In my experience, parents complaining about “why do kids have to learn this garbage? We never learned it when I was kids, why can’t we just do things the way I learned!” almost always don’t actually remember any of what they themselves were taught in school, and often were in fact taught the same methods.
That may be, but doesn’t answer the question when MY kids ask why they have to do it this way, when just subtracting it is easier.
Reading this thread I realize that’s the way I’ve always done addition and subtraction in my head. I can’t imagine using the carry method without writing the problem down. I wasn’t taught this, it just seems the natural way to do it.
“Just subtracting” isn’t easier. What the heck do you mean by “just subtract”? How do you do that? What you think of as “just subtract” is a specific method, and you have to learn how to do that method, just like you have to learn any other method.
By the way, how did people do subtraction before “New Math”? Isn’t all that borrowing stuff part of that? I seem to recall somebody showing me a different method from their halcyon days of yore, but I can’t remember what it was.
They’re forced to sometimes, often with great difficulty. One time I was buying lunch and the total came to $7.87. I pulled a 20 out of my wallet and reached into my pocket to give the cashier 12 cents, but when he saw the $20 bill he already entered that into the register.
What happened next was pretty hilarious. He ended up handing me $13 in bills and some coins that didn’t total 25 cents. I just kept $12.25 and gave him back the rest.
This, I hope, means you are not a math teacher. 
As a real live math teacher, I will attest that the point to being a teacher is to help students learn mathematical tools for solving problems. Which tool a student uses will be dependent upon what they find easiest and best to use in a given circumstance. I gave the example in a different thread recently of a problem that can be solved with anything from guess-and-check to calculus; certainly a fifth-grader would not use calculus to solve it, but a first-year college student might.
In the problem referenced in the OP, this is a typical example of someone trying to throw shade at the Common Core (has nothing to do with “new math” really). Ignoring the mistake of not using “12 + 3 = 15” as the first step, it’s a fairly common way to solve a subtraction problem, especially if you don’t happen to have pen and paper handy. But, as is often the case with criticisms of the Common Core, it picks a problem that is more easily solved (for most people) using column subtraction (since no borrowing is required), and seems to over-complicate the problem.
We can see, however, the value in the method if we pick a slightly different problem, say, 32 - 14. Now, to solve it with “normal” methods requires properly computing a “borrowing” operation. You’d be surprised how many students have trouble doing a simple borrow in a subtraction problem, including honors-level high school students (who are, after all, used to plugging simple things like this in a calculator). If I was teaching this alternate method, I might suggest actually doing 14 + 6 = 20 (it’s much easier for students to get to “10s” than “5s”). But I would ALSO teach a method that would involve making 32 go to 34, then relating that to 20 (so 34 -14 is 20, and this is two less than that, so it’s 18). AND I’d be teaching regular column subtraction (borrow ten from the 3, making it a 2, etc.). And I can think of one or two other easy methods one can teach to accomplish this simple goal.
Why bother teaching all of those methods? Well, suppose that instead of the simple 32 - 14 problem, the problem is 3252 - 1524? Or suppose that the problem is $32 - $14, and you are in a hurry, and don’t have pen and paper handy, and want a good estimate? Other examples can be thought up. The point is that a good mathematician has multiple tools available to work out problems, and is taught how to use those tools effectively. This problem in the OP is an example of the teaching of one such tool.
Why does this sort of teaching method get such stick from parents? Well, there are in my experience two reasons. First, most parents aren’t in the possession of more than one or two tools themselves, so they don’t realize what’s being done has value down the road. They focus on the fact that the problem seems over-complicated and they are unfamiliar with how to help the child resolve it. Second, most elementary teachers are math illiterate, and don’t themselves understand the what of what they are doing, let alone the why. They simply follow some rote algorithm they’ve learned, and apply it in all sorts of ways it shouldn’t be applied. This results in the sort of problem that has become a meme of its own: the Common Core problem (as if the standards of the Common Core require stupid problems!).
As for “new math”, as a child of the 60s, I was taught “new math.” And to this day I am thankful for that fact, because as a result of that teaching I have a very good understanding of set theory (a fundamental underpinning of the “new math”). That stood me in good stead when I was trying to learn higher-order mathematics later in my life, which was the whole POINT to “new math”: to try and give our students a leg up when they eventually got into doing math that required an understanding of set theory. Of course, that turns out to be something like 1% of the population at most, and one does wonder about the tail wagging the dog at that point… :dubious:
Here’s the disconnect “old people” have with “Common Core” math: the why.
I suspect most of us were taught the old, “traditional” way, which was:
[ol]
[li]Here’s a problem.[/li][li]This is how you solve this problem.[/li][li]Here’s a ditto with similar problems that can be solved the same way.[/li][li]Now you do these problems.[/li][li]You have now learned this math.[/li][/ol]
Stupid kids never got it. Smart kids got it immediately or already knew it. Everyone else learned it only long enough to pass the associated test, then it was instantly forgotten.*
In most cases, at no point was “this is why we do it this way” part of the lesson. Either you learned it their way, you figured out another way on your own, or you just didn’t learn it. All of this “Common Core” stuff that frustrates and confuses those of us who learned it the other way (or didn’t) is simply attempting to give kids the tools to figure out the best method, for them, to solve problems, and the way to give them these tools is to peel back the cover and show them the guts of what’s in the math. This takes longer in the early years, but it pays off later when you don’t need to re-teach basic arithmetic and simple mathematical concepts to everyone all over again at every level.
