Best method to add and subtract (Common Core-ish) What's the best method for adding and subtracting?
I have a son in the third grade so as a parent I'm smack dab in the middle of the common core debate (I'm hoping to avoid the Facebook politicization of Common Core and have a more "maths" oriented discussion). I recently came across this: This is math on Common Core
I was taught to borrow and carry but I don't think I ever used that method, except in elementary school when I was forced to show my work. I would do that problem like this:

$243-87$:
$243 - 80 = 163, 163 - 7 = 156$

My gut instinct is that carrying/borrowing is probably the single worst method in terms of computational speed, accuracy, and effectiveness at teaching number sense.
But then I started to wonder about the "Common Core" method in the image. It seems slower, but it does do a good job of teaching intuition about the distance between the numbers so it might be good for developing your number sense. (I put Common Core in quotes because that's not how my son is being taught to do math at his school, which does follow Common Core).
So what do you all think is the best method for doing arithmetic in terms of speed, accuracy, and developing number sense? (Obviously I'm leaving it up to your discretion in terms of how to weight these factors)
 A: I think the common core is not completely deserving of the criticism heaped upon it. As you point out, the methods focus on teaching intuition about numbers and arithmetic. The old methods of teaching arithmetic focus on teaching algorithms--a procedure by which any arithmetic problem can be solved on paper, even if it takes a long time to carry out in one's head. I think this is because until the last several decades, if you wanted to solve an arithmetic problem, no matter how hard, you had to do it by hand. These days, we can let computers do the tough calculations, the important thing is to be familiar with numbers, to be able to interpret them. We should know when an answer to an arithmetic problem seems reasonable.
I'm not saying that people shouldn't learn arithmetic. Only that it is no longer important to memorize algorithms for performing arbitrarily difficult operations from a young age. The human brain is not good with algorithms. The human brain is good at turning a problem into something familiar, almost palpable, and then manipulating it to find a solution. The common core, I think, aims to help students develop mold their problem solving skills in a natural way by showing them intuitive ways to solve problems. The intent is not that students will always do mental math the way they learned it in 3rd grade, but that what they learn in 3rd grade will make them familiar enough and comfortable enough with numbers to find their own best methods of problem solving.
I don't know anyone who solves simple arithmetic problems like the 243-87 in their head using the algorithms that I learned in elementary school; we develop our own methods similar to what the common core teaches. The common core just helps students develop these methods faster. I don't think that the creators  of the common core would claim that the method described in your problem are the fastest or best, just that students are exposed to this and other intuitive methods of problem solving so that they can develop the best and fastest method for their own minds. The best method for doing arithmetic in terms of speed, accuracy, and developing number sense is to do thousands of arithmetic problems in your head. Your brain will naturally figure out the best way.
