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 Topic: Teaching addition to 6 year olds-Doubling, anyone know what this is about? < Next Oldest | Next Newest >
blipey

Posts: 2061
Joined: June 2006

I thought I might run this by the smart people--or the peanut gallery, whichever.

My nephew, who is 6 years old, flunked his math test and I'm not sure why.  They are teaching them to add by doubles.  Does anyone know what this is about?  Now, I got this story from my sister, so I have not seen the test or the teacher's comments.  But, this is what I gather is the case.

Wen asked what 5 + 7 =, he wrote down 12.  This is wrong.  You apparently need to double the smaller number and then add the remainder.  So you would get something like this written down for the proper answer:

5 + 7 = 5 + 5 + 2 = 12

Why would you teach anyone to add in this way?  You are introducing the concept of subtraction into teaching the concept of addition: 5 + 7 = 5 + 5 + (7-5) = 12.

This concept apparently works for other things as well: 3 + 8 = 3 + 3 + 5 = ?  Do you have to break that down to 3 + 3 + 3 + 2 = 11?

When I was told this the only thing that tickled my brain was they were trying to introduce factoring in some way or something because that's not quite right either.  It was baffling to me.

Can anyone tell me what I'm missing and why this concept would be used to teach addition.  Or even if this is a common approach to teaching addition these days?

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But I get the trick question- there isn't any such thing as one molecule of water. -JoeG

And scientists rarely test theories. -Gary Gaulin

carlsonjok

Posts: 3326
Joined: May 2006

 Quote (blipey @ Sep. 25 2007,13:30) I thought I might run this by the smart people--or the peanut gallery, whichever.My nephew, who is 6 years old, flunked his math test and I'm not sure why.  They are teaching them to add by doubles.  Does anyone know what this is about?  Now, I got this story from my sister, so I have not seen the test or the teacher's comments.  But, this is what I gather is the case.Wen asked what 5 + 7 =, he wrote down 12.  This is wrong.  You apparently need to double the smaller number and then add the remainder.  So you would get something like this written down for the proper answer:5 + 7 = 5 + 5 + 2 = 12Why would you teach anyone to add in this way?  You are introducing the concept of subtraction into teaching the concept of addition: 5 + 7 = 5 + 5 + (7-5) = 12.This concept apparently works for other things as well: 3 + 8 = 3 + 3 + 5 = ?  Do you have to break that down to 3 + 3 + 3 + 2 = 11?When I was told this the only thing that tickled my brain was they were trying to introduce factoring in some way or something because that's not quite right either.  It was baffling to me.Can anyone tell me what I'm missing and why this concept would be used to teach addition.  Or even if this is a common approach to teaching addition these days?

My first reaction was that it was completely retarded.  But, on second thought it almost looks like they are not trying to make learning addition easier, so much as teaching addition in a way that makes the leap to multiplication and division easier.  I am not sure how to articulate it better.  But the idea of doubling (or tripling as your 3 + 3 + 3 +2 = 11 would imply) seems like a twist on how I learned multiplication (as a complex set of additions).  And the idea of a remainder seem obviously pointed at the basics of division.

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It's natural to be curious about our world, but the scientific method is just one theory about how to best understand it.  We live in a democracy, which means we should treat every theory equally. - Steven Colbert, I Am America (and So Can You!)

blipey

Posts: 2061
Joined: June 2006

Yes, the thought of making the leap to multiplication was my first thought as well (at least it tied with retarded).  But the more I thought about it, the less I got it.  Sure, it sets up multiplication, but at the expense of actually being able to learn addition.  It also seems that you are teaching addition by introducing concepts that would not have been learned yet (subtraction).  It still doesn't make a lot of sense to me.

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But I get the trick question- there isn't any such thing as one molecule of water. -JoeG

And scientists rarely test theories. -Gary Gaulin

carlsonjok

Posts: 3326
Joined: May 2006

 Quote (blipey @ Sep. 25 2007,16:22) Yes, the thought of making the leap to multiplication was my first thought as well (at least it tied with retarded).  But the more I thought about it, the less I got it.  Sure, it sets up multiplication, but at the expense of actually being able to learn addition.  It also seems that you are teaching addition by introducing concepts that would not have been learned yet (subtraction).  It still doesn't make a lot of sense to me.

