What Does Math Stand For Meme – Recently, a viral math meme established, once and for all, that math is a language. And a shadow once, too.
Where it started is anyone’s guess. But soon people all over the world were discussing the solution to 8 ÷ 2 (2 +2). Some say that it simplifies to 16. Others insist that it is 1.
What Does Math Stand For Meme
Both sides had detailed arguments to back up their calculations. But it turned out that both sides were wrong. (At least in thought there is only one answer). The expression was specially designed to exploit loopholes in our mathematical conventions.
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At first, I dismissed it as another example of social media bullshit. A distraction from all the productive or rewarding things I could be doing with my time.
After all, the best minds in math education have been condemning our fixation on “the answer you get” for years. So why should we debate which set of rules leads to the “correct answer”?
But I soon noticed that some really smart mathematicians joined the fray. Steven Strogatz, a professor of mathematics at Cornell, wrote a New York Times article on the subject. Spoiler alert: he came out with 16. Then, a few weeks later, he wrote a follow-up article, in which he seems to admit that 1 might also be an acceptable solution.
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Eventually, I realized that the real lesson in math wasn’t whether the answer was 1 or 16. The real lesson was the debate itself. What did he say about mathematical truths and conventions? What does it tell us about the language of mathematics?
When you think about it, Google Translate is a pretty amazing tool. It allows you to get very close to communicating in another language. I can’t imagine my honeymoon in Vietnam without her. As my wife and I traveled from Saigon to Hanoi, we used G-Translate to read signs, ask for directions, and make sure we had an idea of what we were ordering at restaurants. We even used it to teach Gin Rummy to our bunkmate on an overnight train.
But despite these successes, my wife and I never pretended to speak Vietnamese. Passing is not the same as speed. PEMDAS is an oversimplification of the language of mathematics. It’s easy to remember. It works by following a few simple steps.
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Before we get into other ways of thinking about this problem, let’s look at the two main arguments for finding an answer.
According to the most common argument, PEMDAS requires that the answer be 16. We are told to start with (P) parentheses and omit (E)xponents (there are none). Next, (M)multiplication and (D)idivision are the same, so we work from left to right. (A) addition and (S) subtraction do not apply, since addition is in parentheses.
So we start by adding 2+2 and we get 8 ÷ 2 (4). Working from left to right, 8 ÷ 2 is 4.
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I won’t lie Deep down I feel like 1 is the correct answer. But the reason has nothing to do with the order of operations. (More on this later).
The first is that the obelus (÷) was originally designed to function as a fraction. The use of fraction bars to show division was done centuries before the use of the obelus. In fact, the International Organization for Standardization says that the obelus should not be used for division. In a fraction, we divide everything above the bar by everything below the bar. It’s like there’s an invisible grouping symbol around everything in the denominator. Could it be the same for everything to the right of obelus?
The other argument is that parentheses apply to numbers inside and next to them. So the 2 outside the parentheses must be divided by the 2 + 2 inside before you can divide.
He F*rickin Hates It Why Would He
If so, how are we having a discussion about a relatively simple calculation? The reality is that mathematics is also about how we communicate those truths.
A mathematical truth is discovered. When Pythagoras discovered that the sum of the squares of two sides in a right triangle is equal to the square of the hypotenuse, he did not take a vote. There was no advice that everyone agreed that we will use A2 + B2 = C2. He observed a timeless fact about the nature of right triangles. If no one can dispute it, it becomes an accepted theorem.
A mathematical convention has no inherent truth. It’s something everyone agrees on. These conventions are still important. The idea that the symbol ‘8’ represents the quantity ‘eight’ is a convention.
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So, like English, mathematics is a language that allows us to communicate about things that exist in the real world. Or things we can imagine.
For language to have meaning, we all must agree that the word ‘bear’ refers to that thing that ran through the woods. But if we choose to call it ‘puffball’, it would still be fatal. So convention doesn’t change the truth. Over time, conventions change. We realize that not all bears are the same. Some are brown, others are polar, etc.
Similarly, PEMDAS does not change the reality of mathematics. It is a system that has provided a useful way of teaching the order of operations to children. But many, including the National Council of Teachers of Mathematics, have been addressing the limitations of PEMDAS for quite some time.
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Without getting too philosophical, it helps to think of mathematical reality as separate from any representation. John van de Walle proposed that there are five representations of mathematical ideas. Neither representation is the “true” representation. All of these are reflections of an underlying mathematical truth.
As we train our next generation of mathematical thinkers, they need to understand this. Perhaps the best sign of mathematical fluency is the ability to translate from one representation to another.
So when we come up short in determining whether the expression equals 1 or 16, it helps to look at the problem from a different angle.
This Meme Was Made For The Mean Math Teachers, Nobody Else.
I was impressed with how Michael Pollard took this approach and shared his work on Twitter. Take the expression (symbolic representation) and translate it into a word problem (contextual representation). He then created drawings (visual representation) to reflect each scenario.
And while most people using PEMDAS came up with 16, it was nearly impossible to create a real-world scenario where this was the answer. In what situation would you divide something by four and then multiply the result by 2+2?
Finally, I suggested an example in which a mother divides 8 Easter eggs between her two children. Inside each egg there are two jelly beans and two gumballs. Each child ends up with 16 candies. Michael was kind enough to show my example as well.
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That example works. About. But isn’t it much more reasonable to imagine that 8 golf balls are divided between two golf carts, each cart carrying two mothers and two children? In this scenario, each player receives a ball.
Are they variable numbers? The answer, of course, is ‘yes’ So if variables are numbers, don’t the rules that apply to variables apply to other numbers as well?
I recently saw a version of the expression go viral on a Facebook group for math teachers. This time, we were asked to divide 12 by 3y Even a PEMDAS purist has to admit that we are dividing by the amount 3y. We are not working from left to right. The simplified version of the expression is 4 ÷ y.
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So if we simplify before substituting -2 for y, we get -2. But if we substitute first and follow PEMDAS, we get -8.
Once again, mathematical conventions are important. But when mathematical convention meets mathematical truth, truth wins. -8 is not equal to -2. Game over, PEMDAS
Instead of teaching PEMDAS, I teach my students demonstrations of number sentences. Not only are they more interesting than memorizing a list of rules, but they give students the opportunity to think deeply about the meaning and purpose of expressions and equations.
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So what does this whole episode prove? It shows that we need to stop relying so heavily on PEMDAS.
A pun is a joke that exploits loopholes in language. “A man walks into a bar. Ouch!”
Bar can mean a counter where drinks are served. Or it can mean a long metal bar. The joke is based on leading us to assume one meaning, before quickly changing to another.
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Finally, like any good language, mathematics has puns. The ingenious creator of this expression found a loophole in the language of mathematics. They forced us to follow the rules. But they showed that the rules may not always make sense.
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