# The new New Math: Byzantine subtraction in Common Core

#### posted at 5:21 pm on October 1, 2014 by Ed Morrissey

When I went to school, I may not have been the math whiz that my son the Mathemagician turned out to be, but I didn’t really have any trouble learning subtraction by, y’know … subtracting. Apparently that’s so passé as to be called the Granny Method in a new Common Core-compliant textbook. Our colleague Erick Erickson found this instruction on subtraction in his daughter’s third-grade textbook that almost looks like intentional satire:

The picture above is from my third grade daughter’s math book. This is the only page that explains that method for subtraction. There are, for the record, four ways to subtract that my third grader must learn.

This is the only page explaining that method. This is the only example. The very next page goes to arrays. The page after that goes to multiplication. This is it.

The traditional method of subtracting, borrowing and carrying numbers, is derisively called the “Granny Method.” The new method makes no freaking sense to either my third grader or my wife.

We send our child to a Christian private school. We thought our child could escape this madness. But standardized tests, the SAT, and the ACT are all moving over to Common Core. So our child has to learn this insanity. But we cannot help her. The book offers only one example.

I’m pretty good with patterns, so I see what the intent is with this method. It’s to build the answer through a series of additions, taking four steps on paper plus a number of cognitive judgments along the way. What I can’t see is why anyone would ever need to use this method to actually subtract one number from another. In the old New Math, breaking equations down into components based on the places in the numbers could boost understanding of algebra and help one learn to do more complex equations in the head. That’s clearly not the case here — the “counting-up method” requires a paper calculation and more complicated cognitive judgments than simply subtracting and carrying over. Furthermore, as one of Erick’s commenters noted, even if one argues that it prepares children for higher math functions, how do you deal with negative numbers using this method?

As Erick concludes, the only possible value in putting this in a textbook is just that it’s new. I’m all for new when new improves on old, but … this is sheer nonsense.

Famous mathematician and humorist Tom Lehrer lampooned “New Math” in the 1960s. Now this looks like the good ol’ days.

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### Breaking on Hot Air

The real problem?

Give the math teachers a math test, give the english teachers a grammar test, give the history teachers a history test…than you will find out the real problem.

Learning different math methods, when the kids are ready, should be taught. Having several different ways of adding or subtracting, is just showing kids that you can solve problems in a variety of ways…but it had to be taught properly.

I would bet 25% of the teachers wouldn’t be able to pass a 12th grade comprehensive exam…

And that’s the problem…ungood teachers…

right2bright on October 2, 2014 at 8:32 AM

Would it be possible to only teach this method in February?

rogerb on October 2, 2014 at 8:33 AM

I’ll be the voice of dissent: I actually like the bizarre subtraction method.

But that’s not saying that I would teach it as the primary method. My preference would be that the conventional method remain the primary subtraction method. I would introduce the alternate method as a curiosity after my students are sufficiently practiced in the conventional method.

But in engineering, alternate methods can be very useful as a check on your primary methods. In my view, the bizarre subtraction method would serve that same function.

I wouldn’t test my students on it, except to offer it as a bonus problem on a test, as a way of checking one of the harder subtraction problems on the same test.

If there are people out there who think the method is “stupid” or “useless”, I would characterize that as small-mindedness. Alternate ways to arrive at a destination are useful, even if they are seldom used.

Summary: I would “expose” my students to the alternate subtraction method. I wouldn’t teach it as the primary method.

Steelweaver52 on October 2, 2014 at 8:38 AM

I don’t know why you have a dog in this fight

I have a dog in this fight because of all the pantywaist hyperventilating–essentially asserting that having to understand math, as well as do it, will make U.S. students worse compared to the world rather than better. Of course the rest of the keeps excelling by doing what folks here are mocking. You have to do both to be the best–both understand and do it right.

You would never, ever, in a million years need to teach someone how to “get” subtraction by subtracting 38 from 325

Oh, [begin snarc] by all means protect our kids from having to learn a concept with one digit (as you suggest) and then be asked to apply it with two and three digits. How horrible! This will make them worse at math than the rest of the world–working with more than one digit at a time. [end snarc] Such foolishness is contemptible because of the harm it does our children.

G. Charles on October 2, 2014 at 8:46 AM

alternate methods can be very useful as a check on your primary methods

Absolutely. Moreover, it is a check (and reinforcement) on understanding the concept at hand. Once the concept is understood, just do it the quickest and easiest way.

Likewise, these alternative methods, if taught well, are taught in just one day to one week, that’s it. Math-challenged parents are being overprotective of their kids’ feelings and end up holding them back in their math abilities, sometimes for a lifetime.