Third thought:  Definitely retarded.  It makes no sense to teach someone to do one addition by a method that involves two additions and one subtraction.

[Cranky old man]

What the hell are they teaching kids in schools these days?!?!?1?one?  I learned addition on an abacus (for serious) and, by golly, if it was good enough for me, it is good enough for those whippersnappers!!!1!!1!

[/Cranky old man]

Okay, I'll return to the peanut gallery and hope a smart person comes along.

Added in edit: Teaching addition by subtraction is what  would best be described as Enron arithmetic.

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It's natural to be curious about our world, but the scientific method is just one theory about how to best understand it.  We live in a democracy, which means we should treat every theory equally. - Steven Colbert, I Am America (and So Can You!)

swbarnes2

Posts: 78
Joined: Mar. 2006

 Quote (blipey @ Sep. 25 2007,13:30)

Weird.

When I was 6, I would have done it:

5+7 = 7 + (3 + 2) = 10 + 2 = 12.

That I think is a decent way to think about it: that it doesn't matter how you group the additions, as long as everything ends up in, so you can group them in such a way to make the addition easier.

The thing with that doubling way is that you would never use it when adding two 2-digit numbers.  In two years, the strategy won't be helpful.

BWE

Posts: 1902
Joined: Jan. 2006

Tom Lehrer New Math Lyrics:

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Who said that ev'ry wish would be heard and answered
When wished on the morning star
Somebody thought of that, and someone believed it
Look what it's done so far

The Daily Wingnut

stevestory

Posts: 13407
Joined: Oct. 2005

From looking around the internet a bit, it looks like the answer may be the following: Kids are first taught how to add 1 and 2 to numbers, then they learn to double small numbers. 1+1=2, 2+2=4, 3+3=6, etc. So breaking the smaller number out of the larger number turns every problem into doubling and adding small numbers.

Ftk

Posts: 2239
Joined: Mar. 2007

 Quote So breaking the smaller number out of the larger number turns every problem into doubling and adding small numbers.

That's pretty much it.  My youngest learned this way initially, and then he also had to memorize all his addition and subtraction facts.

They started out memorizing their doubles and then they'd "double plus"...

So 5+7= 5+5+2, because they know 5+5=10 and you count up 2 from 5 to 7.  So the sum = 12.

or...

6+9= 6+6+3, because they know 6+6=12 and you count up 3 to get from 6 to 9. So the sum = 15.

I think it just helps them think about it from a different perspective.  It's helpful to some and others prefer to toss them off by memory.  Like I said, he learned both.

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"Evolution is a creationism and just as illogical [as] the other pantheistic creation myths"  -forastero

stevestory

Posts: 13407
Joined: Oct. 2005

 Quote (swbarnes2 @ Sep. 25 2007,18:25) [quote=blipey,Sep. 25 2007,13:30][/quote]Weird.When I was 6, I would have done it:5+7 = 7 + (3 + 2) = 10 + 2 = 12.That I think is a decent way to think about it: that it doesn't matter how you group the additions, as long as everything ends up in, so you can group them in such a way to make the addition easier.The thing with that doubling way is that you would never use it when adding two 2-digit numbers.  In two years, the strategy won't be helpful.

carlsonjok

Posts: 3326
Joined: May 2006

 Quote (stevestory @ Sep. 25 2007,21:25) I'm not sure why the one technique I never use in my head is lining the numbers up as you would on paper. Maybe because you have to remember both the completed digits and the carry while doing the next column?

With an abundant supply of empties, why would you ever have to do arithmetic in your head?

HAR HAR. THIS IS YOU DOING THE MATHS.

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It's natural to be curious about our world, but the scientific method is just one theory about how to best understand it.  We live in a democracy, which means we should treat every theory equally. - Steven Colbert, I Am America (and So Can You!)

