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Normally I just post responses to questions people ask, but we haven't had any interesting questions this week, so I thought I'd take a few minutes to answer a question that gets asked a lot (even though no one has specifically asked me!)
Here's the question: "Why is the Common Core method of doing subtraction so different from, and more complicated than, the old way of doing it?"
The standard example that goes with this question looks like this:
There are several answers to the question, and I'm going to summarize them before going into details.
- The method on the right is not the "Common Core way" of doing subtraction.
- The method on the right is as old as the way on the left, and most schools have taught it for generations.
- The people who created this example (or the video you saw) were deliberately trying to mislead you.
Not the "Common Core Way"
The algorithm students are being taught to do subtraction looks exactly like the one on the left. Students write the two numbers in a column, do subtraction by place values, doing borrowing where appropriate. It's the good old stand-by - it works, it's effective, it's mathematically sound, and it will never go away.
So what is the thing on the right, if it's not a replacement for the "old" way of doing things?
It's ANOTHER Old Way
It's the traditional method taught for doing mental arithmetic. If you need to do a math problem without the aid of a pencil and paper (or a calculator) the method on the right, once you've learned it, is vastly superior.
Take the following example: what's 262 - 187? I was able to do this mentally, using the "common core" method, more quickly than you could write the problem down on paper. What did I do? I said, "I need to add 3 to get from 187 to 190, then another 10 to get to 200, then another 62 to get to 262, so the answer is 62 + 10 + 3 = 75. Meanwhile, you're still thinking about borrowing from the tens and the hundreds place, and trying to do it in your head.
This method is so superior (when it comes to doing mental math) that teachers have been teaching it for generations. I learned it, and when I checked with my parents, they confirmed that they had learned it as well. In fact, my mother attests to the fact that when she was a teenager, it was impossible to get a job in retail if you couldn't do that. It was necessary for making change.
I also have heard from someone that it is still required in their firm because cashiers have to be able to make change even if there's a power failure and their register system goes down!
Dishonesty In Media
I've seen so many of these images and videos purporting to prove that "The Common Core way is horrible," and they all have one thing in common. They don't use examples like 262 - 187; they all use ridiculous numbers that make the "common core way" look horrible and cumbersome, and the "old way" simple. Of course it's easier to use the "old way" when subtracting 12 from 32 mentally! Duh! There's no need to even THINK about pencil and paper for that.
But here's the thing...try randomly picking numbers and attempting to do both processes mentally. You'll discover what people in the business world have known for centuries - the method on the right is hands down the winner.
And if the method on the right is the hands-down winner* - isn't it strange that 100% of the images and videos produced make it look otherwise? If the majority of random examples show you one thing, but 100% of the propaganda you've seen shows you something else, that should tell you something...you are being deliberately misled and deceived.
Are there issues with Common Core? Oh, I'm sure there probably are. But here's the thing...if you want to complain about Common Core, you need to complain about the right thing. If you complain that this method is being taught, I hate to say it, but you're probably accomplishing nothing except making your local school officials think, "Wow, this guy is some kind of nitwit..."
So figure out what the real problems with the math curriculum are. One parent told me, "My kid is too young to learn this technique." Fine! If you think that's the case, then complain about that! But THINK before you complain. Make sure your complaints are real and valid before you bother the (probably) overworked and (likely) underpaid educators who are working hard to help prepare your child for adulthood in a crazy, complicated world!
* Last summer contractors were hired to come in and dig a hole for the foundation of our new home. After they left, we were looking at the hole they dug and saying, "That hole doesn't look like it's deep enough." So we did some measuring. Of course, the depth had to be measured not from the ground, but from a pre-determined point above the level of the ground, which meant we needed to do some subtracting, and therefore (since we didn't have calculators on hand) some mental arithmetic. I discovered something I never knew before that day: the "common core way" not only works for integers and decimals, it also works when your measurements are in a combination of feet, inches and fractions of inches. I could never have calculated that difference mentally without this technique that I learned as a student. And after double-checking ourselves a couple times, we were able to call the contractor and say, "You did this wrong." He came back in with his laser level and verified that he was wrong and we were right. Do I thank "Common Core" for that? Of course not! I thank my math teachers who taught me how to do this long before Common Core was even an idea in anyone's brain.