G. Charles on October 2, 2014 at 9:01 AM

As someone who was pretty good at math in school, the Common Core Math is just confusing and bizarre. Do parents have to teach their kids to do math the proper way now?

Illinidiva on October 2, 2014 at 9:10 AM

Sooooo, I have a degree in Mathematics and Computer Science. I understand the method and it is “easy” when applied to simple problems. But let’s try this one: 2038707 – 2879. Go. I’ll wait. Got it yet? Some of you might be able to do that in your head, but the “solid method” this lesson teaches would not be the best way to do it in your head. The more places in each number, the more steps. The number of steps is based on the relative difference in 10’s places between the two numbers. So if I do 4126 – 22 by this method it takes five “counting up” steps that yield the numbers 8, 70, 3900, 100 and 26 to add up. Note that the step to transition to the thousands place requires that they understand base-10 arithmetic. The third step would require you to jump to the “largest thousand” possible (4000) then back to the largest hundred (4100). A bit convoluted and not intuitive unless you already understand how numbers are constructed.

This method is not inherently “bad” but is unnecessarily complex. Borrowing 10s is simpler and, once understood, easier. I can see this as a tool to teach how numbers are built, but not as a practical method for actual everyday use except for small numbers.

BillyWilly on October 2, 2014 at 9:11 AM

Give the math teachers a math test, give the english teachers a grammar test, give the history teachers a history test…than you will find out the real problem.

I strongly agree.
“Ungood” teachers often can’t even teach the “normal” way of math adequately because they don’t have a good handle on math themselves. It is rather unhelpful for most students (although the brightest will usually overcome, regardless) for poor teachers to teach multiple methods poorly.

Overseas where students are excelling at math compared to us–using these very methods that people hate on this thread–the math teachers know their math well.

I suppose I am arguing, then, that good teachers in the U.S. should not be held back from using the best proven math curricula in today’s world because some (math-challenged) parents mock these newer approaches as ridiculous.

G. Charles on October 2, 2014 at 9:21 AM

So counting up and adding 4 numbers is less prone to error than subtracting 2 numbers? The places where one is prone to error is quite numberous with this method. The method is a total failure.

TerryW on October 2, 2014 at 9:29 AM

Serious question for you, G. Charles, can you provide documentation that overseas students are “using these very methods?” If so, to what degree and to what purpose? Are they basically teaching kids to comprehend numbers and how they are formed (note, primarily in base 10 for this example)? Precisely what are they trying to teach with “these very methods?” Are those concepts being taught here, to third graders?

BillyWilly on October 2, 2014 at 9:29 AM

let’s try this one: 2038707 – 2879

You quickly “do this” by rounding/estimating and apply the “subtraction by addition” to arrive at an estimated answer of “203600 or so.”

not as a practical method for actual everyday use except for small numbers.

Agreed. Not for actual everyday use except for small or estimated numbers. Even then it may not be one’s everyday approach of choice, but it’s worth understanding.

G. Charles on October 2, 2014 at 9:33 AM

can you provide documentation

These hotly contested math questions just reek of the Singapore Math curriculum.

G. Charles on October 2, 2014 at 9:36 AM

This method is the same idea as “counting back” change, a useful skill when you working a cash drawer and don’t have a register to do the math for you.

March Hare on October 2, 2014 at 9:45 AM

This method is the same idea as “counting back” change, a useful skill when you working a cash drawer and don’t have a register to do the math for you.

March Hare on October 2, 2014 at 9:45 AM

So you’re saying this is training them for when they power goes out at the McDonald’s where they work in about six years??? :)

BillyWilly on October 2, 2014 at 9:52 AM

This method is how cashiers used to count your change in the old days. So Common Core is preparing our kids for the menial workplace of 1973.

segesta on October 2, 2014 at 9:55 AM

Yet another strong argument for home schooling.

Mr. Bultitude on October 2, 2014 at 10:01 AM

So you’re saying this is training them for when they power goes out at the McDonald’s…?

Yes. I’m saying that they should not be less math-prepared than a menial workplace worker from 1973. Are you saying they should be less prepared?

G. Charles on October 2, 2014 at 10:05 AM

This method is we used to call “counting back change”. It is how a store clerk would do it without the help of a cash register.

It is a good method for doing it on the fly with cash, but I wouldn’t attempt to teach it to a 3rd grader.

strickler on October 2, 2014 at 10:06 AM

Alright, I see what they are doing here. I also have a math/cs degree and I am going to chime in a bit. They aren’t teaching the simplest method for subtraction they are teaching students to follow four algorithms that solve a subtraction problem.

One of the things I realized in school is how hard this sort of thinking is for many people. I was a TA and helped teach the first weed out cs class at my school data structures. In that class students were introduced to data trees and recursive algorithms and various sorting methods. It was the first class students learned to write an algorithm to manipulate data in some way. A large portion of students just couldn’t do it, even though it was relatively simple stuff. It requires a sort of thinking that was completely foreign to them.

