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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

(Permalink) Posted: 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 = 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?

--------------
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: 3324
Joined: May 2006

(Permalink) Posted: Sep. 25 2007,13:58   

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 = 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?

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.

--------------
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

(Permalink) Posted: 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.

--------------
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: 3324
Joined: May 2006

(Permalink) Posted: Sep. 25 2007,16:41   

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.

--------------
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

(Permalink) Posted: Sep. 25 2007,17:25   

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: 1898
Joined: Jan. 2006

(Permalink) Posted: Sep. 25 2007,17:35   

Tom Lehrer New Math Lyrics:
Quote

Some of you who have small children may have perhaps been put in the
embarrassing position of being unable to do your child's arithmetic homework
because of the current revolution in mathematics teaching known as the New
Math. So as a public service here tonight I thought I would offer a brief
lesson in the New Math. Tonight we're going to cover subtraction. This is the
first room I've worked for a while that didn't have a blackboard so we will
have to make due with more primitive visual aids, as they say in the &quot;ed biz.&quot;
Consider the following subtraction problem, which I will put up here: 342 -
173.

Now remember how we used to do that. three from two is nine; carry the one, and
if you're under 35 or went to a private school you say seven from three is six,
but if you're over 35 and went to a public school you say eight from four is
six; carry the one so we have 169, but in the new approach, as you know, the
important thing is to understand what you're doing rather than to get the right
answer. Here's how they do it now.

You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens,
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add them to the two and get twelve,
And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.

From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right.)
And so you have thirteen tens,
And you take away seven,
And that leaves five...

Well, six actually.
But the idea is the important thing.

Now go back to the hundreds place,
And you're left with two.
And you take away one from two,
And that leaves...?

Everybody get one?
Not bad for the first day!

Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!
Now that actually is not the answer that I had in mind, because the book that I
got this problem out of wants you to do it in base eight. But don't panic. Base
eight is just like base ten really - if you're missing two fingers. Shall we
have a go at it? Hang on.

You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones,
And you add them to the two,
and you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven.

Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours.

&quot;Sixty-four? How did sixty-four get into it?&quot; I hear you cry.
Well, sixty-four is eight squared, don't you see?
(Well, you ask a silly question, and you get a silly answer.)

From the three you then use one
To make eight ones,
And you add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four.
Now go back to the sixty-fours,
And you're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands.
One, that's right!
Whoever got one can stay after the show and clean the erasers.

Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to read math.
It's so simple,
So very simple,
That only a child can do it!

Come back tomorrow night. We're gonna do fractions.


--------------
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: 10127
Joined: Oct. 2005

(Permalink) Posted: Sep. 25 2007,20:56   

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

(Permalink) Posted: Sep. 25 2007,21:13   

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.

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

  
stevestory



Posts: 10127
Joined: Oct. 2005

(Permalink) Posted: Sep. 25 2007,21:25   

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.

There are several strategies for adding numbers that people use in different circumestances. If you're asked to add 65+37 you might group the 65 and 35 together to get 100, then add 2. If you're asked to add 87 and 97, you might temporarily add 3 to 97, then add 100+87, then subtract 3. If you're asked to add 27 to 48 you might add 20+40, then add to that 8+7. 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?

   
carlsonjok



Posts: 3324
Joined: May 2006

(Permalink) Posted: Sep. 25 2007,22:08   

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.


--------------
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

(Permalink) Posted: Sep. 25 2007,22:12   

ROTFL....!   :D

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

  
Richard Simons



Posts: 425
Joined: Oct. 2006

(Permalink) Posted: 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.

--------------
All sweeping statements are wrong.

  
stevestory



Posts: 10127
Joined: Oct. 2005

(Permalink) Posted: Sep. 25 2007,23:25   

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: 10127
Joined: Oct. 2005

(Permalink) Posted: Sep. 25 2007,23:27   

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

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

   
blipey



Posts: 2061
Joined: June 2006

(Permalink) Posted: Sep. 26 2007,10:19   

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.

--------------
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

(Permalink) Posted: Sep. 26 2007,10:29   

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.

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

  
improvius



Posts: 807
Joined: Jan. 2006

(Permalink) Posted: Sep. 26 2007,10:36   

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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