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Yeah, that would work for me as well (although that first solution looks to me pretty much common core, just reversed).
I suspect this all grew out of some PhD in Education writing their thesis on, "Why Johnny can't carry a 9". Then (as is often the case), they choose the worst solution.
TTFN - Kent
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It seems to me that those of us who are really good at mental arithmetic have always solved problems differently depending on context. The reality is that we rarely use long subtraction, but use all manner of shortcuts. It's a little like programming: We take a first look at the problem; determine a method, based on experience; we implement. As we learn new tricks and put them into practice we add them to our list of methods, sometimes replacing old ones (I still, rarely, use DOS batch file coding!)
The trouble with teaching maths using that approach is that kids need to start learning one way. If an experienced maths teacher says that they found it easier to teach this way, I'd take his word for it. Bad explanations and bad examples only serve to reinforce our prejudices ("That's not how I was taught to do it!") As programmers, I would hope that we'd be open to consider new techniques?
I do think that there is merit in learning the "granny" method too, because sometimes the "simpler" tricks break down and the problem is too complex to solve with a hack!
Life is like a s**t sandwich; the more bread you have, the less s**t you eat.
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So here's an other idea. Teach the reasonable algorithm, and then actually explain it. Wow! Shocking, I know. I bet no one thought of that.
It is after all not that hard to see why it works and what you're doing. If students didn't get it, it's because no one explained it.
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The problem with this system is that it works for subtraction and it is very easy, probably easier then the traditional carry method we all learnt. But that is it. It ONLY works for subtraction. The multiplication method is different, division is different.
In other words common core ignores what is common.
A + B = C --> C - A = B & C - B = A
A x B = C --> C / A = B & C / B = A
And as soon as you move into negatives, algebra and real geometry it's useless.
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Presenting a reasonable, rational argument? Do you belong on the Internet? 
Yeah, I was thinking of it in isolation (where I still think as a first method it makes more sense than the traditional method). However, as you point out, other than in isolation it doesn't make sense. Plus - as others have pointed out - this is being taught to older kids who supposedly have already integrated the older method, confusing them. Definitely makes less sense to me now.
Fortunately, no kids in the system.
TTFN - Kent
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Kent Sharkey wrote: Or in other words, it's preparing them for their likely future life as a McD clerk.
This is the real problem - education not for education's sake, but to become a good little worker/consumer in later life.
Alberto Brandolini: The amount of energy necessary to refute bullshit is an order of magnitude bigger than to produce it.
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My kid was taught lattice multiplication in the common core ciriculum, a technique some 700 years old. It required the abiliy to draw neatly, something my 3rd/4th grader could not do (neither can I) and he got the wrong answer 8-9 times out of 10,because of this inability to draw neatly. Doing long multiplication the tradional way he got the right answer 8-9 times out of ten. When I queried his teacher about this rediculous method, she replied "Gee, I don't really understand it either, but I'm required to do this now.".  
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment
"Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst
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My son's just started 6th grade.
We are constantly emailing his math teacher with WTF's.
He constantly writes back, "Yes, this new way is confusing, but..."
If it's not broken, fix it until it is
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They're teaching this in grade six?  Doesn't that mean that they're now trying to override the way they already learned? Then that definitely doesn't make sense.
TTFN - Kent
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No one said it made sense
If it's not broken, fix it until it is
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Kent Sharkey wrote: Doesn't that mean that they're now trying to override the way they already learned?
Yes. One of the biggest problems in the US is the constantly changing curriculum requirements. This means that what you taught in 6th grade might be re-taught in 7th, or that the new 7th grader is expected to have been taught something different in 6th grade as a the basis for what they are going to learn in 7th grade. My son, who was getting a math-teaching degree at SUNY New Paltz, explains that the curriculum can literally change 2 or 2 times in a school year.
Furthermore, because of "No child left behind" and other rubbish (and we can't blame Bush, the tenets of NCLB goes back to the 50's, if not earlier actually) the teacher MUST teach to the curriculum, paced at whatever some bureaucrat decided, because the teacher is graded on how the kids score, so teaching does nothing more than attempt to teach how to pass a test.
Every teacher I've talked with hates this system, but what do you expect from a curriculum that was decided in a national conference where all the decision makers were business people, and only one, yes one, I kid you not, teacher was invited to said conference.
This country is so FUBAR. Sadly, when I talked to a couple college kids from France, they say their educational system is even worse!!!