And if you think about it, simply learning and following a problem solving process is a huge part of math. Take linear algebra, matrix math requires a fairly simple process but can take many many steps to solve a problem. The method of teaching in the article would do well to prepare students for it.

If the goal here is simply to teach subtraction, yes this new math. But it may do well to prepare them for what’s to come.

jhffmn on October 2, 2014 at 10:23 AM

This method is the same idea as “counting back” change, a useful skill when you working a cash drawer and don’t have a register to do the math for you.

March Hare on October 2, 2014 at 9:45 AM

the saddest thing i see is when someone does this or even with the assistance of the register to tell them how much to give back … and they can’t deal with the intricacies of varying denominations of coins. \$0.80 gets counted out as 2 quarters and 3 dimes. pitiful.

counting back works. it can be learned (obviously) without having to understand how it works. but the best thing about the “Granny Method” is that (as Tom Lehrer correctly states) it teaches the understanding of WHY it works; “understand what you’re doing”.

there is NOTHING in that Byzantine method’s example to explain why.

HOW do these methods get selected as teaching methods? what studies were conducted to compare this method or that as being effective?

WaldoTJ on October 2, 2014 at 10:29 AM

And to be fair, public education math is a travesty. If what I remember is correct, students can graduate without even taking calculus. Students only need to take algebra 2 to graduate. Then they get to community college and have to take math 102 or some such. And maybe, maybe if they do something in the sciences take one or two years of calculus.

It’s no wonder all the engineering grad students are from china and India.

jhffmn on October 2, 2014 at 10:33 AM

Aren’t you using the “Granny Method” when you add up all the circled numbers?

CA_Conservative on October 2, 2014 at 10:34 AM

jhffmn on October 2, 2014 at 10:23 AM

Would it stand to reason, then, that the traditional teaching method would be better suited for all kids, and those who could more easily adapt to “that way of thinking” (ie Singapore method) be provided accelerated learning opportunities? Seems win-win to me. I’m not against the new system as an option for some students, but when applied to all via Federal mandate, that’s wrong.

Bee on October 2, 2014 at 10:36 AM

OK…but I wouldn’t attempt to teach it to a 3rd grader.

Willy prompted me to do a google search. Let’s see what 3rd grades from high-achieving countries are doing. Here are some questions from a 3rd grade Singapore Math worksheet (where getting to the 10’s place(s) as intermediary steps is taught):

Shara will travel 650 miles on a train trip. She has traveled 365 miles so far. How many more miles will she travel? (Chapter 5, Page 121, Number 1)

Twana bought a book about dogs for \$16.75. She gave the store clerk a \$20 bill. How much change did she receive? (Chapter 12, Page 338, Number 20)

Taylor had 8 dimes and 30 pennies in her purse. She spent half of the dimes. What is the value of the money left in her purse? (Chapter 3, Page 47, Number 7)

In the school chorus, there are 22 third-graders and 17 second graders. Fourteen of these students also play the piano. How many do not play the piano? (Chapter 2, Page 34, Number 52)

Last week Mr. Masumoto sold 215 ballpoint pens. He sold 4 times as many pencils as pens. How many pencils did he sell? (Chapter 21, Page 593, Number 29)

There were 350 balloons, but 30 burst. Eight clowns share the remaining balloons equally. How many balloons will each clown carry to give away at the parade? (Chapter 22, Page 611, Number 20

Stella has \$4.45 in her piggy bank. Dan has \$0.50 less than Stella. Al has twice as much money as Dan. How much money does Al have? (Chapter 21, Page 603, Number 23)

With good teachers, 3rd graders can do a lot more than most folks realize.

G. Charles on October 2, 2014 at 10:41 AM

Bee on October 2, 2014 at 10:36 AM

I won’t argue in favor of federal education mandates. But I do think students need to actually be prepared for advanced math and computer science. All students should be expected to learn math beyond what is taught today.

jhffmn on October 2, 2014 at 10:42 AM

The very thing that this new math is supposed to get is more enrollees and graduates of STEM. As it turns out, it may not do that.

But Zimba also acknowledges that ending with the Common Core standards in math could preclude students from attending elite colleges or pursuing STEM careers.

“If you’re a young person who wants to become an engineer, or who wants admission … to an elite university, you would be advised to take mathematics beyond the college- and career-level,” he said. “If you want to take calculus your freshman year in college, you will need to take more mathematics than is in the Common Core.”

That is coming from one of the Common Core writers. Smart power.

