Tuesday, October 23, 2012

Order of Operations and the American School System

One of the fundamental theories in Mathematics is the Order of Operations. The Order of Operations determines in what order you do the operations solve math problems.

When I was in school, as you learned how to do the various operations, you learned in what order to do them. Thus when you finally covered all of the operations, you knew exactly which order to solve them in, and it was second nature. When you went over the Order of Operations, it was a "duh" moment. We were then given a handy mnemonic to remember the order for the rest of your days. PEMDAS!!
  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction
Easy, right? In Mathematics there is only one order. This is universal... until you get to non euclidean type Mathematics, but that is for another day.

So, I started seeing on the web these very strange questions. Things like "What does 2+2+2+2+2+2+2+2-2+2 x 0 equal?" It should be obvious, the answer is 14. You use the Order of Operations and first multiply 2x0 that is zero, so what is left is 2+2+2+2+2+2+2+2-2+0. Then you do all of the addition and get 16-2. Finally you do the subtraction and get the final answer, 14. Young people were coming up with something completely different. Many said the answer was 0, because anything multiplied by 0 is 0. I could not believe it.

Excuses for the failures ranged from "I suck at math." to "I never learned that in school." to my very favorite, "I'll never use this shit!!"

I got to thinking. It was a significant amount of people. The only thing I can come up with was that it WASN'T being taught in the schools any more, or it wasn't being stressed as much anymore. The instruction of Mathematics and Science are increasingly not being taught in schools. Why? I don't know. Math and Science are not very well taught anymore. Is it because there are no teachers? Is it because Math and Science are black and white, right or wrong? Are teachers so focused on student self-esteem that they simply do not put that much emphasis on Math and Science?

Math and Science are fundamental to a child's education. Why? They teach HOW to think. They teach HOW to solve problems. They teach critical thinking on abstractions. They teach HOW problems can be solved even if some of the steps are missing.
In everyday life you are presented with problems that need solutions. You always have some sort of parameters governing the solution. What does that sound like? Math.
In everyday life there are problems that need solutions, but you don't know exactly what is causing the problem. You need a framework to find out the problem, so that you can devise a solution. What teaches that?? Science.

Without critical and abstract thinking skills and a good knowledge on how to use the Scientific Method to solve problems, how can you make good decisions on your future? Is this why we saw so many people fall victim to loans with Adjustable Rate Mortgages? Was it that the buyer could not conceive what would happen when their rate changed? Did they not have the ability to comprehend the Math involved in calculating their mortgage and how the payment would change when the rate changed? Could they not do the basic calculations involved in figuring out how much they could pay every month, based on their income?

Instead we have a population that is easily manipulated by mathematics that simply does not work out, because they "suck at math." Saying you suck at math is putting a sign around your neck that says "Take advantage of me. I can not think critically, nor do I have any desire to attempt to."


KenJ said...

Point taken.

Just in case the answer of 14 was intentional and I didn't miss something obvious (one can never rule out the possibility of a blog commenter being completely mistaken), it looks like the problem requires adding 2 fourteen times (28) before subtracting the final 2 for 26.

NattoNinja said...

Yup you are absolutely correct. I pasted too many twos!!

Edited for correct number of twos