- Apologies for using the terms “stupid/smart kids.” I’m aware everyone has different abilities and just because one is or is not instantly proficient in math does not necessarily mean they are “stupid” or “smart,” but it was merely the simplest way to describe what I was trying to explain.
One of the issues I’ve had with Common Core math instruction is that it graded kids on mastering all these multiple ways to do things, rather than offering kids a toolkit of methods and only grading on correct answers. Common Core attempts to explicitly teach calculation methods that, IMHO and with no cites, people either grok intuitively early on or never will.
Also IMHO and no cites, but anecdotal to my personal experience: The mental-math methods of people that are whizzes at calculation (chiefly +, -, x, /) are generally non-transportable between people. Whizzes see patterns in numbers with barely any explicit teaching/learning of these patterns.
pulykamell, if I recall correctly it was something like:
458
-279
You can’t take 9 from 8 so instead pretend that instead of 8, you have 18 and do 18-9 to get 9 and carry the one forward.
Now we have to either reduce the 5 by 1 or increase the 7 by 1, either way you get the same answer: (1)4-7 or (1)5-8 is 7. Carry the one forward.
Reduce the 4 by 1 or increase the 2 by 1 to get 1.
It’s not dissimilar from the standard method but I can see how to a young student, it looks more opaque in terms of what you’re actually doing with the numbers. In fact it’s really not different at all so Tom Lehrer’s New Math song is even more hilarious in that it’s basically making up a reason to get upset.
Common Core itself does not call for grading kids on mastering all of the methods. Common Core just requires that students be able to do the problems somehow or other. Now, some teachers might grade students on being able to do all of the methods, but that’s a problem with those teachers, not with Common Core.
Answering my own question, I think what I remember seeing is what’s called “The Austrian method.” I believe this is it.
Then Common Core mathematics, in my locale, was consistently taught incorrectly.
The point would almost be moot now – Common Core was whisked away here after a few years – but lots of Common Core materials and tests still get distributed. Again, though, a local issue.
Of course it’s easier than doing it the way shown in the original OP.
I don’t care if that is Common Core, or New Math, or whatever. It’s easier and faster to use the “borrowing” method, for lack of a better term, then it is to draw boxes and put numbers in, then add the numbers and such.
Are we talking about the old New Math or the new New Math? 
I born in 1963, and was taught the method with borrowing ( which was explained to me as “borrowing from tens place to put it in the ones place”). My daughter was taught a different way ( which I didn’t complain about) but the funny thing was my mother would try to help my daughter with her homework and get frustrated , and say all that stuff about why do they have to learn this garbage. I would then look at what my mother did and say “What the hell was that?” I can’t even remember what it was, it was so alien to me. There was much more of a difference between how I was taught and how my mother was than between me and my kids. And I have a h better sense of math than people just a few years older than me. For example, a few years ago I was involved with a program that ran for 30 days and had 100 slots. We were talking about how many people we could serve if we lengthened the program to 45 day. I said “around 800” and the others in the meeting (who were about ten years older than me ) couldn’t figure out how I could do that in my head. I explained, but the explanation took longer than it took me to figure it out.
A lack of this "math sense" is also the reason you will see cashiers get flustered when the enter $100 as the amount tendered rather than $10 and can't figure out how much change to give you when the cash register say you are supposed to get $95.46 in change. Someone who understands how it works will just give you the $5.46 without really thinking about itThe drawing boxes and putting numbers in is part of teaching the method, and unless you limit yourself to only that specific example given in the OP there’s no “of course” its easier unless you fundamentally misunderstand what’s involved in both methods and the teaching of them.
How about doing 3000-2999? Is that easier using the old method? Or did you unconsciously use the new method?
How about 3000 - 2780? Isn’t “That’s 20+200 = 220 away” faster than “I’ll borrow from the 3 so make that 2, then borrow from that again so that’s 9, and so that’s 29(10)0 - 2780, Which is 220”?
How about you need to do 14375 - 5386? How would you check your answer afterwards?
I used the “I know it’s 1” method.
I noticed you didn’t draw any boxes and write numbers in them and then add the numbers.
I actually use the “What number added to 6 makes 15, carry the 1 and so on” method. But I found that hard to explain how to do. Still faster than drawing boxes, writing numbers in them, then adding the numbers up, and then subtracting or whatever. Anything is faster than that.
You’re correct. Your way is the best way and the simplest. There is no possible greater depth of understanding that could be gained from showing children different methods of adding and subtracting. Teachers have children do this because they are cruel and vicious and it pleases them to actively hinder the child’s ability to do math. There is no pedagogical value in anything you don’t immediately understand, manson.
What’s really an amazing coincidence here is that the method that manson learned, that he has been using his entire life, is a method which… and get this, because it’s really quite surprising… he can do better than he can do other methods! Gosh, what a tremendous surprise!