me that the poll may function that way. Does it? I thought this was engagement bait in which the poll’s author lists only wrong answers as options
I mean, obviously ten.
But I at least understand 16.
I deeply worry about the percentage just next to the other three numbers.
13 is probably the next most chosen because it’s closest to 10.
Not including the correct answer is also a form of engagement bait to get additional comments and such saying “wait the real answer is 10, wtf?”
Why worry? You can see them on the right side of the image
It not even remotely possible to make an odd number out of that.
The numbers on the right-hand side are what I’m actually working about.
I was trying yo make a shitty joke conflating you worrying (having concern) with you worrrying (wondering what).
sorry about that, completely wooshed me
Saul Goodman
If it helps, I saw what you did there, and I exhaled slightly harder out of my nose while smiling wryly. It’s even better the op didn’t get it. So like, well done and stuff 😊
The other choices are people that wanted to awnser ten but could not because it wasn’t a choice. So they took a random number or the one closest to ten
Why worry about obviously fake bullshit?
Your obviously is only a convention and not everyone agree with that. Not even all peogramming languages or calculators.
If you wanted obviously, it would have to have different order or parentheses or both. Of course everything in math is convention but I mean more obvious.
2+2*4 is obvious with PEDMAS, but hardy obvious to common people
2+(2*4) is more obvious to common people
2*4+2 is even more obvious to people not good with math. I would say this is the preferred form.
(2*4)+2 doesn’t really add more to it, it just emphasises it more, but unnecessarily.
Nope. Rules of Maths
Neither. Multiplication is always before Addition, hence “obviously”
Nope. The vast majority of it is proven rules
Weird then how many people were able to get this right without brackets for centuries before we started using brackets in Maths (which we’ve only had for 300 years)
Tell that obvious to over half the population who get this wrong
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.
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.
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.
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.
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.
I learned BEDMAS. Doesn’t really change your comment other than effectively “spelling” of a single term
I feel like people should at least remember math at a 4th grade level and be able to get 10. What is the point of making it obvious the universe will never ever arrange itself in such a fashion. The point is if you remember simple rules you applied for a 10-15 years.
common people who are not good at math…
PEMDAS is in the 5th-grade curriculum.
My obviously is gated to people who can hadle 5th-grade math.
I would say we should not provide the mathematically illiterate any say in the matter. They need to spend 10 minutes on Youtube and learn it.
Try RPN for a whole different beast
I am familiar with RPN. At least RPN is always unambiguous
There’s just 5 lots of 2. If it’s hard then think of x being just a bunch of + smooshed together. So
2 + 2 x 4
expands to
2 + 2 + 2 + 2 + 2
or contracts to
5 x 2
You’ve completely not understood that order of operations is an arbitrary convention. How did you decide to expand the definition of multiplication before evaluating the addition? Convention.
You can’t write 2 + 2 ÷ 2 like this, so how are you gonna decide whether to decide to divide or add first?
No, you’ve completely not understood that they are universal rules of Maths
The definition of Multiplication as being repeated addition
Yes you can
The rules of Maths, which says Division must be before Addition
How are you gonna write 2 + 2 ÷ 2 with repeated addition?
That doesn’t mean it has to be expanded first. You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2) and you are unable to tell me what mathematical law prohibits it.
If this were a universal law, reverse polish notation wouldn’t work as it does. In RPL, 2 2 + 3 × is 12 but 2 3 × 2 + is 8. If you had to expand multiplication first, how would it work? The same can be done with prefix notation, and the same can be done with “pre-school” order of operations.
Different programming languages have different orders of operations, and those languages work just fine.
Your argument amounts to saying that it makes the most sense to do multiplication before addition. Which is true, but that only gives you a convention, not a rule.
PEMDAS isn’t obvious to “common people”? Why not? It doesn’t seem like an arbitrary convention to me…
If “×” means “groups of,” then “2+2×4” means “two plus two groups of four” which only makes sense, to me, to be read as “two plus two groups of four” rather than “two plus two groups of four”
Sure the order of operations could be arbitrarily different, but I feel like we settled on that order because it simply makes more sense intuitively.
I’m aware of the possibility that it only feels natural and intuitive to me because I was taught that way, but I at least don’t think that applies to this specific example
Everyone is taught the rules of Maths
It means repeated addition actually
No, it means 2+2+2+2+2
No they can’t
It’s because Multiplication is defined as repeated addition, so if you don’t do it before addition you get wrong answers
Clearly not if most of these answers are incorrect. If it was obvious, there wouldn’t be as many answers as there are.
It didn’t occur to me that the poll may function that way. Does it? I thought this was engagement bait in which the poll’s author lists only wrong answers as options