Patriot Vet on October 2, 2014 at 10:48 AM

I teach Pre-Algebra and Algebra 1 overseas. I teach Common Core standards with the assistance of Prentice Hall textbooks written “before the Core”. I don’t teach whole-number subtraction, but I teach fraction and decimal operations, and I use this “counting-up method” most every time I do mental math. I use something similar with rational numbers (positive/negative numbers). Knowing these shortcuts gives me credibility because I don’t need to use the traditional algorithm. Guess what? I use it anyway. The “counting-up method” existed before Common Core, as did many of the strategies for which CCSS takes blame. It is a lousy computation method for most drill-and-skill math problems, but it has its uses.

Even when I taught elementary math, I presented the standard algorithm, but I almost always presented some trick or shortcut. As many have mentioned, it works as a check to see if you’ve correctly followed the algorithm.

bteacher99 on October 2, 2014 at 10:55 AM

Likewise, these alternative methods, if taught well, are taught in just one day to one week, that’s it.

G. Charles on October 2, 2014 at 9:01 AM

And that’s one day or week they could be doing drills to reinforce the actual usable method. But drills are rote, and therefore, passé.

This crap is stupid. It’s stupid because it’s a halfway decent idea taken to extremes. It’s like a heresy in Christianity – it’s almost always one good thing taken to an extreme and to the exclusion of all other doctrine, leading to an end result that actually isn’t right.

GWB on October 2, 2014 at 10:56 AM

I’m not a Common Core backer, I don’t want it. But I do want some of the math, and more overall, not less.

Bee wrote it would be “win/win” for all to receive traditional math and only accelerated students to get “Singapore”-type math. She may be right if there are only poor to mediocre teachers. But with good teachers I think 90% or more can grasp these “alternate” approaches and the fundamental concepts they help reveal.

G. Charles on October 2, 2014 at 11:00 AM

I found that math problem:

2038707 – 2879

121 gets me to 3000. 2035707 + 121 is 2035828.

Of course, Google.com can do it just as easily as a calculator these days, but it is possible to use counting-up for even such a problem as this. Were there decimals or roots, I’d probably choose something other than mental math. The algorithms from my high-school days might do the trick, or I might simply reach for a calculator. When students learn how to think, they are able to choose the best method and the best tools.

bteacher99 on October 2, 2014 at 11:01 AM

halfway decent idea taken to extremes

What is extreme is to say “rote” is good enough without understanding concepts. The balance is to expect precise manipulation of math problems and also to expect one understand the concepts behind the number manipulation (which would then aid with more extensive application of the rote knowledge).

G. Charles on October 2, 2014 at 11:12 AM

Also, I’m starting to think the real problem with our education system is all the people who think should be dumb down to the point of not discouraging below average students.

Our society collectively seems to think everything needs to be dumbed down to the lowest common denominator.

jhffmn on October 2, 2014 at 11:19 AM

What is extreme is to say “rote” is good enough without understanding concepts.

G. Charles on October 2, 2014 at 11:12 AM

Understanding comes through repetition. Recent studies have confirmed something that teachers have reliably used for millennia.

GWB on October 2, 2014 at 11:35 AM

The Tom Lehrer song is great! Actually, I was involved in the New Math introduction back in the 1970’s that he was signing about. And, we did have to learn in other bases. My parents and grandparents were unable to help me with my homework.

LaserTSV on October 2, 2014 at 11:41 AM

My wife was a math teacher and college chem teacher. She maintained two things forever.

One – math is not taught like anything else because your mind has to be capable of grasping the concept. That is why you cannot start algebra too early or calc too early. Most kids won’t get it. The few who are wired for it you can advance up as it becomes apparent as jhffmn noted above that they get it.

Two – Asians strength in computation seems to be facilitated by their language. Very fast, with often times merely stresses and quick tonal changes to differentiate meaning. Their language programs them to “think fast” – though not necessarily better. For anyone who has worked in STEM type industries you find they are amazing on computations – but not so hot on communications. So they are great process improvers – which is why they manufacture mature processes so well. Design and creativity is not their strength – where our slow but very detailed language provides better detail and understanding and transfer of concepts and ideas between people. It is merely how the strengths of any group also have their weaknesses as well.

I’m not sure how much of the second point has been borne out by any research, but it sure seems to fit what I have experienced.

Zomcon JEM on October 2, 2014 at 12:04 PM

Why would the Collective be concerned over math, when it needs to spend most of its time teaching students tall tales of Che Guevara, social justice fantasy making, and forcing them to engage in fascism under the aegis of activism.

Star Bird on October 2, 2014 at 12:11 PM

For 325 – 38, mentally I would convert that to

325 – (40 – 2)

malclave on October 1, 2014 at 9:18 PM

That’s how my brain does it, too.

