

This Is What Common Core Looks Like - loupereira
http://www.erickerickson.org/blog/2014/09/30/this-is-what-common-core-looks-like/

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sp332
Common core is not a curriculum. It is not a textbook. It is not a method of
subtraction. There are badly-written textbooks both in and outside of Common
Core.

Edit: Here we go, Common Core math standards. Grade 2 starts on page 17.
[http://www.corestandards.org/wp-
content/uploads/Math_Standar...](http://www.corestandards.org/wp-
content/uploads/Math_Standards.pdf) Have a look, it's only 4 pages long.

To be specific, this is a third-grade textbook. Students learn subtraction in
previous grades, so this is just a quick review before moving on to third-
grade topics like multiplication. Notice the problems at the bottom don't
require students to use this particular method. If your third-grader can't
subtract, they were already behind before you switched to Common Core.

Also, is the method given really that hard to understand? It's probably not my
favorite way to subtract, but it's kinda cool.

~~~
seanflyon
Just to be clear

"But standardized tests, the SAT, and the ACT are all moving over to Common
Core. So our child has to learn this insanity."

which implies that standardized tests test for this particular "counting up"
subtraction method. If I understand your statement you are saying that this is
not the case.

Right?

~~~
AnimalMuppet
It's really hard for a standardized test to measure _how_ you subtracted.
(Yes, I am aware that it could be done.) But what it really measures is, can
you subtract? Do you get the right answers?

Personally, I don't like this approach, because to do one subtraction, you
have to do four additions. That's kind of inefficient, in my view. But as
sp332 pointed out, the kids should already know how to subtract numbers by
this point. If a kid didn't get it before, this curriculum throws a new method
at them, hoping that this one will make sense to them. I'm not sure that I
have a problem with the approach (though it wouldn't hurt tweak it so as to
not confuse the kids who already know how to subtract).

~~~
sp332
I doubt the count-up method was intended to be a new method. I think the new
curriculum had it in the second-grade book, and assumed that former second-
graders had seen it there. It's not the textbook makers' fault that the school
changed between years.

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mturmon
This seems like generated outrage.

The OP should take a minute to think about how the method of subtraction
works, and then explain it to his kid.

I associate this panic reaction (OP: "this new method makes no freaking
sense") with people who are math-phobic. The solution is to just settle down
and think about it. (Common core, third grade objectives, number 1: "Make
sense of problems and persevere in solving them.")

And, one thing I've learned about elementary educators is that they don't want
to fight with parents. (Unsurprising!) So if you say (like OP did), "This
common core math sucks," they are going to say, "yes, we don't like it
either." If you said it was an interesting way to do subtraction, they'd agree
with that too.

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cafard
Back in the days before computerized cash registers, this was typically how
cashiers made change. Hand one $5 for a $1.34 purchase, and the cashier counts
it back out as

(penny) $1.35 (nickel) $1.50 (quarters) $1.75, $2 (dollar bills) $3, $4, $5

Some still do it that way.

In _Teacher in America_ , chapter "Let _x_ Equal ...", Jacques Barzun
mentioned as an example of widespread innumeracy the half-trained cashiers who
did not know this technique. That was written in the early 1940s.

~~~
wahern
It's actually a very useful method for quickly finding the difference between
two numbers. And I would think that any computer programmer would appreciate
the algorithm. The algorithm is a classic divide-and-conquer technique that is
perfect for quickly performing arithmetic in ones head. And it would also be a
good entre into teaching things like associativity and commutativity.

I use something similar to avoid getting too much change at a cashier, and to
use up loose change (pennies, nickels, etc), except I usually count down and
add in the difference. So, for example, if some bubble gum cost $1.28, I might
give the cashier $2.03. Then, assuming the bewildered cashier doesn't try to
give me the pennies back, I get three quarters for laundry, instead of two
quarters, two dimes, and two pennies.

If I don't need laundry change, I'll count up or down searching for the amount
that will maximally reduce the number of coins in my pocket (without avoiding
bills, which would just be annoying to everybody). With practice you can do
this in a split second, and it really blows the mind of some cashiers.

