You've probably seen this image making the rounds on social media. It shows a method of doing basic subtraction that's intended to appear wildly nonsensical and much harder to follow than the "Old Fashion" [sic] way of just putting the 12 under the 32 and coming up with an answer. This method of teaching is often attributed to Common Core, a set of educational standards recently rolled out in the US.

But, explains math teacher and skeptic blogger Hemant Mehta, this image actually makes a lot more sense than it may seem to on first glance. In fact, for one thing, this method of teaching math isn't really new (our producer Jason Weisberger remembers learning it in high school). It's also not much different from the math you learned back when you were learning how to count change. It's meant to help kids be able to do math in their heads, without borrowing or scratch-paper notations or counting on fingers. What's more, he says, it has absolutely nothing to do with Common Core, which doesn't specify *how *subjects have to be taught.

I admit it’s totally confusing but here’s what it’s saying:

If you want to subtract 12 from 32, there’s a better way to think about it. Forget the algorithm. Instead, count up from 12 to an “easier” number like 15. (You’ve gone up 3.) Then, go up to 20. (You’ve gone up another 5.) Then jump to 30. (Another 10). Then, finally, to 32. (Another 2.)

I know. That’s still ridiculous. Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)

You sure as hell aren’t going to get out a sheet of paper ...

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“Worry not.” (posted to r/pics by kekembas17)

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Or you could just cancel the twos, and subtract 1 from 3 to get your answer...

The "new" system here is fine, except that it requires a relatively large amount of mental overhead to keep all of the sub-results straight, it's almost as bad as doing it the traditional way. It's a good method to keep on the toolbelt. Most people don't realize it until they get to algebra, but most grade school (and college!) math is really just pattern matching to figure out the correct algorithm to use. Once you figure out what pattern the problem is in the rest is cake.

That said, this method is really helpful in cases where the traditional method is really difficult: When the individual digits on the subtractor (I've forgotten the proper term for this) are larger than the digits on the initial number and you have to do a lot of carries. And as it turns out, that pattern is extremely common in grade school math homework (usually almost every equation will follow that pattern because it's trickier and they want you to practice it more).

I don't understand why all those steps are necessary, though. To use the example, if I buy a $4.30 coffee and only have a twenty, I round the $4.30 up to 5, which means I only have to do 20-15, then subtract $4.30 from 5 and I get 70 cents. Add 15 to .70 and I have $15.70. That's also four steps, but it seems easier to me than whatever is going on here.

edit: And I agree with the first comment, all you have to do is cancel out the twos (or mentally round them down to 30-10) and there you go.

Going to 15 in the example seems unnecessary to me.

A formal application of this method would probably break down on power of 10, as most people have a pretty strong grasp on addition and subtraction with single digit numbers. So:

4622 - 1873

7 + 20 + 100 + 2000 + 600 + 20 + 2 or 2749.

One nice thing with this method is you're only adding two single digit numbers for each digit of the final answer. So it's 2, then 6 + 1, then 2 + 2, then finally 2 + 7. My example turned out to be a little extra easy because it didn't have any carries in the final addition, but that's because I chose an example that explicitly looks like something you would get 1,000 times as a fourth grader and would be annoying to do in the traditional system.

Funny how these things go in cycles, isn't it.

There was another period of time when people couldn't understand the new-fangled methods used to teach mathematics to children.

Someone made a song about it

Of course, the funny thing is, the method parodied back then is exactly the same one that is being defended now as the "old" method.

My sister teaches elementary school, and while I had an easy time with math, she had to really try to get math to stick in her mind. As a result she views math differently than I do, and she hated anything-math until she took a class on math pedagogy where she learned about the many ways to teach math. It's a very good thing for her career that math was tough for her, because she can explain one thing in several ways, helping a student find whichever way (or metaphor, or algorithm, or explanation) actually helps them. That way of doing it feels convoluted and strange to me, but that doesn't mean it wouldn't be the way to open a door for another person to get it.

Also, thank you for this:

Number sense helps in life a lot more than having a bunch of steps memorized.