In the United States most adults learned to add by simply adding two numbers and carrying over when necessary like this:
Now teachers have been told to teach other methods for adding.
Adding by decomposing (or taking apart) numbers is included in the countries Common Core Standards. With this method one of the numbers to be added is broken apart into chunks that are easier to add. For example:
Studies have shown that this method can aid students in learning to add larger numbers in their head.
In other countries, (like Brazil and India) kids are taught to add larger numbers in steps starting with the largest digit. For example in the problem 347 + 238 the hundreds column would be added first, then the tens column, then the ones column ( with one extra being added to the tens column because 7 + 8 = 15).
I never realized that there were other methods for adding until I became a teacher. Now I realize that parents are frequently confused when their child comes home and shows them how to add using a method they are not familiar with. Like may adults, I still choose to add the way I learned as a kid, but I see the value in teaching kids these other methods.