Here.
Conservatives say that ‘new math’ (Common Core math, whatever) is ridiculously complicated. Not being a conservative, and not having children, I don’t know.
What is the process going on in the ‘new math’ problem in the link? I only know the old way.
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The goal is to break the second number up into chunks that are easy to add on to the first number. 37 becomes 5+2+10++10+10, because it’s easier to do arithmetic is your head that way. You can see the numbers increase by those amounts below. It’s a handy skill.
I think that process is somewhat analogous to the way cashiers count out change (if they ever actually do that anymore, what with today’s modern cash registers that compute the change for you).
ETA: See also: New Math by Tom Lehrer. “It’s so simple – so very simple – that only a child can do it!”
So it’s long addition?
I use that technique to do addition in my head sometimes. I’m not sure why 7 has to be broken up into 5 + 2 though.
You pick up this real fast the first time you count change as a cashier. Yeah, registers today tell the cashier what change to give, but way back when you learned to count in blocks of 1, 5, 10, and 25. Knuckleheads who had trouble with 53+37 of course would have trouble with 53+(30+7) cause hey, it looks harder.
that’s because “conservatives” are a bunch of cranky old white people who think the way things were when they were kids was absolutely 100% perfect and should never change ever.
anyway, when I looked at it I had no clue, but after reading BetsQ and Senegoid’s posts I got it. It’s just an alternative representation of addition. there’s no “one true way” to do it.
I see.
But it’s more cumbersome and harder to do in your head than just adding the numbers together.
I get it now. But holy fuck! Really?
It’s like programming in hexadecimal.
The idea is to understand what you’re doing not necessarily to get the right answer.
It’s not about learning one way to do it. It’s about learning how to do it in seemingly different ways (that basically are all the same but only appear to be different). Some people learn in different ways. For me, differential calculus made little sense to me until I learned integral calculus the next semester. Somehow a light went off in my head and it then made perfect sense, but it took looking at it in a different way for that to happen.
I’m not convinced that teachers know how to teach any of these new-fangled methods so’s they make any sense. Maybe some do. I get the impression that a lot of them are just teaching a rote method (so what’s new?) instead of explaining any mathematical theory of how and why it works (and even if they did that, it would be controversial if that’s the way math oughta be taught).
Have any of you seen that new-fangled method of multiplying two two-digit numbers, sometimes called the “area method” or the “proportional area method”? I understood it instantly when I saw it (having been a math major at college), but it’s not at all obvious that it should make much sense to a 2nd-grader or whatever grade they teach that. I’ve seen some tutorials on-line, and one lengthy video (sorry, can’t find it now; maybe I’ll try some more) that droned on and on and never really said anything clearly.
NONE of the tutorials, discussions, or videos even so much as mentioned the underlying rock-bottom-basic mathematical principal that makes it work.
It’s nothing more than repeated application of the Distributive Law of Multiplication With Respect to Addition, illustrated by drawing some rectangles, fercrissakes. Don’t they teach that any more?
You missed my ETA at the end of Post #3, didn’tcha?
Yeah, I got called away while I was writing the post.
Sometimes a “trick” can look a lot harder and messier but actually be easier.
I learned a “trick” for squaring any two-digit number in one’s head. (Not necessarily quickly, in my case, but one can become proficient with practice.) But note how messy it looks at first glance:
We start with the formula from algebra: ( a + b )[sup]2[/sup] = a[sup]2[/sup] + 2ab + b[sup]2[/sup]
Now, suppose we want to figure 67[sup]2[/sup]
Think: 67[sup]2[/sup]
= ( 60 + 7 )[sup]2[/sup]
= 60[sup]2[/sup] + 2(60)(7) + 7[sup]2[/sup]
= 3600 + 840 + 49
= 4489
(Yes, I did that in my head before I wrote it out here.)
It looks messy, but note that it breaks the computation down into pieces in a particular way that seems easy to keep all the pieces in your head at once. I find it helps to work out and add up the pieces in the opposite order:
7[sup]2[/sup] + 2(60)(7) + 60[sup]2[/sup]
= 49 + 840 + 3600
= 4489
(The trick, of course, is to understand what you’re doing and get the right answer ! )
no, it’s just a different way than you were taught. Hopefully you don’t believe the way you were taught is the One True Way and there can never be anything as good or better.
I think it’s worth pointing out that despite what all too many otherwise conservative people (who somehow turn into the hippies at the Freedom School in “Billy Jack” when it comes to education) think, Common Core is a set of standards for what concepts should be mastered by what age. It says nothing about how those concepts should be taught.
None of these so-called “Common Core methods” have anything to do with Common Core.
I was trained in the ‘old way’ ( I’m in my late 40’s ), but honestly I think as explained above that is kinda how I do basic math in my head. I break down larger numbers into smaller chunks and then calculate them however they need to be calculated, then add the whole mess together. I suspect it is an approach that works better for some types of minds rather than others.
It always interests me how folks get to the same endpoint doing simple math in their head by different pathways. But not the actual math itself, because math doesn’t interest me at all ;).
Shouldn’t the answer be 01 30, or am I using too old a style?
It’s only more cumbersome and harder than the older technique (breaking up the digits by order of magnitude, adding them separately, “taking ones” or “carrying ones” as required) if you have already learned the older technique. But (a) for young children, learning the old technique is difficult, and is in fact impossible until you have achieved a certain capacity for abstract thought, and (b) many of them succeed in learning it by brute effort, and learn to apply it to get the right result while having no idea what they are doing, or why it produces the right result. And if that’s your objective, you can achieve the same result just by giving them all a pocket calculator and not teaching them any arithmetic at all.
The object of the new maths, as others have said, is to introduce children to techniques which will (a) produce the right result, and (b) foster an understanding of what they are doing.
See, though, I’m not very convinced that teaching the new methods actually necessarily accomplishes that, unless they are explained in a very clear and logical way, and I’m not certain that math teachers are actually taught to do that. Instead, they just demonstrate one method or another of doing a problem, and then imagine that the kids will just “see” it.
For example, I noted above that the new method of teaching multiplication (actually, all methods of multiplication more modern than Roman Numerals) are based on the Distributive Law. But is that ever explained or demonstrated? I never saw it done, even when I was learning to multiply. I don’t know that it’s being done with any newer “New Math” or “Common Core” methods. (Showing how it follows from the Distributive Law, that is.) Is it?
Are kiddies in the earliest grades even still taught the Five Fundamental Laws of Arithmetic any more?