American Math Common Core Teaching is Nonsensical

[IceJad]

Math Education Across Nations: The Best and Worst Performers - Smartick's Data Visualizations

Explore nations' math education and discover top and worst performers, revealing student achievement disparities

www.smartick.com

Modern America has never been good in math. And now I see why. Who teaches additions by dividing numbers into 10s and 1s then counting them individually by their categories then only move the surplus from the 1s to the 10s category. An utterly slow method on top of teaching incorrect principles of addition. What in the world is "this one wants to be with its friends so it goes up to 50". Story time?

Place all the number you want to add vertically and start adding the far right column digits together. If it exceed 10 write down the last digit then add the surplus digit into the next column and do the same until you have run out of columns. The mom was right.

And it is call Common Core? That is far from common. The rest of the world doesn't do that. We understand that our basic numbering system uses base 10 but we don't add by dividing each number into its 10s and 1s and make up story fanciful story for why you have to carry forward a number.

 

[Nithavela]

From what I've read, while common core is not completely nonsensical and can even have some benefits when teaching the foundations of math, the drawbacks really outweigh this kind of teaching method. It should be dropped asap in favour of the old way of teaching math, until something better comes around.

 

[Ana the Ist]

Math Education Across Nations: The Best and Worst Performers - Smartick's Data Visualizations

Explore nations' math education and discover top and worst performers, revealing student achievement disparities

www.smartick.com

Modern America has never been good in math. And now I see why. Who teaches additions by dividing numbers into 10s and 1s then counting them individually by their categories then only move the surplus from the 1s to the 10s category. An utterly slow method on top of teaching incorrect principles of addition. What in the world is "this one wants to be with its friends so it goes up to 50". Story time?

Place all the number you want to add vertically and start adding the far right column digits together. If it exceed 10 write down the last digit then add the surplus digit into the next column and do the same until you have run out of columns. The mom was right.

And it is call Common Core? That is far from common. The rest of the world doesn't do that. We understand that our basic numbering system uses base 10 but we don't add by dividing each number into its 10s and 1s and make up story fanciful story for why you have to carry forward a number.

Well....as crazy as it's going to sound, I'm not sure we should write this off.

What he's doing is considering the numbers differently than his mom....as a set of tens and ones. I don't think it's obvious that he's going to be faster than his mom....she's had more practice...but at her age I don't know if he's going to be slower.

This is the way they teach children in China I believe, except they use an abacus (and the extra sensory memory probably helps), but they basically learn to add subtract divide and multiply on sets of ones, tens, hundreds, etc. China is killing us at math btw.

I myself had the fortune of winning a mathematics contest I was unaware I was in during 3rd grade. My prize was a big box of math. I kept the box. By 6th grade I was struggling to get through a basic single digit multiplication table of 20 or 30 in the required 3 or so minutes. Essentially, we were expected to simply know these things, and I didn't. I ended up divising certain shortcuts I could perform for different digits like 9 that I've never met anyone else who used. Once I saw math differently, I was able to do it pretty well. I had to do it myself though...the way it was taught I struggled with.

 

[IceJad]

Well....as crazy as it's going to sound, I'm not sure we should write this off.

What he's doing is considering the numbers differently than his mom....as a set of tens and ones. I don't think it's obvious that he's going to be faster than his mom....she's had more practice...but at her age I don't know if he's going to be slower.

This is the way they teach children in China I believe, except they use an abacus (and the extra sensory memory probably helps), but they basically learn to add subtract divide and multiply on sets of ones, tens, hundreds, etc. China is killing us at math btw.

I myself had the fortune of winning a mathematics contest I was unaware I was in during 3rd grade. My prize was a big box of math. I kept the box. By 6th grade I was struggling to get through a basic single digit multiplication table of 20 or 30 in the required 3 or so minutes. Essentially, we were expected to simply know these things, and I didn't. I ended up divising certain shortcuts I could perform for different digits like 9 that I've never met anyone else who used. Once I saw math differently, I was able to do it pretty well. I had to do it myself though...the way it was taught I struggled with.

