American Math Common Core Teaching is Nonsensical

[DaisyDay]

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.

Common Core, a set of standards devised by various state governors, only says WHAT should be taught at each level; it is up to the individual states to determine HOW to teach. The really good idea behind this is to see which methods of teaching get the best results.

Instead, certain types decided that this was the elites trying to control them. SMH.

 

[probinson]

Common Core, a set of standards devised by various state governors, only says WHAT should be taught at each level; it is up to the individual states to determine HOW to teach. The really good idea behind this is to see which methods of teaching get the best results.

This isn't entirely accurate. The standards saying WHAT should be taught are VERY SPECIFIC.

If the standard said that a child should be able to add 2-digit numbers, then I would agree. It would be up to each school and/or teacher to determine how best to teach that. But it doesn't just say that. It says specifically:

Understand place value.​

CCSS.MATH.CONTENT.1.NBT.B.2
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:​

CCSS.MATH.CONTENT.1.NBT.B.2.A
10 can be thought of as a bundle of ten ones — called a "ten."​

CCSS.MATH.CONTENT.1.NBT.B.2.B
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.​

CCSS.MATH.CONTENT.1.NBT.B.2.C
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).​

This isn't just saying WHAT to teach, but really getting into HOW it must be taught. That's why my kids brought home "Common Core Math" compliant school books. The common core math standards are incredibly detailed and dictate exactly what must be taught.

So while it may be accurate to say that Common Core is a standard, it is a VERY detailed standard, which dictates not just WHAT must be taught but also HOW and WHEN.

Again, I think that most of the methodology in common core is sound. I only take issue with the fact that common core requires everyone to learn the exact same things at the exact same pace at the exact same time. This can be incredibly frustrating and discouraging for kids who might struggle and/or learn a little more slowly than the common core dictates they must.

 

[iluvatar5150]

This isn't entirely accurate. The standards saying WHAT should be taught are VERY SPECIFIC.

If the standard said that a child should be able to add 2-digit numbers, then I would agree. It would be up to each school and/or teacher to determine how best to teach that. But it doesn't just say that. It says specifically:

Understand place value.​

CCSS.MATH.CONTENT.1.NBT.B.2​

Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:​

CCSS.MATH.CONTENT.1.NBT.B.2.A​

10 can be thought of as a bundle of ten ones — called a "ten."​

CCSS.MATH.CONTENT.1.NBT.B.2.B​

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.​

CCSS.MATH.CONTENT.1.NBT.B.2.C​

The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).​

This isn't just saying WHAT to teach, but really getting into HOW it must be taught. That's why my kids brought home "Common Core Math" compliant school books. The common core math standards are incredibly detailed and dictate exactly what must be taught.

So while it may be accurate to say that Common Core is a standard, it is a VERY detailed standard, which dictates not just WHAT must be taught but also HOW and WHEN.

Again, I think that most of the methodology in common core is sound. I only take issue with the fact that common core requires everyone to learn the exact same things at the exact same pace at the exact same time. This can be incredibly frustrating and discouraging for kids who might struggle and/or learn a little more slowly than the common core dictates they must.

eh... I'd say that example is still about the WHAT, not the HOW. This isn't about adding numbers; it's about thinking of or conceiving numbers - i.e. what does it mean when one number is to the left of another.

 

[probinson]

eh... I'd say that example is still about the WHAT, not the HOW. This isn't about adding numbers; it's about thinking of or conceiving numbers - i.e. what does it mean when one number is to the left of another.

Perhaps that wasn't the best example.

Add and subtract within 20.​

CCSS.MATH.CONTENT.1.OA.C.5
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).​

CCSS.MATH.CONTENT.1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).​

The statement "Add and subtract within 20, demonstrating a fluency for addition and subtraction within 10." is the WHAT. "Use strategies such as..." is the HOW.

 

[Bradskii]

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.

Funny how different people do it different ways. 47+16 immediately becomes 57+6 for me.

 

[Bradskii]

There's definetely something to be said for not just memorising multiplications by rote.

I'm not sure about that. If you didn't know that 9 x 7 is 63 then how do you 'work it out'?

 

[probinson]

Funny how different people do it different ways. 47+16 immediately becomes 57+6 for me.

