The Order of Operations is Wrong... Morally Wrong

...but the order of operations is for elementary schoolers...

No one said there'd be math.

The video irritated me. I agree he is setting up a strawman--that is not how I learned order of operations. And I went to public school!

Liosse de Velishaf said:

I think that the host is creating a straw-man, and that the amount of wrong he is is detrimental to his broader point.

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Isn't he even wrong about the order of operations itself? Last time I took a class, the order of operations went addition and subtraction left to right while he's mistaking it as addition before subtraction and completely missing the left to right part and that's what he's using as the basis of his "this might give you the wrong answer argument." Yes, you might get the wrong answer if you do it wrong. The rest of his argument is just as silly.

Okay wow this is making me irrationally angry.

You don't need to pair anything up with parnetheses, that's a complete waste of time. You need to realize that operations come in pairs, +-, */ etc. With this understood you can convert everything into one form and see clearly what's going on that way and do everything in the right order. Who the fuck would write 6/3/3? That doesn't make any sense unless it's some kind of date or something.

Also, if your math education ended with PEMDAS and no further understanding of how operations worked, then chances are you don't like math much anyway and appreciate a helpful algorithm so you don't have to think too hard about something you don't like.

Maths has always left me utterly confused.

This video has left me utterly confused.

I need more coffee.

This sort of thing makes my brain hurt.

That's exactly how I was taught in elementary school, and even later on, to a degree. It's also how my kids were taught. If he's talking about how schools teach, and have taught for a lot of years, in my state, he's exactly right.

For the most part, I had to discover distribution on my own, and I'm glad I did because the distributive property of math is what makes it easy to do algebra in your head.

I don't know. The way he explains both PEMDAS and his "alternative" left me completely lost. And if I'm completely lost, that makes me kind of concerned for everyone else...

PEMDAS? What's that? I grew up with BEDMAS.

Liosse de Velishaf said:

Is it a real problem, though?

First, the strawman I referred to was that the order of operations can give you the wrong answer. That's incorrect, especially with the example he used in the video. Apparently some people were taught the order of operations incorrectly? But that doesn't make the order of operations incorrect, just the people teaching it.

Second, order of operations is not in fact a mindless procedure. It's an expression of the standard syntax of writing math equations. It's not telling anyone how operations or association or distribution works. It's telling them what is meant when someone writes an equation down. It's also taught in elementary math because it's an elementary concept. At least when I was taught math, we learned stuff like distribution and association in pre-algebra or algebra. Its not like kids are never taught anything after the order of operations.

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It's a very real problem, and one of the main reasons the US is so far behind many other countries in math.

It is an elementary concept, if you buy into the notion that it's all elementary students are capable of handling. While it is important to teach this concept, it's a serious mistake to teach only this concept early on. It is mindless, and it's why math is considered the most boring class in school.

And the truth is, unless the student is in an advanced class for those with high IQs, schools don't teach much other than mindless math, even in high school. The average high school graduate is lucky if he can remember how to do even basic math, let alone anything advanced.

As taught to the average student, math is both mindless and boring. What gets imprinted on the very young usually remains with the older students. The US is almost alone in how early such things as distributive math, and other, even more complicated concepts are taught, and because of this, in how early students finish what we call high school level, and move on to college level.

Real math simply isn't being taught here, at least to the average student. As long a sthis is teh case, we're never going to place very high in world ranking. I mean, seriously, the average high school graduate can't even do basic math, let alone handle algebra, or anything above algebra.

Right....

Putting in a bunch of unnecessary parentheses is going to make things easier to understand...

His logic does not resemble our Earth logic.

Myrealana said:

Right....

Putting in a bunch of unnecessary parentheses is going to make things easier to understand...

His logic does not resemble our Earth logic.

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I don't think he's advocating actually using those parentheses, just understanding that they're implicitly there.
8 - 1 + 2 is not ambiguous if you understand that it's
(8) +(-1) +(2), not (8) - (1+2)
Actually it's not ambiguous at all if you understand that addition and subtraction are equivalent expressions and you should do the order of operations from left to right as taught. I'm not sure what he's getting at there.

I do agree with him that understanding how math works instead of just memorizing how to get answers can set you free to solve equations in all kinds of ways. I have to wonder if this kind of intuitive understanding can be taught right off the bat, though? I'd always assumed that people gain that intuitive understanding from following the rules as taught over and over and over until they become kind of second nature.

Liosse de Velishaf said:

What a lot of people in the thread appear to be arguing is that it's irrelevant whether his Order of Operations example is correct, because they like the larger point he makes about deeper understanding of the concepts.

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Right, and I like that point, too. I just feel like he's trying to put the cart before the horse.

I do sometimes think the bigger pictures gets lost in the details with math and science instruction, though. I'll never forget how my high school physics teacher taught us about entropy. He explained that there is a fixed amount of usable energy in the universe, and that once that energy is used up, no more work can take place. No more life, or solar systems, or stars. Everything evens out and the cosmos become static. The Heat Death of the Universe. Gave me chills. When I took physics in college, I was excited to revisit entropy. But all we learned were equations. No bigger picture. No Heat Death of the Universe. I mean, I guess you can be an okay scientist without understanding or caring about the more philosophical elements of our relationship with the natural world, but what's the point?

Liosse de Velishaf said:

coding

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Parenthesis are a must for formulas in Excel:

mid(A2,(find(A2,".")+1)) for instance will give you the digits after a decimal point in an Excel cell, e.g. 58.345 = 345.

Maybe the youtuber can make a video about Excel.
His fixation on parenthesis will be perfectly fitting and justified then.

ps that background bass playing in the vid is annoying.

On a positive note, he has neat penmanship.

Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Okay, I have Very Strong Feelings about math education. I've been teaching math via private tutoring for years and years, mainly to middle and high school students (some college, some elementary), and my degree's in math. I cannot. Stand. how some of my students' teachers concentrate solely on mindless mechanics without explaining the underlying concepts or how they connect. My students are freakin' excited when I explain to them why things work and how they connect with other things they know, and it makes the mechanics easier.

You know what has never bothered me, ever, in the way it's taught? The order of operations.

You know what none of my students have ever been confused by, even the ones who still have trouble with basic algebra? The order of operations. (Sometimes they mess it up, but they're not *confused* by it -- and an "order of operations" reminder is met with, "oh, right!")

Liosse de Velishaf said:

First, the strawman I referred to was that the order of operations can give you the wrong answer. That's incorrect, especially with the example he used in the video. Apparently some people were taught the order of operations incorrectly? But that doesn't make the order of operations incorrect, just the people teaching it.

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This. I've never run across anyone who was taught it incorrectly like this. I'm sure they exist, but it's not (to my knowledge) a virulent widespread problem like the video implies. I was certainly taught it quite correctly (and I went to public school, also). The video is basically saying, "if you do it wrong, you'll get the wrong answer!" Which . . . duh?

And even if people teaching it incorrectly IS a widespread problem, that's not the fault of the concept, that's the fault of the teaching.

Second, order of operations is not in fact a mindless procedure. It's an expression of the standard syntax of writing math equations. It's not telling anyone how operations or association or distribution works. It's telling them what is meant when someone writes an equation down. It's also taught in elementary math because it's an elementary concept.

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(bold mine)

THIS THIS THIS SO MUCH THIS.

I took a graduate course in mathematical logic when I was in college. The first 2-3 weeks were entirely learning syntax of the logical language we were going to be using. You NEED that if you are going to understand that language well enough to communicate in it. It's like learning a programming language -- you need to know what the thing you're writing is going to spit out on the other end, what it means to the computer (or in this case, to other people).

And by the way, syntax explanation should continue in middle and high school. Like, that sin and cos and log are operations or how negative exponents have nothing to do with negatives. The number of times one of my students has said they're "dividing by log" . . .

Syntax is important. It's also something we abstract away from as we move forward in math -- as we should! I'm going to complain about mindlessness in math as much as anyone -- I've ranted about it on my blog and Twitter before -- but mindlessness is different from abstraction. Once you learn a concept, there's a point where doing it without thinking about it is a very good thing, so that you can learn more advanced concepts layered on top of it without thinking about what 1+1 is each time. (You should just be able to peel back the layers of abstraction if you want to and remember why you're doing each of the things you aren't thinking about each time.) If I thought about what a derivative was every time I took one, and thought about the fact that I could prove the shortcut I was using via the limit definition that uses the difference quotient and that the difference quotient comes from slope and that slope is . . . etc., I'd never get any math done. But that doesn't mean I can't explain all that very well when asked. There's just a point where we stop thinking about it to add another layer on, and that's not mindlessness, it's abstraction.

Liosse de Velishaf said:

I just don't know why we're blaming that on the Order of Operations. It's more of a broader curricula problem, in my mind.

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This. There are many problems, but the order of operations (as a concept, if taught correctly) is not one of them.

If there are teachers out there teaching it incorrectly, then those teachers are a problem. But the order of operations concept is not.

Myrealana said:

Right....

Putting in a bunch of unnecessary parentheses is going to make things easier to understand...

His logic does not resemble our Earth logic.

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My feelings exactly.

In all seriousness, students have trouble, in general, parsing large amounts of parentheses -- it's hard for the eye to look at. When my students need large numbers of parentheses for a graphing calculator, it causes untold errors. Also, I TAed a Scheme-based (think LISP) computer science course in college, and talk about trouble matching parentheses. There's a reason we've invented computer software capable of matching them for coding purposes.

There might be an argument for adding in the parens on very simple expressions when first teaching the order of operations, to emphasize what that order is implying, but IMO that should be a means to teaching the order of operations, not a replacement for it. Even his example had so many parentheses *I* had trouble looking at it!

tl;dr: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

slhuang said:

Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

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To jump on board here I have to add that as much as you want it to be, the Order of Operations doesn't stay in elementary school and it is still a topic taught in algebra 1 (subject I teach).

I would argue that a statistically insignificant amount of students have been taught how to solve these expressions wrong. Everyone wants something simple they can remember and PEMDAS does just that. They remember the phrase and just go from there. If you want to really shake things up with the Order of Operations, just don't make it look like a word through initialism. When my students can't remember the "either one, whichever comes first" or "subtraction is really just adding a negative and division is..." I tell them to write the Order of Operations like this:
P
E
MD
AS

And then to treat it like levels you move down. Start with the most important and go down each step.

The other annoying thing is that this isn't the extent students solve problems and it is like basic practice to make sure they can do something other than punch numbers into a calculator (which if they don't have a scientific one with a display they can't just type it in the order they read it).
In my class you see...5 * 4 - 6 / 2 for about 5 seconds and then you get.... 3(2x - 6) - 4 = 7x - 10 because variables are where it's at and yes distribution is awesome and necessary and it's covered plenty for students, not computers.

So to the original question, yes this is a set up and I feel the video is missing the point. Is Algebra taught the best way? No, because curriculum has to pander to everyone all at once and you know that doesn't work for everyone. If we're going to pick a fight, pick a fight with the hundreds of standards teachers are expected to cover each year with only 150 days to squeeze it in (I know there are 180 days in a school year in the US, but you lose out a lot to state testing, working around holidays, and exams so 150 instructional days...which also have to include your own assessments, is pushing it).