While his answer is not wrong the methodology is cumbersome and doesn't quite match an abacus style of calculation. When using an abacus you first need to configure it to the first number in your equation. Then start doing the addition from left to right. Meaning adding the largest 10s then move to the lower 1s. Such as 193 + 107. You would be adding 100+100 then 90+00 then 3+7. Every time you have a column exceeding 10 you add to the column prior. It is backward to conventional addition but with practice it is actually faster than conventional addition. I was thought a bit of abacus when I was young. I'm an ethnic Chinese (not from China) however I never gotten use to the abacus or adding from left digit to the right. But my parents can at an amazing speed in their heads. I personally use the conventional adding from right digit to the left.

In the video the kid was still adding from right to left which defeat the purpose of an abacus like addition. In fact it is the conventional method with extra steps.

And by the way a belated congrats on winning a math contest. I was not very good in math in contrast to the stereotype of an East Asian. I'm not bad per say, very much above average but in comparison to my friends I'm far lacking.

 

[Bradskii]

Modern America has never been good in math. And now I see why

Am I missing something? He did exactly the same as his Mom. He's adding the 7 and the 6 to give 13. Leaving the 3 there and carrying the 1 to add to the 4 and the 1. He just showed it graphically so he could see what was happening, rather than doing it by rote. But the method is identical.

 

[Larniavc]

Math Education Across Nations: The Best and Worst Performers - Smartick's Data Visualizations

Explore nations' math education and discover top and worst performers, revealing student achievement disparities

www.smartick.com

Modern America has never been good in math. And now I see why. Who teaches additions by dividing numbers into 10s and 1s then counting them individually by their categories then only move the surplus from the 1s to the 10s category. An utterly slow method on top of teaching incorrect principles of addition. What in the world is "this one wants to be with its friends so it goes up to 50". Story time?

Place all the number you want to add vertically and start adding the far right column digits together. If it exceed 10 write down the last digit then add the surplus digit into the next column and do the same until you have run out of columns. The mom was right.

And it is call Common Core? That is far from common. The rest of the world doesn't do that. We understand that our basic numbering system uses base 10 but we don't add by dividing each number into its 10s and 1s and make up story fanciful story for why you have to carry forward a number.

Isn’t this just the generation confusion that nearly always happens when the older generation opines on how ‘wrong’ the ways of the younger generation are?

 

[IceJad]

Am I missing something? He did exactly the same as his Mom. He's adding the 7 and the 6 to give 13. Leaving the 3 there and carrying the 1 to add to the 4 and the 1. He just showed it graphically so he could see what was happening, rather than doing it by rote. But the method is identical.

The visualization part and the reason to carry a number over are the unhelpful parts. The mom's method with is the standard across the world is far more intuitive and easier as a concept to understand. Dividing your numbers into boxes and drawing lines to represent the number is cumbersome. The kid then counted the lines in each box. Then he does another round of thinking to add the surplus one to the 10s box. This kind of teaching method cultivate visualization instead of conceptual mathematics. He boy is still counting instead of forcing him to start mental addition. In small numbers this is doable when the number grows to 1000s and 10000s this is not helpful.

 

[IceJad]

Isn’t this just the generation confusion that nearly always happens when the older generation opines on how ‘wrong’ the ways of the younger generation are?

It is not a generational thing. The method I use is the same as the one my mom thought me and my teachers thought me. When it works it works regardless of generations. Just look at the East Asian nations.

 

[Bradskii]

The visualization part and the reason to carry a number over are the unhelpful parts. The mom's method with is the standard across the world is far more intuitive and easier as a concept to understand. Dividing your numbers into boxes and drawing lines to represent the number is cumbersome. The kid then counted the lines in each box. Then he does another round of thinking to add the surplus one to the 10s box. This kind of teaching method cultivate visualization instead of conceptual mathematics. He boy is still counting instead of forcing him to start mental addition. In small numbers this is doable when the number grows to 1000s and 10000s this is not helpful.