325-38 becomes (325-40)+2

325-40=285
285+2=287

The method others mentioned that involved “turning 5 into 2” or some such isn’t as terrible as it sounds. When considering 8+5 my brain turns it into 10+3. I think that is what that method is trying to teach, it’s just being explained very, very badly.

GAbred on October 2, 2014 at 12:12 PM

What is extreme is to say “rote” is good enough without understanding concepts.

G. Charles on October 2, 2014 at 11:12 AM

Understanding comes through repetition. Recent studies have confirmed something that teachers have reliably used for millennia.

GWB on October 2, 2014 at 11:35 AM

Repetition does create mastery – all learning books out there today say this – the old adage of practice makes perfect is true. Concepts usually have to be introduced later in ones development – I am not qualified to say whether or not this age level can handle this concept. What I can tell you is that we teach in steps of understanding based upon conceptualization capabilities. I don’t care how good you are at arithmetic, if you cannot handle the concept of algebra – you will never learn how to do it. You mind has to mature. That is the danger in moving kids in math to fast.

I find this method we are debating to be confusingly explained – just as estimation exercises were back in my day – this looks like a similar concept to that. Just stated confusingly for a third grader. However – even for estimation or this Singapore method – if the child has not learned and mastered basic computation – this will go right over their head. This seems to me something maybe that we all are missing. Learning concepts cannot happen until the basics are learned – and all of that is done by rote, by some version of it or another. The example story questions up above I was doing in the third and fourth grade when I grew up – so I don’t see any great difference there – they are all very age appropriate anywhere.

Zomcon JEM on October 2, 2014 at 12:21 PM

I’m just waiting for the announcement that instead of “times tables”, Common Core will require elementary school students to use log charts.

malclave on October 1, 2014 at 5:32 PM

Log charts won’t help: you have to be able to add and subtract in order to use them!

This silly and dysfunctional “Common Core” nonsense is just another way the extreme leftists are using to undermine our country…by dumbing it down.

Alternative methods might be useful for double-checking answers. For example, the “casting out nines” technique is a century-old method for checking the addition and/or subtraction of long strings of numbers (as one does in verifying adding machine tapes). But this obtuse silliness, used as a “new way to learn math” instead of a supplementary technique, is merely an impediment to learning fundamentals.

Because of my training and background in the birth of the computer industry (to design the early computers, you had to ‘re-invent’ basic math operations in order to design the machines), I have a lot more formal and a lot more on-the-job math background than the vast majority of math teachers. And my opinion is that this methodology is really mind-numbing stupid: it doesn’t actually teach math or math-machine (calculator) proficiency. The only possible value in this technique is that it probably sells new textbooks to schools which don’t need them, for the benefit of a few authors who have nothing better to do and don’t care about children.

landlines on October 2, 2014 at 12:29 PM

I tried this method to subtract 90-33 and couldn’t get it to work following the example. to 33 I added 7 to get to the nearest 10 which is 40. To 40 I added 60 to get to the nearest 100. But since 90 is less 100 it didn’t seem to conform with the example. Am I correct or still getting a D in math?

HueMoss on October 2, 2014 at 12:45 PM

Recently I was listening to a program on NPR where a teacher in the UK was discussing how they are beginning to teach 3-5 year olds about computer science, including concepts like languages and coding. One major component of this curriculum is the study of algorithms. This subtraction method would be a good example of a simple algorithm, if it is understood as such. As an easy way for a person to find the solution to an everyday math problem in their head, let’s just say I’m not a fan.

littleguy on October 2, 2014 at 12:48 PM

Two – Asians strength in computation seems to be facilitated by their language. Very fast, with often times merely stresses and quick tonal changes to differentiate meaning. Their language programs them to “think fast” – though not necessarily better.

Zomcon JEM on October 2, 2014 at 12:04 PM

Which Asian languages would that be? I speak a couple and they’re very different from each other.

DarkCurrent on October 2, 2014 at 12:57 PM

One major component of this curriculum is the study of algorithms.

littleguy on October 2, 2014 at 12:48 PM

NOBODY would use the algorithm presented to do subtraction in a computer.

Also, since the “common core math” methods require a full sheet of paper for every addition and/or subtraction problem, doesn’t this lead to the death of the “paperless office”?

landlines on October 2, 2014 at 12:59 PM

Okay… it took me a while of looking at this before I understood it. It’s not actually a bad thing to teach, but it should not be taught as the primary method.

Looking at a lot of the common core math I’ve come to realize that they are trying to teach some of the tricks and number manipulation that generates a much deeper and fuller understanding of math and numbers and how they relate to each other.

Most of these things are things that I figured out on my own just from playing around with numbers in my mind, and probably reflect the difference between those that excel at math and those that merely learn enough.

