Some high-falutin’ math-wiz guy on the Internet thinks that PEMDAS is stupid:

For those of you who do not recall, PEMDAS is the shorthand for the order of operations in math. Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Except that from the start, we were not taught that was a rigid order. To use parenthesis, it was: Parenthesis, Exponents, Multiplication or Division, and Addition or Subtraction. Judging by the comment section, this was the most common way of teaching it. No matter how many times people say “No, PEMDAS means you have to put Addition before Subtraction!”

He says that PEMDAS means that 8-2+1 is five. Except that I was taught by PEMDAS, and was taught that the answer is seven. I arrive at the right destination, but according to this guy the “wrong” way because I don’t expressly consider the -2 to be + (-2).

Which brings us to his larger critique, which is the algorithmic versus conceptual math debate. My own position is that concepts are important (I was indeed taught that “-2” is the same as “+(-2)”), but that you start with the “what” before moving to the “why.” That way, even if you don’t get the “why” you do at least understand the “what.”

More to the point, though, it makes me think of the whole vs phonics debate. Conceptual math is good for kids that are naturally good at or interested in math. It seems to be boosted by those same people, who seem to believe that if others understood math the way that they do they would be adept at it. Meanwhile, I think it will hobble the kids who will simply never understand the “why” by making learning the “what” more difficult.

Which is pretty much how whole language worked. Phonics was annoying for the verbally gifted because it was crude, unreliable, and forced-walking when they were capable of running. It, too, was a program advanced by the best and brightest and well-suited for bright kids. It was also a disaster for everyone else.

Since we seem to be moving towards the new way of doing things, I hope that I am wrong about this and it will indeed be the innovation that its proponents say it will.

Category: School

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