I want you to take a look at this picture. This picture makes me angry.
Very angry.
I don’t know if it’s photoshopped or if it’s real. I found it on a friend’s feed on Facebook this morning, and there was already a small listing of comments between folks debating what is shown in this photo. I of course chimed in, being a [former] teacher of elementary school myself.
Take a second, and solve the problem – see which answer you get.
Done?
The correct answer is 16.
But this picture is incredibly, and inexcusably misleading.
The answer is not 16 because the new Common Core curriculum gave us new, proper math. And despite what the picture says, both answers are not equally correct (in fact that makes zero sense). It’s because of my dear Aunt Sally, and your ability to kindly please excuse her.
Did I lose you? Sorry. Please Excuse My Dear Aunt Sally. PEMDAS, or, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction – or, Order of Operations.
20 / 5 (2 * 2), do parentheses first so the problem becomes 20 / 5 (4)
But the rules of order of operations states that given only multiplication and division (same for addition and subtraction), you work left to right. You do not do the multiplication first just because M comes before D in PEMDAS.
So, working left to right, it becomes 4 (4).
Then multiply, and get 16.
If you incorrectly did the multiplication first, multiplying the 5 and the 4, you’d get 20 / 20, which equals the 1 shown in the picture. But that is incorrect order of operations, and incorrect math.
It is not incorrect because that is how ‘the old way’ taught it. It’s incorrect because you didn’t pay attention to the details of PEMDAS.
The big to-do about Common Core is that is supposedly introduces alternate critical thinking and problem solving skills – because there was something wrong with the ones already being taught? I went through elementary school in the mid/late 80’s, and graduated high school in 1999. I’m a product of ‘the old way,’ like all my friends – and guess what – I’m a damn good problem solver. We all are. I knew how to read and solve a word problem be understanding clues in 5th grade. When I taught 5th grade (for 5 years), they didn’t know that “how many more” meant they needed to subtract. They didn’t know their multiplication facts immediately. They still did addition on their fingers.Â
The cause of this is two-fold:
1) So much emphasis being put on testing and preparing for the end-of-year tests leaves little wiggle room for exploring subject matter. It’s a get it done get it done get it done next learning standard world in the classroom these days. If some kids don’t get it, too bad we have to move on, and those kids can go to remediation class, or something. (Large emphasis on the “or something” because really we have no more TAs, and don’t want them pulled out of other subjects for remediation in another.) There’s no time to pause and ‘go deeper,’ even though that’s some of what Common Core purports to do. Teacher’s fear the tests because it effects their evaluations.
2) Common Core’s apparent lack of support for rote memorization. I don’t care what kind of problem solvers you think you’re making, but in order to solve those problems, students need to know that 6×5=30 without even thinking twice about it. Drill drill drill. Memorize. Parents make them memorize other important things – their phone number, address, stranger danger, etc etc. Why not the simple math skills required to function in the world?
One of the major problems of Common Core is that is pushes age-inappropriate learning requirements. We’re giving tests to Kindergarteners now? Unbelievable. The youngest learners learn the most through exploration learning. Common Core twists those formative years into rigidly structured test prep again. (Not to mention a teacher’s evaluation being tied to how well at 5 year old does on a standardized test….) ((let that sink in))
Common Core is supposed to enhance critical thinking skills. Well, as it’s followed the first class of students up through the grade levels (introducing a new grade level to it each year as it went along), by the time they get to an age/grade level where something like mathematical word problems require those skills – they haven’t got them, and even if they could think abstractly, they still don’t know that “how many more” means they need to subtract, or that 4 x 3 is 12. (Because they weren’t taught to memorize it).
So when you look at that picture, remember, the answer is 16.
Not because of common core.
Not because of the old way.
But because that’s how you fucking do math.
yankee.velo.foxtrot 
Everyone who has some common sense would know that the answer to that is 16 since you have to calculate from left to right for MD and AS operations. Whoever said otherwise must be a retard…
OK. Good. It WAS 16. I was scared for a second.
The whole common core thing is idiotic. I memorized multiplication on my own in Kindergarten and then suddenly I had to write multiplication as 6×8=8×5+8×1 in 3rd grade. WHY?!? I don’t know! Why can’t it just be 6×8=48?!?
welcome to algebra, dude. Just wait till you’ve got x’s and y’s!
I still remember when whole word theory took away phonics. Teaching my kids to read out loud always lead to to break down words to make it easier to learn.
Order of operations is crap…It’s not really math, it’s just arbitrary “rules”…It could, therefore, be “changed”
Its crap, no one presents a math problem to themselves in real life where you have to use the arbitrary “order of operations”
PEMDAS is more of a language. It makes it so people are able to be on the same page. So yes it’s made up, but so is everything. Without some sort of order they would be no way to get a consistent answer. Most people may not need the order in everyday life but specifically in the field of math it’s absolutely necessary.
ah…did it occur to anyone here to check if PEMDAS is actually in or from the Common Core? Because it isn’t… even in the common core. You are confusing what the schoolbooks and teachers do with something that has very general guidelines, common core never even mentions the left-to-right rule. Just saying.
the common core does mention doing operations in the conventional order without brackets but thats just them reflecting the left-to-right rule that predates the common core.
Also could someone explain the “old way” to me, please? Does that mean “always multiply first”? I believe PEMDAS has been in effect from before the 70’s. Does anyone know?Thanks
20
——————-
5(4*4)
You think that could ever equal 16?
Oh deary me! We’re going to see a lot more collapsing bridges once that is applied to the real world.
That’s not how the equation is written. Order of operations is different when you pose it as a fraction like you did. But when written as a algebraic sentence, the order of operations I wrote is correct.
If you type the algebraic sentence into an old (very old) calculator, the answer produced is 1. If you use a modern calculator, the answer is 16. The programming and teaching of PEMDAS used to be quite literal around the 70s/80s and those old calculators reflect this.
This article/rant is incorrect and demonstrates a lack of knowledge of how mathematics has been taught in the past. I have old calculators that are programmed with the older way of doing the order of operations. The old calculators will produce the answer of 1. A lomg time ago, PEMDAS was indeed taught quite literally, with multiplication occurring before division. The old calculators and quite a few old textbooks demonstrate this.
My own recollection is that, aside from the parentheses, PEMDAS wasn’t taught at all prior to algebra, back in those days. The rule was to just operate from left to right, applying whichever operation was encountered next, except where parentheses indicated otherwise. If it was ever taught with all the multiplication occurring before the division, that was always incorrect instruction.
As for the old calculators, most of them didn’t have parentheses keys, so there was no way to enter this expression as written, not without (most often incorrect) interpretation by the user. There were RPN calculators that used a stack to allow grouping of operations, but again, that relied upon the user’s interpretation. I’ve never seen a textbook that treats the MD in PEMDAS in the literal way you’ve described. Can you provide a reference?
I will say, regarding the article/rant, that the point of the original photo was not clear to me, and I had to read most of the post in order to discover that it was directed against the false arguments in favor of Common Core, rather than those opposing it. (Taken out of context, I could not tell what the point of the original photo was.) In the end, the inclusion of an F-bomb for emphasis pretty much ruined it for me.