It’s not a bad idea to explicitly teach these things to younger students in the hope improving the general populations math skills. The problem is threefold:

1: Current teachers do not know how to teach this stuff. The people who really understand this are mainly mathematics professors, and a few prodigies in other fields. There has been no real effort I can see to teach teachers how to teach this. Probably because the effort will be incredibly expensive and time consuming.

2: The textbooks appear to have been written by that math professor from hell who writes a complex equation on the board, derives a solution, and when asked how just stares at you and says “it’s obvious” and is completely unable to explain the methods or concepts to you. The textbooks don’t actually teach. Combined with problem #1 and the fact that most parents only know traditional methods this means that no one is actually teaching the concepts that Common Core Math is supposed to teach. This ensures failure.

3: There seems to be no sense of priority or structure. Sure it is helpful to know all these other methods and tricks, and ways of thinking deeply about how understand numbers. But the priority needs to be on teaching methods to students so they can quickly find the right answer. The old traditional standard method is the best for this. That should have focus. The other methods should either be introduced as early ways to think about the concept before moving on to the traditional, or as later as alternative ways of thinking about the subject. They should not be prioritized over the old standard.

Sackett on October 2, 2014 at 1:38 PM

It was referenced as Chinese/Japanese from her experience.

Zomcon JEM on October 2, 2014 at 2:00 PM

Sackett on October 2, 2014 at 1:38 PM

That’s a very good summary of the issues. I agree that this method is meant to teach the concepts that go into subtraction and number manipulation and not just subtraction. I think you are right, though. Most teachers won’t teach it that way. Some will. Many in this forum have latched onto the concept (of teaching in a deeper way) so many teachers will too. But many won’t or won’t have time to deal with it. My mom, dad, and two siblings are or were teachers. Difficult job at any level, so we need to be sure they can really teach kids how to think (that’s what school is for, primarily).

I don’t think there is anything nefarious about this, but it’s presented without explanation (in the text) and context (why should you use this method? what is it teaching you?). Okay idea, bad execution.

BillyWilly on October 2, 2014 at 2:05 PM

A. This is really only useful as a ‘tool’ if the student has difficulty comprehending subtraction but has a firm grasp of addition.

I’ve always told my kids that math is all about knowing what tricks, shortcuts or tools you have at your disposal. As such, I have no problem with teaching additional methods even if it seems cumbersome and/or unwieldy to us (since we adults already learned and used our subtraction methods for years).

B. Carrying numbers, such as the case with 23-9, requires making notation to cross out the 2, replace with a 1 in the ten’s column, add 10 to 3 in the one’s column, and then subtract 9 from 13. Finish by bringing down the 1. The steps involved in ‘long’ subtraction can be equally lengthy in steps as the method above, but requires an additional set of skills.

I like to note that when teachers do addition, they also teach carrying numbers, such as when doing 13+9, we are taught to carry a 1 into the ten’s column. Thus, the “old math” I learned in elementary school was complimentary in that both subtraction and addition utilized the carrying method. However, the “counting-up” method will never (as long as they are discussing positive integers) have to be burdened with carrying numbers, which *is* pretty sly/slick.

C. I’ve used a similar technique to ‘counting-up’ subtraction (but faster, less steps) with teaching my kids subtraction when they were young; I’d have them take the largest digit and remove the subsequent digits, subtract the number and then add back in the part they removed.

Using the example above, I’d have them do either of the following;

325 – 38 –> (300+25) – (13+25) = => 300 – 13 = 287.
325 – 38 –> 300 (+25) – 38 = 300-38 (+25) = 262+25 = 287.

Basically, there is more than one way to skin a cat, and the more techniques kids have, the better prepared they’ll be when they get past using numerals and start doing equations with unknowns and/or concepts. I always told my kids, the “blobs” (the numbers) don’t matter, the operations you can do on them and the rules that are applied remain constant. So, don’t concentrate on the answer as much as the method for deriving the answer, because the problems can change, but the method(s) to solve the problem remain as long as you recognize what needs to be done.

Geministorm on October 2, 2014 at 2:11 PM

It was referenced as Chinese/Japanese from her experience.

Zomcon JEM on October 2, 2014 at 2:00 PM

Just happen to be the two I speak. Very different languages.

DarkCurrent on October 2, 2014 at 2:17 PM

Better than this method is to teach kids ‘difference’ and recognizing patterns. I know for myself, when I see a problem such as the above, I know that the difference between 325 and 38 is a loss of 13 from 300, so I arrive at 287 in (essentially) two steps.

Here’s another method that can be used that is similar to ‘counting-up’, but approaches it from the other value.