The little dots and the lines he put there are there to just help him count. Nothing more. The boxes he drew are to compartmentalise the units from the tens. He gets a visual aid to what show what his mother was doing. I wouldn't worry about him doing this for the next few years. It's illustrating the concept only. Once he understands what he's doing then he'll speed up the process and mentally add them in his head rather than drawing lines and counting dots. At what age that happens, I don't know. But I swear, guys in their twenties in the last place I worked would reach for the calculator if they had to add 2 three figure numbers or multiply 24 by 3.

When I did addition when very young we did something similar in drawing vertical lines dividing the units, the tens, the hundreds etc. Add the unit, as he did and he has a ten. Move it over to the left - as his mother did. Add the tens and he has a hundred - move it to the left. It's exactly the same method.

I had a fantastic maths teacher when I was about 13. Rather than tell us: This is the rule...and chalk up A squared + B squared = C squared on the blackboard and give us lots of examples to work out, he spent a complete lesson showing us how you prove Pythagoras. Easy basic steps that we could all understand. And you could see the little light bulbs firing all over the classroom. We all 'got it'. It wasn't a rule then. It was a theorum.

Teach kids why it works. Not just how it works.

 

[iluvatar5150]

The visualization part and the reason to carry a number over are the unhelpful parts. The mom's method with is the standard across the world is far more intuitive and easier as a concept to understand. Dividing your numbers into boxes and drawing lines to represent the number is cumbersome. The kid then counted the lines in each box. Then he does another round of thinking to add the surplus one to the 10s box. This kind of teaching method cultivate visualization instead of conceptual mathematics. He boy is still counting instead of forcing him to start mental addition. In small numbers this is doable when the number grows to 1000s and 10000s this is not helpful.

Hold up, are you concerned about intuitiveness and concepts, or are you concerned about being able to do math in his head? Because those are two very different things. There's nothing unintuitive or poorly conceived about this kid's method - as already noted, it's identical to what the mother's doing. They're both summing the ones and then carrying over to the tens column. The kid just has a visual aid to help him keep track of the counting.

The argument that his method doesn't scale well into the thousands and tens of thousands is silly, because neither does the mother's method. He's not adding entire numbers like this; he's adding single columns. To get a single column into the 1000's and 10,000's, you'd need a math problem with hundreds or thousands of rows. Nobody's doing that in their head, either.

 

[Larniavc]

It is not a generational thing. The method I use is the same as the one my mom thought me and my teachers thought me. When it works it works regardless of generations. Just look at the East Asian nations.

That’s the very definition of a generational thing.

 

[The IbanezerScrooge]

People who complain about common core only do so because they don't understand what's actually being taught, and, more importantly, why. Listen to parents who complain at school board meetings. All they're really complaining about is their own lack of understanding of the methods and the reasons, not that it's "wrong", just their own deficiencies in being able to help their kids with math.

If you actually make an effort to understand what common core math is teaching you come to realize that most of us already do this semi-intuitively in our heads, especially when it comes to figuring up things to do with money. Really think about how you figure up how much change you should get back or how much something costs when you apply a discount percentage. You're not standing there writing rows of numbers and carrying 1's in your head.

 

[RocksInMyHead]

All they're really complaining about is their own lack of understanding of the methods and the reasons, not that it's "wrong", just their own deficiencies in being able to help their kids with math.

To be fair, if your kid comes to you looking for help on their math homework, and you try to help them in the way that you were taught (pre common core) only to be told that you're "doing it wrong," that can be frustrating. In an ideal world, parents would read through their kids' textbooks and learn the new methodology alongside them, but realistically that's not going to happen 90% of the time, whether due to lack of time, lack of interest, or lack of intelligence.

 

[Arcangl86]

It's also worth reminding people that Common Core doesn't mandate curriculum. It sets standards of things Children should be able to do and it's up to the local authorities to figure out how to do that. And honestly, I rather a kid use visual learning aids if it gives them a core sense of what's happening then simply memorizing rote algorithms like many of us do.

