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.
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.
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.