Raise 325 to the next 100 (since 325’s most significant digit is in the hundreds, thus if we were using 925, you’d raise to 1000), by adding 75 = 400. Do the same to 38; 38+75=113. Now, subtract 113 from 400 = 287…just trickery to do 300-13 as previously shown.

Geministorm on October 2, 2014 at 2:18 PM

They are different – as much as German and English are different or as English and French? Realizing that in the differences of the three languages I referenced they all would have superior idea transmission characteristics to Chinese for example.

Zomcon JEM on October 2, 2014 at 2:23 PM

As mentioned above, the primary problem is that the teachers themselves were not raised/taught using Common Core, so they will have a weak understanding of this methodology. Essentially, it is just manipulation of numbers using accepted rules, which **might** allow some children a better grasp of subtraction, but I highly doubt there has been any long term studies or means testing.

Personally, I’ve always just bombarded my kids with my little thought exercises, shortcuts and techniques (drives them crazy/to tears) and then later on, the light goes ‘on’ and they start using what I’ve taught them and they just speed through their math classes. I’ve had my fair share of run-ins with the public school math teachers, but in the end, I win out because I have always told my kids that I’m an 18th level Math Wizard, and until their teachers/professors are higher level than me, that they can demonstrate what their teacher is expecting from them on the homework/test, but my way is the RIGHT way and I’ll handle any problems their teachers give them if they use my techniques.

Geministorm on October 2, 2014 at 2:31 PM

They are different – as much as German and English are different or as English and French? Realizing that in the differences of the three languages I referenced they all would have superior idea transmission characteristics to Chinese for example.

Zomcon JEM on October 2, 2014 at 2:23 PM

Japanese and Chinese are much further apart than German and English, both Germanic languages. They’re not even in the same language family.

Japanese is not tonal and has a completely different and much more complex grammar than Chinese. The only similarities between the two are the result of Japanese adopting the Chinese writing system early in their history. The kana were invented because of the vast differences in grammar.

DarkCurrent on October 2, 2014 at 2:35 PM

let’s try this one: 2038707 – 2879

You quickly “do this” by rounding/estimating and apply the “subtraction by addition” to arrive at an estimated answer of “203600 or so.”

not as a practical method for actual everyday use except for small numbers.

Agreed. Not for actual everyday use except for small or estimated numbers. Even then it may not be one’s everyday approach of choice, but it’s worth understanding.

G. Charles on October 2, 2014 at 9:33 AM

I know I’m a bit late to the party, but it looks like you didn’t check your work, G Charles! You MEANT to arrive at an estimated answer of “2036000“, not “203600”, right?

Remember, Granny always told you to check your work!

rhbandsp on October 2, 2014 at 3:48 PM

I see – that is interesting to know – thanks. How would Korean fit into that?

Zomcon JEM on October 2, 2014 at 4:05 PM

And I am assuming by the same language family you are using Germanic, Romantic as your family designations?

Zomcon JEM on October 2, 2014 at 4:06 PM

I see – that is interesting to know – thanks. How would Korean fit into that?

Zomcon JEM on October 2, 2014 at 4:05 PM

Korean is entirely different yet again.

DarkCurrent on October 2, 2014 at 4:19 PM

And I am assuming by the same language family you are using Germanic, Romantic as your family designations?

Zomcon JEM on October 2, 2014 at 4:06 PM

No, Chinese and Japanese are much farther apart than that. The Germanic and Romance languages are branches of the Indo-European language family, while the Sino-Tibetan and Japonic language families have no apparent genetic relationship.

DarkCurrent on October 2, 2014 at 4:24 PM

Can’t wait for these kids to graduate from architecture and engineering schools.

They will use calculators on every test in college. Any engineer who does arithmetic on pencil/paper is wasting his employer’s money anyway.

hanzblinx on October 2, 2014 at 4:36 PM

BillyWilly on October 2, 2014 at 9:11 AM

I had 2035828 in my head faster than I could use a calculator.

“Adding up” 38 to 325 provides four new ways to make an error. It may make it easier for some to comprehend, but deriding the one-equation direct method as “granny” gives away the game. Using that term means that the curriculum writers deride it as the least-preferable option. To me, it was second-best. I have always used a hybrid of the two in mental calculations.

hanzblinx on October 2, 2014 at 4:36 PM

We used a book of tables and progammable calculators in the 1980s. Professors knew that we already could do math. We were at the university to learn advanced subjects.

Picaro on October 2, 2014 at 6:57 PM

I do not have a problem with this. I always struggled with math in school. I worked my tail off to get good grades in Algebra, Geometry, and Trigonometry. What I like about this is the pattern recognition skills it teaches. It doesn’t necessarily require paper to count up!

My grandfather always had a knack for doing math in his head – he was sharp, sharp, sharp. He was a whiz in business, too.

