Yeah, this new-fangled method that Lehrer seems to find so confusing looks to be just “borrowing,” which is how I was taught to do subtraction and how I’ve always done it. Meanwhile, I can’t make heads or tails out of what he calls “the way we used to do that.”
Here’s an excerpt of a post I made in reply to an OP about the teaching of cursive writing in school way back in 2006.
[QUOTE=Bill Door]
I went to elementary school in the late fifties/early sixties, and I was taught to do long division of Roman numerals. Not converting Roman numerals to Arabic, doing the division, followed by converting back, which was faster, as I demonstrated in the fourth grade. We were taught, and forced to divide numbers like MMCCCXII by CLVI using some esoteric technique whose details are thankfully forgotten. This was not in some “enriched” program, but in regular classes.
Why were we taught this? Because professionals in the field as the end result of careful consideration and thorough analysis put it in the curriculum. I’m hopeful, but not certain, that this is not still taught, but I’m also certain that things equally or more useless are taught today. You could swallow an encyclopedia and puke a better curriculum than some schools are using.
That being said, cursive writing is obsolete, and the time utilized for teaching it is best spent teaching something else. If you want to teach cursive writing, put it in art class where it belongs.
[/QUOTE]
I’m disappointed to find that my prediction of things equally or more useless being taught was true. What I don’t blame for this is Common Core. It was always thus. It’s likely better now, most people have forgotten all the useless crap they learned in school and only remember the stuff that worked. Confirmation bias wins again. That’s why TV and movies had a “Golden Age”. Because we’ve forgotten all the shit you had to wade through to get to a couple of nuggets.
It’s funny, I did 12x12 and subtracted 12. People is weird.
yes, two ten frames. One is a blank for filling out, the 2nd , is a 7 seven frame in one line , but we understand he means to do it as two lots of 5.
However, both the ten frame and the array method teach MENTAL SHORTCUTS… that we who are good at maths do, no matter what culture we are.
Suppose you were asked to do 8 * 10 - 30 ? .
Many people would instantly see that and think, so "510… so 50", the number 80 was never thought… The short cut was to see 30 as "3 10 " because the first part was *10…
I’m not one of the “sorry buddy” posters but my stepson just started 6th grade and he’s doing just fine in math under the Common Core standards. I’m 45 and sure I went through the same reaction at one time (“This doesn’t make any sense. It’s not how I learned it.”).
What have I seen his classes learning over the years? The usual addition, subtraction, memorizing multiplication tables up through 12x12, learning your basic division and multiplication, fractions, decimals, converting between those things, math with decimals, getting into long multiplication & division, they’re starting basic algebra this year, etc. So really, the same stuff I learned and pretty much on the same schedule. The only big differences I’ve seen were in how some of the early concepts were taught, and from what I’ve heard (from actual elementary school math teachers) that’s come out of recognition that kids don’t all learn the exact same way - method A might be great for half the kids but method B will work better for some of them and method C for the rest. Some of the terminology isn’t familiar to me but once my kid shows me how they do it, OK, easy to grasp. If he’s got a couple of ways to solve a problem and he chooses the one that works best for him, no problem.
Heck, that’s often what I’ll do if he’s got a question - we’ll work through it the way he’s comfortable with but afterwards I’ll show him an alternative or two to demonstrate that there may be other ways to come to the same correct answer.
As the afore-mentioned Richard Feynman mentions early in his book, it’s just having a different set of tools in your toolbox.
I’ll put myself in the same group that’s pointing out that crappy materials being pitched by some textbook company don’t mean that CC itself is bad.
Let’s turn this around. Did you, yourself, have an elementary-aged child during the period 1998-2004? I’m not talking about what your heard, but were you actually parenting a child in elementary school during that period?
If you were not, then you don’t know what you are talking about, because we have been through it. This stuff that you think is so new and weird is the SAME stuff we went through more than a decade ago. (Okay, EngageNY wasn’t around then, but these methods that sound so strange to you were around, with the main difference being that the words “Common Core” weren’t used.)