Ftk

Posts: 2239
Joined: Mar. 2007

ROTFL....!

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"Evolution is a creationism and just as illogical [as] the other pantheistic creation myths"  -forastero

Richard Simons

Posts: 425
Joined: Oct. 2006

I agree that the procedure does seem a little odd, but what gets me is that a correct answer, found by a correct method, was marked wrong.

I am currently teaching basic mathematics, up to about Grade 9, to adults and one thing I stress to them is that very often there is more than one correct way of solving a problem, although one may be preferred (most people find it easier, it tends to result in less mistakes, it leads on to more advanced techniques, etc). Unless the question called for a specific method, I mark as correct any valid method that gives the correct answer.

Marking a correct answer as wrong is a sure-fire way to cause a learner to lose interest in the subject.

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All sweeping statements are wrong.

stevestory

Posts: 13407
Joined: Oct. 2005

Quote (carlsonjok @ Sep. 25 2007,23:08)
 Quote (stevestory @ Sep. 25 2007,21:25) I'm not sure why the one technique I never use in my head is lining the numbers up as you would on paper. Maybe because you have to remember both the completed digits and the carry while doing the next column?

With an abundant supply of empties, why would you ever have to do arithmetic in your head?

HAR HAR. THIS IS YOU DOING THE MATHS.

When I'm on the floor like that, the bottles tend to have way less CSI.

stevestory

Posts: 13407
Joined: Oct. 2005

Are those bottles mostly Harps? If so, I approve.

Edited by stevestory on Sep. 26 2007,00:28

blipey

Posts: 2061
Joined: June 2006

 Quote (Richard Simons @ Sep. 25 2007,23:20) I agree that the procedure does seem a little odd, but what gets me is that a correct answer, found by a correct method, was marked wrong.I am currently teaching basic mathematics, up to about Grade 9, to adults and one thing I stress to them is that very often there is more than one correct way of solving a problem, although one may be preferred (most people find it easier, it tends to result in less mistakes, it leads on to more advanced techniques, etc). Unless the question called for a specific method, I mark as correct any valid method that gives the correct answer.Marking a correct answer as wrong is a sure-fire way to cause a learner to lose interest in the subject.

I agree with this.  I don't know if the paper required him to add using the doubling method or not.  If it did, I understand the marking, but that method of teaching really gets on my nerves.  As you said, there are usually multiple ways to learn a subject and requiring everyone to use the same method is not a healthy educational method in my opinion.

My brain does wrap around the idea of doubling as a method for addition, but I still don't see its overall usefulness as THE METHOD for learning addition.  Perhaps it is not though.

@ Ftk:

That was a better description of methodology than I got from my sister, thanks.

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But I get the trick question- there isn't any such thing as one molecule of water. -JoeG

And scientists rarely test theories. -Gary Gaulin

Ftk

Posts: 2239
Joined: Mar. 2007

Blipey,

I'm of course guessing, but I'd bet the teacher told them that she was looking for them to answer the equations in a double plus format.  My kid's teacher was pretty specific about that.  I can't imagine she'd just count it wrong even though the answer was correct, unless she was asking for this format specifically.

As Steve mentioned in his post above, there are many ways to get to the sum of an equation, and I believe this gives them practice in this respect.  I doubt she's insisting that this is the only way that it can be done.

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"Evolution is a creationism and just as illogical [as] the other pantheistic creation myths"  -forastero

improvius

Posts: 807
Joined: Jan. 2006

 Quote (Richard Simons @ Sep. 26 2007,00:20) Marking a correct answer as wrong is a sure-fire way to cause a learner to lose interest in the subject.

I tend to agree.  I always excelled at math, but I would frequently get points taken off for "not showing my work" (which I did mostly in my head).  Eventually I lost interest, though I can't say for certain if or to what extent I was put off by that kind of grading.

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 Quote (afdave @ Oct. 02 2006,18:37) Many Jews were in comfortable oblivion about Hitler ... until it was too late.Many scientists will persist in comfortable oblivion about their Creator ... until it is too late.

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