Marc
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Marc Clifton wrote: Yes. One of the biggest problems in the US is the constantly changing curriculum requirements. This means that what you taught in 6th grade might be re-taught in 7th
Marc Clifton wrote: My son, who was getting a math-teaching degree at SUNY New Paltz, explains that the curriculum can literally change 2 or 2 times in a school year.
That's exactly the kind of stuff that the common core is supposed to get rid of.
A lot of the districts get locked into proprietary systems for curricula and tracking progress, which puts a lot of limits on teachers. The foundation I work for is working on getting all states to adopt a common data standard for student level data, so that they can be freed from vendor lock-in along with fixing many other common woes.
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Andy Brummer wrote: The foundation I work for is working on getting all states to adopt a common data standard for student level data,
How can you do that with the amount of cultural and economic diversity that is found, not just among different states, but among schools within a state?
Marc
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It's a beast of a standard. For example there are many ways to calculate attendance. By class, for a particular homeroom class, minimum number of hours per day, etc. However there are a limited number of fields required to enable all those calculations. The standard has all the fields and leaves the calculation up to the district.
There are a number of different areas, like discipline, attendance, grades, household information. Each one is a related sub-standard. Then there are extensions which are not official but can be shared between implementations and depend on the core standards.
It doesn't give 100% abstraction, but we've had vendors estimate that it saved them 80% of their mapping effort between states, which is huge. Here's the standard's website: http://www.ed-fi.org/[^]
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Also, here is another school that the foundation funds that addresses the curricula issue in a completely different way:
Quote: The School of One’s mission is to provide
students with personalized, effective, and
dynamic classroom instruction customized to
their particular academic needs, interests, and
learning preferences.
To organize this type of learning, each
student receives a unique daily schedule based
on his or her academic strengths and needs.
As a result, students within the school can
receive profoundly different instruction. Each
student’s schedule is tailored to ability and
to the ways he or she learns best. Teachers
acquire data about student achievement each
day and then adapt their live instructional
lessons accordingly.
School of one NYC[^]
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Marc Clifton wrote: Every teacher I've talked with hates this system, but what do you expect from a curriculum that was decided in a national conference
I think that's a large part of it. Teachers hate it and students will also as it is incorporated, but this is the way to force more national standards -- central control -- upon every little city out there. Plus this way we can teach all the children to pull the same levers. "I hear and and obey..."  No need for thinking, that's for the smart people.
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Well maybe it's good for exposing kids to different techniques for doing calculations, especially if they want to do sums in their head, as there isn't one perfect easy method for every sum (with the obvious exception of using a calculator). It's better knowing a few methods of reaching the answer and choosing the best one, rather than knowing only one method and attempting to use it for everything.
With the example from Kent Sharkey's link 325 - 38, in my head I would do this:
38 + 2 = 40
40 - 25 = 15
300 - 15 = 285
285 + 2 = 287
Maybe it's a little strange, but as I don't do a lot of mental arithmetic I adjust the numbers so I can add or subtract easier while keeping the quantity of intermediate numbers I'll have to remember to a minimum.
I also like to do division in my head in a similar fashion, but that's more recursive and to get an accurate answer I have to remember a bunch of numbers along the way, probably best just to use a calculator.
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Hmmmm... 38 - 25 = 13 , and 100 - 13 = 87 , so 287 .
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I'd do 300 - (38 - 25) without even thinking about it.
The common core method is not something that should be taught. It is something that should be learned via the ah-hah moments that occur inside your head when you get a good handle on arithmetic. If you understand numbers, the tricky methods will come naturally.
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Well of course. But for me 38 - 25 takes more effort than fiddling the numbers in my head, either by adding or subtracting to reach easier to work with numbers, or breaking it down into smaller sums, for example ((30-20) + (8-5)) (although that requires me to remember more numbers at a time).
If I had to do mental arithmetic more than few times a month (beyond counting change) than perhaps I'd have an easier time with it.
I'd also like to point out that I don't sit there and think "Perhaps if I add two or three here, and then..." the route to the answer comes without much thought.
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I was going to pipe up with the same explanation that everyone else did, It's a good way to do subtraction in your head. I learned that and more as a child. The common core doesn't seem that weird to me, but it sucks that they don't have any physical materials to work with like I did.
For example this is one way I learned multiplication:
Checkerboard[^]
This is what I worked with for addition:
Bead frame[^]
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I can't watch YT videos at work... oh the tease! 
Jeremy Falcon
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I think they are trying to bring back magic in our cold dry intellectual world! 
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I think that is stupid way to do math. Sorry, but that is how I feel.
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No need to apologize man. I like the premise personally, I just don't particularly see how the implementation is good.
Jeremy Falcon
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