 

[probinson]

The methodology behind common core math is sound. Understanding numbers being made up of tens and ones is quite helpful for mental math. For example, another method taught in common core is to get one of the numbers to be a multiple of ten. So In the OP example of 47+16, you can also treat that as 50+13 by simply taking the 3 off of the 16 and adding it to the 47, and then it's even easier to say that 50+13=63. When the mother does it and "carries the one", she doesn't explain why. I would wager that many people who know how to "carry the one" have no idea how to put into words what they're doing. But it's the same thing as the kid in the video saying that the one in his 13 "wants to be with his friends".

IMHO, it's not the methodology in common core that is the problem with the system. As some have pointed out, the methodology in common core is quite sound and actually teaches the why behind the math. The problem that I see with common core is that it assumes that all people learn the same things at the same pace all the time. When my kids went through common core math, they did well as long as they could keep up. But on those occasions where they struggled with something, the common core just keeps going, assuming that you've already mastered last week's lesson, and if you haven't, you can start to become overwhelmed trying to play catch up in a hurry.

There is little room for different learning styles and paces in common core, and that is my concern with the standards.

 

[durangodawood]

We dont need to learn math. We have immigrants for that.

 

[iluvatar5150]

When my kids went through common core math, they did well as long as they could keep up. But on those occasions where they struggled with something, the common core just keeps going, assuming that you've already mastered last week's lesson, and if you haven't, you can start to become overwhelmed trying to play catch up in a hurry.

There is little room for different learning styles and paces in common core, and that is my concern with the standards.

Isn't that true of most any institutionalized group learning?

 

[probinson]

Isn't that true of most any institutionalized group learning?

Yes to some degree, but IMHO common core standards add pressure, to the schools and to the students. Common core standards state that every child should be able to do X, Y and Z by the 6th week of 2nd grade (as one example), but maybe it will take some kids until the 12th week of 2nd grade to master those skills. And that's just fine.

I remember sitting across from a guidance counselor when my son was in first grade. They had a list of 50 core concepts. They were things like "under", 'behind", "beside", "above", etc. He only knew 43 of them (so they said) and they were concerned because they said he should know all 50 of them by now. I told the guidance counselor I was not even a little bit concerned, and that my wife and I would work with him on the 7 concepts he didn't know. Turns out, he knew them just fine. He didn't test well, but when we got home, I said, "Go put that ball under the table", which he did without even thinking about it.

They were ready to pull my son from his class and assign him a "support" teacher because he didn't meet their standards (on a test). But I advocated for him and said, even if he doesn't know the word "under" right now, that doesn't indicate there's any kind of learning issue here. That's where any type of "standard" can become problematic.

 

[Paulos23]

Well....as crazy as it's going to sound, I'm not sure we should write this off.

What he's doing is considering the numbers differently than his mom....as a set of tens and ones. I don't think it's obvious that he's going to be faster than his mom....she's had more practice...but at her age I don't know if he's going to be slower.

This is the way they teach children in China I believe, except they use an abacus (and the extra sensory memory probably helps), but they basically learn to add subtract divide and multiply on sets of ones, tens, hundreds, etc. China is killing us at math btw.

I myself had the fortune of winning a mathematics contest I was unaware I was in during 3rd grade. My prize was a big box of math. I kept the box. By 6th grade I was struggling to get through a basic single digit multiplication table of 20 or 30 in the required 3 or so minutes. Essentially, we were expected to simply know these things, and I didn't. I ended up divising certain shortcuts I could perform for different digits like 9 that I've never met anyone else who used. Once I saw math differently, I was able to do it pretty well. I had to do it myself though...the way it was taught I struggled with.

Something I figured out about common core is that most of the mental shortcuts I do are there on the page. It was just odd to me because I never had to put it on the page before.

It is a good way to help kids get those mental shortcuts and tools for math for the ones that don't pick it up quickly.

 

[Nithavela]

Something I figured out about common core is that most of the mental shortcuts I do are there on the page. It was just odd to me because I never had to put it on the page before.

It is a good way to help kids get those mental shortcuts and tools for math for the ones that don't pick it up quickly.

There's definetely something to be said for not just memorising multiplications by rote. I bet a few parts of common core should still be in a math teacher's repertoire for students who benefit for them. But as with all things in teaching, one size does not fit all.