No, we weren’t happy about the math program back then either, and neither were the teachers. You’re not alone because this has been an ongoing issue for many years. The fact that it is new TO YOU does not in fact make it new, and that’s what you’re missing. Common Core didn’t come with a new way of teaching; the curriculum your district chose to use implemented a method of pedagogy that has been very fashionable in educational circles in recent years, including in states like Texas that have explicitly rejected the Common Core. (Carnegie Math, for example, is approved by the Texas State Board of Education as aligned with the TEKS [Texas Essential Knowledge and Skills] curriculum standards. Do you want to make a wild guess what methods of teaching are in that series?)
For all of you who are saying CC is just a set of standards, you are almost right. But look at this example I picked at random - 3rd Grade
Notice that it is not just standards but also HOW they are going to approach those standards. It’s not just standards - it’s curricula. Let’s look at area. Here are the standards:
Students recognize area as an attribute of two-dimensional regions.
Students understand that rectangular arrays can be decomposed into identical rows or into identical columns.
But as a teacher using common core, i’m expected to use the methodology.
They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area.
By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.
So saying CC is just standards and not methodology (i.e. teaching students how to do math) is simply incorrect. And yes, I can see teachers interpreting CC as (for example) finding area a different way as incorrect.
ETA:
Saint Cad - BA Mathematics, MS Mathematics, NBCT (A/YA Mathematics), 18 years teaching math in middle school, high school, college.
So, since I wasn’t able to not like the way kids were being taught in 98-04 I have to like the way they’re being taught now? I’m not sure what your point is.
Maybe you should have been more angry at them then instead of telling me I should lay back and think of England now.
All I know is that the math instruction circa 1980 was perfection 
My point is that you are angry at the wrong thing.
If the Common Core standards are completely abolished tomorrow, and a law is passed to make it illegal to use the CC standards or refer to them in any way, your kids are still going to be taught in the same way, because this is the fashionable way to teach math today, the way that has been sold to curriculum managers for some years.
Getting mad about Common Core is pointless and wrong-headed. If you want to make a real change, get mad about poorly designed curriculum materials being pushed by inadequately trained teachers and micromanaged by educational administrators divorced from reality.
Common Core is a diversion. It’s being used very cynically to deflect attention and blame from very real problems in education. You don’t need to lay back and think of England, but if England is under attack from Germany, the Royal Navy should spend its energies worrying about Germany, not Bolivia.
I think the point is that the problems you have did not originate with, and are not inextricable from, the Common Core concept. So addressing your objections to “Common Core” is less than ideal.
My daughter is in 4th grade like yours and, I can’t remember exactly, but I’m pretty sure she was doing carrying and borrowing last year. She’s certainly mastered it now and does it in her head. I have to remind her to write down what she carried/borrowed on her work. I haven’t had any problem understanding any of the things she does and if you ask her teachers about Common Core, they say what people in this thread say. Not much has changed, but some schools picked some weird shit to teach thinking it was important to Common Core.
If you have a problem with the course worksheets or whatever from the teacher, ask the teacher who is forcing him/her to use those teaching methods and/or worksheets. If the teacher says “Common Core” then that is a crap answer, because the Common Core people didn’t go to the classroom and force the teacher to use them.
Then go to the person the teacher named and ask THEM who is forcing them to use those crappy worksheets and teaching methods, and if they say “Common Core” then that is a crap answer (see above)
Eventually you will get to the person or people responsible for selecting that teaching method and/or worksheets and homework, then complain to them for picking crappy teaching methods. And if they say “Common Core makes us” then ask them to point out where in the Common Core standards it says to use those particular crappy worksheets and teaching methods.
My only stake is that you blame the right thing. I don’t have a school aged child, but I have been employed by a major education organization to help them adapt to the Common Core.
