I have been seeing this image of this math problem supposedly comparing the “old fashion[ed] way" to the "new [common core] way" of teaching, and people around the net are shaking their heads at the absurdity of it.
I agree.
THIS problem looks absurd when comparing two different math strategies, and the way the method is laid out in this photo is also significantly exaggerated (which I'll get into later). But the people mocking this new math strategy (and the person who created this image) clearly do not understand either the method or the reasoning behind it. They say things like, "China is laughing at us right now." Yes, China is laughing at us right now. Because they can't believe it has taken us so long to teach math in this way and they really can't believe that educated grown-ups can't even grasp it, and instead are having hissy fits over it because they don't understand it.
Let me explain. First, mocking a problem like this one as an example of this math strategy would be like harassing a 4-year-old for counting on her fingers when you ask her what 2 + 2 equals. When kids are young, they are still trying to understand numbers as representations of other things- like fingers- and they have to take it one step at a time. So, they begin with counting on their fingers. This particular problem, with its long, drawn-out, rounding up and down answer, is the common core version of counting on fingers: it’s the next step in understanding how numbers relate.
You might have also noticed, if you have kids in public schools, the use in recent years of math tools like number lines and hundreds charts. At first I didn't understand these, but once I did, it made a great deal of sense to me. These tools teach kids to understand numbers as a sequential buildup organized in sections of 10. They understand numbers spatially, not just in the abstract.
One of the issues I have with this particular example problem is that the frustrated student or parent decided to exaggerate the method by rounding to 5, rather than 10. Personally, I have never seen that done, and it looks to me just like the author's way of trying to make it look even more ridiculous. Either that, or they REALLY didn't get how to do it (and no wonder they were frustrated).
Let's go back to that problem: 32-12. A grownup who has been doing math for years can clearly see that, since both numbers end in two and 3-1 equals 2, then the answer is 20. Easy, right? Big fat duh. Very uncomplicated.
Let's say, however, that you, the grownup, are given a slightly harder problem, like 326- 78. A little bit harder to do in your head, right?
Now let's take the common-core-educated student who will be using the rounding up and down strategies. If given this harder problem he will not ask for a piece of paper and start borrowing and carrying. He will say:
"Well, 78 rounded up is 80- just had to add 2.
If you round that up to 100 you'll have 20 left.
20 plus 2 is 22.
326 rounded to the nearest hundred leaves 26.
300- 100 equals 200.
26 plus 22 equals 48.
So the answer is 248.”
Of course, he probably won't need to say all that. By the time he gets that far, it will be second nature and he will be able to do it very quickly in his head without even thinking about each step.
How has he gotten to that answer? Using the exact strategy being mocked all over the web. He has used number lines and hundreds charts- he knows numbers are not just abstract digits with rules to be followed that only make sense if you have a piece of paper and pencil. He can see how the numbers relate in his head, and he has been doing this ever since he was learning to solve problems like 32-12, so he can easily manipulate large numbers without writing a single thing. He has spent time knowing what plus what equals 10, and he understands how blocks of 10 stack up to build bigger numbers. He has practiced rounding up and down, understanding how adding differences leads to the right answer.
It's not rocket science, people. It's basic math.
I would also like to point out that, at least in my kids' school, this is not the only method that is taught. Kids are also taught borrowing and carrying, and they are encouraged to use whatever method is more comfortable for them. There are many kids whose analytical minds thrive with the shortcuts that borrowing and carrying provide. But, thanks to this mathematical foundation, they also understand exactly why they cross out that 2 and make it a 1, and why that 1 gets tacked on next to the 6 to make 16. And the kids who are not mathematically-minded, whose minds work better with pictures and space, they finally have a method that embraces their way of seeing the world and gives them an effective strategy to solve difficult problems in a linear way.
The great thing is that the beauty of this method goes beyond basic subtraction. By learning to separate numbers into their individual parts and whittle each part down to its simplest form, it becomes a stepping stone to higher math, allowing them to not only understand how to get to the right answer, but understand why it is the right answer.
So please, please stop complaining, people. Before you mock something, take the time to truly understand it and the reasoning behind it. It might not be as bad as you think.
