Today I discovered another reason we should ban it.
In addition to neglecting the opposite of exponents (roots), PEMDAS is ambiguous on “parenthesis.”
The P that stands for parenthesis also means brackets and braces.
“Everybody knows this,” you might think. And you’d be right.
But what they don’t know is that P also means anything isolated – like things under radicals, inside absolute value bars and embedded in numerators and denominators.
Parentheses are on a different level, too.
Furthermore, parenthesis (and all its brothers) aren’t actual operations. So they don’t even belong with a list of operations.
They are bossy snot-boxes that tell you what to do if things aren’t so obvious.
Parenthesis are the trump card in the game of arithmetic. (tweet this)
So students are clueless.
I gave a quiz in College Algebra. Students were asked to plug x = 2 into the equation y = |x – 3| .
Many of the students calculated this as y = 5.
- y = |x – 3|
- y = |2 – 3|
- y = |2 + 3|
- y = |5|
- y = 5
What happened at step #3?
Yup – that was my question too.
And the response every time was, “Absolute value bars mean to change everything to positive, so the -3 turns into +3.”
If students understood isolation, this might not happen.
Furthermore, if absolute value was included in the order of operations, this might not happen.
And if we didn’t shove a confusing and incorrect mnemonic device like PEMDAS down their throats, this might not happen!
Do you have a reason to ban PEMDAS? Share in the comments!
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