Granted, everyone uses calculators nowadays, but I think that this method actually encourages mental math – recognizing the patterns, and giving kids a way to estimate numbers without having a calculator.

I like it. I have a second grader who is doing this Common Core homework. I don’t see the problem with this NEW way of viewing math problems. Traditional subtraction is laborious and BORING! Why learn something that you’re just going to use a calculator for anyway???

But I probably stand alone among my conservative peers.

Nicole Coulter on October 2, 2014 at 7:03 PM

I am also one of the lucky parents with a now 6th grader and 5ht grader.

I was actually good at math … and still do my math by writing it out ( you should see the looks I get from the “kids” and I am only 36″….and I cant understand how to do much of the math home work my kids bring home now.
I know how to get to the right answers, but I cant figure out the “method” I have to use with the kids at any giving moment. I have voiced my displeasure with the schools, along with many parents…of course it does not seem to matter.

watertown on October 2, 2014 at 7:08 PM

This kind of works and it’s even the kind of thing I actually do in my head, knowing how basic mathematics works. But I don’t see how you can meaningfully teach it.

Blacklake on October 2, 2014 at 8:23 PM

I have a lot of misgivings about this method and the reasoning behind it. I have seen too much frustration in children trying to figure it out and where the wrong answer can also be the right if they tried makes no sense, other than to a socialist who thinks a child’s self-esteem is harmed by failure.

I have seen a lot of incompetence among my former colleagues that cause me to wonder how poorly they would teach this to already befuddled students. As for the students, those that would do well before will do well with this, or at least be more successful than their peers. Wait until they hit reality of the real world. Imagine one of them working in a bank, or as a carpenter, negotiating a new car deal, or any job that requires math calculations in their head. Not all students will be successful and they will fail, but failure is still the right answer as long as they tried and could tell you how they got they got the wrong answer. That is another idiotic concept of this new common core.

That aside this really had nothing to do with math or education. It is just the next step removing parental influence from their children and giving it to the state. If you have or ever have had children in elementary school, you probably encountered situations where your child insists that how the teacher did it was the right way and your way is wrong or not as good as the teachers. This new approach effectively not only makes it difficult for a parent to help their child understand what they are learning, it removes them from the entire education process. In doing that, the state has gained complete control; it becomes the parent which is the intended goal, along with the social indoctrination that insures the government control in the future. The ultimate goal is to allow the state to determine at a young age what education the child should receive to best benefit the state. Those familiar with the old USSR, or Cuba, will recognize that education system.

As for all that counting change backwards, your sipping the cool aid.

Franklyn on October 2, 2014 at 10:36 PM

It’s so much easier to just convert the numbers into binary, flip the bits on the bottom number and add 1, thus doing the necessary 2’s complement conversion, and then add the two numbers together. If there’s an overflow bit, discard it. Convert the resulting binary number back into decimal and there you go.

Learned that back in the 101b’th grade.

unclesmrgol on October 3, 2014 at 1:00 AM

(325 – 38) = (338 – 38) – (3+10) = (300 – 13) = (290 – 3) = 287

check: 287 + 38 = (307 + 18) = (317 + 8) = 325

Counting up works nicely for adding.

unclesmrgol on October 3, 2014 at 1:08 AM

This method is we used to call “counting back change”. It is how a store clerk would do it without the help of a cash register.

It is a good method for doing it on the fly with cash, but I wouldn’t attempt to teach it to a 3rd grader.

strickler on October 2, 2014 at 10:06 AM

True, and if you’ve ever had to try teaching a math-challenged teenager how to count back change, you’d know it’s not a great way to learn math. Only the kids that are already good at math the traditional way learn how to count back change quickly.

SD on October 3, 2014 at 11:21 AM

DC – sorry I was back so late. Thanks for the linguistic lessons – very interesting. I have been trying to go back and remember if she said just Chinese or Asian and I added Japanese. She just always remarked what very strong computation people they were. The vast majority were Chinese, and she remarked that one student she advised had been through Calc 3 and had missed one problem in the total of all her college Calc courses. Just amazingly strong in that aspect. Of course as foreign students they were going to be very strong students anyway to be in those programs at a major Midwestern research institution.

Zomcon JEM on October 3, 2014 at 5:45 PM

Franklyn on October 2, 2014 at 10:36 PM

Nailed it. Third paragraph is pretty much all anyone needs to know about Commie Core.

The Mega Independent on October 4, 2014 at 1:22 AM

Subtract 789 from 1234 by using the root vegetable and color up method.

789 is POTATO CELERY KYLE

1234 is BROWN GREEN LIGHT GREEN YELLOW

ALIGN COLORS TO THE VEGETABLES

POTATO TO BROWN
KYLE TO GREEN
CELERY TO LIGHT YELLOW