That's the other issue I have with the common core math standards. On the surface, it's good to teach various methods for how to arrive at the correct answer. However as your post demonstrates, people do it different ways. It's kind of weird that we expect children to be able to demonstrate "fluency" in ALL of the ways listed in the common core standards. What works for one may not make sense for another.

 

[probinson]

I'm not sure about that. If you didn't know that 9 x 7 is 63 then how do you 'work it out'?

Again, building on the principles of the common core standards of working with 10s, you can easily find this multiple of 9 by counting up seven tens and subtracting one seven (since there are only nine sevens). (10 x 7) - 7.

I would agree that knowing your times tables is beneficial. It's like knowing your alphabet. But the key in any mathematical methodology is explaining why.

 

[Bradskii]

That's the other issue I have with the common core math standards. On the surface, it's good to teach various methods for how to arrive at the correct answer. However as your post demonstrates, people do it different ways. It's kind of weird that we expect children to be able to demonstrate "fluency" in ALL of the ways listed in the common core standards. What works for one may not make sense for another.

I think we develop different ways based on what we were taught - which in my case was pretty much what you listed in post 22. Divide (two figure) numbers up into tens and ones. Then work it out whichever way you think is best.

But your other examples such as: 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14. Now that seems to be a bridge too far. I had to look at that for a few seconds to understand what was being done. I think that you have to know single digit additions and multiplications by rote. Working out 8 + 6 in three separate stages is overkill.

Edit: Actually, thinking about it, it's probably what I do subconsciously anyway. It just looks quite odd written out. Using a random example of 19 + 6, I don't add 9 + 6, get 15, place the 5, carry the one etc. That's clumsy. I just take 1 off the right and add to the left to make 20 and 5.

 

[Nithavela]

I'm not sure about that. If you didn't know that 9 x 7 is 63 then how do you 'work it out'?

(10 x 7) - (1 x 7)

 

[probinson]

Working out 8 + 6 in three separate stages is overkill.

If only it were three...

Each week my kids would bring home yet another new and, uh, interesting way to solve simple math problems. And I get it. It's good to have a toolbox full of ways to approach math problems depending on the numbers you're presented. But the common core standards expect for all students to demonstrate fluency in all methods. IMHO, that's unnecessary. As the standard I quoted states for first grade, the goal is to "Add and subtract within 20, demonstrating a fluency for addition and subtraction within 10." How they demonstrate that fluency shouldn't be nearly as important as if they can do the math and explain the why.

 

[Bradskii]

Again, building on the principles of the common core standards of working with 10s, you can easily find this multiple of 9 by counting up seven tens and subtracting one nine. (10 x 7) - 9.

Oops. You should have taken off a 7! See me after class.

Yeah, but I get what you say. I do that for larger numbers, so 13 x 19 is ((13 x 20) - 13). I guess the principle should be explained using smaller ones. Fair comment.

 

[Bradskii]

(10 x 7) - (1 x 7)

I concede...

 

[probinson]

Edit: Actually, thinking about it, it's probably what I do subconsciously anyway. It just looks quite odd written out. Using a random example of 19 + 6, I don't add 9 + 6, get 15, place the 5, carry the one etc. That's clumsy. I just take 1 off the right and add to the left to make 20 and 5.

In elementary school, they use manipulatives to help kids understand that concept.

It might look something like this. A student will have 19 blue squares and 6 red squares.

19	6
BBBBB BBBBB BBBBB BBBB	RRRRR R
20	5
BBBBB BBBBB BBBBB BBBBR	RRRRR

By moving the item from the "6" column over to the "19" column and having the students count, they can more easily understand why they are taking one from the 6 and adding it to the 19 and why that still equates to 25.

Of course, this does seem cumbersome, but I suspect many adults do this mentally without even thinking about it.

 

[probinson]

Oops. You should have taken off a 7! See me after class.

Whoops. My mistake. I went back and fixed it.

 

[public hermit]

I kind of like that approach because it doesn't seem to require a lot of memory work. I think the only reason the old way worked for us geezers is because a good bit of rote memorization was instilled in us, and that enabled us to work the problems. He's counting 1s and getting the basic concept of how things work in sets of 10, I think. If I understand it, I find it appealing even if it does seem laborious.