If you’d come into the Common Core about 3-4 years ago, you’d have seen that the most controversial part was actually the English curriculum. The Common Core puts a heavy emphasis on non-fiction, which many English teachers objected to. The math part was pretty non-controversial, as it was developed from existing standards that have been in place for some time. None of this stuff was made up out of whole cloth. They looked at successful education systems- in US states and internationally- and used what they do.
About 3 years ago, a small group of Tea Party blogger based out of…I think New Hampshire…started heavily pushing the idea that the Common Core was a plot by Obama to sell our children to the UN. I’m only slightly exaggerating here. At one time they were raving that the Common Core required facial recognition cameras to live stream every class to the evildoers in Washington.
Local politicians picked it up, and suddenly Tea Partiers around the country turned on this bipartisan initiative. States with poor education systems jumped on the bandwagon, because they realized they will look bad if results can be compared across state lines.
So when you reflexively buy in to automatically blaming the Common Core, you are buying into a cynically manufactured effort to undermine an actually pretty sound effort.
Place the blame where it belongs- fly-by-night publishers, whatever causes districts to choose bad publishers, whatever. The Common Core itself is not what you are mad at.
My kid is in 4th grade, so that’s pretty much when I first learned about CC. In reading she uses something called Accelerated Reader (arbookfind.com). Is that part of what you implemented? I have no idea how widely it’s used, but I have a whole set of issues with that program as well. However, I don’t hear a lot of parents complaining about it, so tell the teachers my concerns about it here and there but otherwise just play the game. Funny thing is, she’s not that strong of a reader, but if you work the system, you can get ahead pretty easily, so we do that and concentrate on math.
Accelerated Reader has been out since 1984.
Parent of a 4th grader and a 6th grader here. This is my kids’ second year with Common Core standards. Joey P, I’m really sorry your family is having a tough time with the Common Core math curriculum at your kid’s school. But I have to echo some of the others - I think it is a curriculum problem, not a Common Core problem. Last year I had to help my kids only a few times with math, and I could understand the worksheets easily when they needed my help. I don’t remember seeing these dots you speak of, so it seems our curriculum is different. Our family hasn’t had any issues at all with the transition to Common Core.
Of course, I have a lot of parent Facebook friends, and a lot of them are upset about Common Core, but most of them seem to be complaining about the fact that the curriculum is new and different, not about anything substantive.
And to the OP, I had the same question upon seeing that image. I have a feeling that it doesn’t correspond to any actual math procedure.
My main complaint with all this is that of all the articles covering this none of them thought to ask this question.
The weird thing is that both the “New Math” approach that Lehrer mocks and the approach he describes as “how we used to do that” (for those “under 35 or [who] went to a private school”) are exactly the same!: when subtracting a larger digit from a smaller one, you may “borrow” (in modern terminology; in Lehrer’s words, this is a “carry”) a 1 from the next digit over in the value being subtracted from.
The only difference is that in the New Math part of the song, there is some explanation as to why this borrowing is conceptually appropriate, as well as a second verse in which the example is worked out in base eight (illustrating that there’s nothing special about ten for the concepts)**.
The algorithm is exactly the same! The New Math just comes with some explanation of why the algorithm makes sense, while the non-New Math description of the algorithm is provided with no explanation.
[*: There’s a minor difference in what Lehrer calls the traditional method for those “over 35 [who] went to a public school”: here, instead of reducing by 1 the next digit over in the value being subtracted from, one instead increases by 1 the next digit over in the value being subtracted.]
[**: In explaining the base eight example, Lehrer still dips back and forth into base ten, apparently just to make things sound more complicated than they need be]
Here is a nice blog post explaining why the dad who wrote that check doesn’t know what he’s talking about.
JoeyP, you majored in math in college. Your reaction to not understanding what you’re seeing should be embarrassment and rather than petulantly refusing to go to a “remedial education” class for your daughter’s sake you should be rushing to be the first in line. 
Honestly? It’s not that hard. If you don’t understand it after a little poking around to find out what’s up, the simple fact is, you don’t know how to do math. You know how to run some algorithms, but you don’t understand numbers. Majored-in-math or no.