Isaac Asimov said something to the effect that smart people will tend to
figure out these algorithms on their own. So it's kind of ironic that now
somebody is complaining that it's being taught to kids. I suppose the only
real legitimate criticism here is that, according to the link, there's only
one example of this method, and then it's never mentioned again. If anything,
it should be expounded upon.

~~~
deciplex
It's a good method for making change, but for doing subtraction in general it
is (in my opinion) not so great, the reason being that you have to keep track
of more figures in your short term memory, when compared to left-to-right.

To do subtraction by counting up you need to remember: the minuend, how far
you've already counted up, and the number you've already counted up to. So,
three figures. Subtraction left-to-right (or right-to-left) only requires you
remember two numbers: what remains of the minuend, and what remains of the
subtrahend. It's pretty easy even for primary school kids once they practice a
bit.

Of course, when you're making change, you don't actually care how far you've
counted up, because you're not really after the difference exactly, you're
only trying to arrive at the correct number of coins and bills. So you can
forget that part, or rather you can leave it to the coins in your hand to
remember for you, and now you're back to two numbers. But I'd bet that if I
asked you to tell me on the spot what the difference was _without looking at
the change in your hand_ you'd struggle to tell me.

Making change by subtraction left-to-right is cumbersome because, while you
still only need to remember two numbers, after you calculate the difference in
your head you must now count out the change, whereas with counting up you're
already done.

Different tools for different purposes. I agree with Asimov.

~~~
wahern
In practice you're not doing every step consciously.

Take, for example, subtracting 188 from 500. Count up to 200 to get 12. The
difference between 500 and 200, however, is automatic. It takes no thought at
all. So you arrive at 312.

Sometimes you can count down, too. Take 512 - 333. That's just 200 - 21. You
can find 21 by doing it left-to-right if you want (it's how I just did it).

I'm not saying it's some kind of magical way to handle arithmetic, and it's
not something you use to the exclusion of other techniques. Rather, what
you're doing is converting the problem to something that is easier to solve.
Left-to-right is a very useful, general, and systematic approach to do that,
but there are faster ways depending on context. You can analogize it to
programming in that you can trade CPU (left-to-right) for memory (cached
tables of differences) to arrive at an optimal algorithm for the problem at
hand.

So I would just re-iterate that learning these techniques isn't simply for the
sake of doing arithmetic faster in your head. Rather, understanding how and
why they work, and how to select the methods, improves numeracy in general.

And FWIW, I never look at the change in my hand. I don't literally count up
like a cashier might when handing you change. To be honest, until _just_ right
now I never really fully comprehended exactly what they were doing. I knew it
was similar, but it only now just clicked that they were counting up in a
fashion similar to what I've always just done in my mind's eye by breaking up
and rounding numbers. (Not that I think I'm particularly good at this--please
don't walk up to me on the street and drill me ;)

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PaulHoule
As a homeschooler I think Common Core is a good thing in that it tells you
what you need to cover, and it means that I can choose from a lot of different
curricula which include it.

If you work through Kahn Academy math, you will certainly run through some of
these areas where kids are pushed to do some kind of math problem in a highly
stylized way that (i) they struggle with and (ii) don't see the relevance of.
Elementary school teachers have told me the same thing, but it is not the end
of the world.

There is "no one true way" to do arithmetic. When I was in the fourth grade I
had the worst time with 3-by-3 digit multiplication. That didn't stop me from
getting a B.S. in Physics and Math, with an A average in my majors, and also
getting a PhD in theoretical physics. Recently I read that a lot of other
people who were "good at math" struggled with the curriculum when I was a kid
so nothing is going to be perfect.

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holychiz
I'll echo the comment that Common Core is not a textbook nor a particular way
to add/subtract. It's a standard to establish baseline knowledge US kids must
master. That blog post is raging about a new way to do subtract which seems to
be out of reach for his comprehension, can't teach an old dog kindda thing, so
he blames it on Common Core. He also mentioned that there are 4 new ways to do
subtraction. This should be good news. Kids/people learns to do things
differently. 4 different ways means kids have more arsenals to tackle their
problems. I wish I had that learning opportunity! Specifically about that
subtraction, did you noticed that it'd make it easier to do the math in your
head? maybe there is a reason for the madness after all.

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jdanner
Common Core is just fine as a set of standards and has a good shot at being
adopted around the world, so we need to get over it. Common Core is going to
lead to a lot more innovative solutions, because the market of students on it
will be large. It's very nice from a computer science standpoint as well.
Check out the game we built at Zeal. While it's a nice simple game on the
surface, behind the scenes we are maintaining a complete map of everything
every child has mastered in Common Core Math and Literacy K-8, which lets us
figure out an ordering of skills to learn and what to do if a child is
struggling on a given skill. This is the kind of thing that has been solved in
every other industry, but Common Core enables in education.

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DanBC
> They cannot help their children. The math makes no sense and seems to offer
> no practical purpose other than it is new.

First of all parents were not able to help their children with old methods
either. Give someone a pen and paper and ask them how to add 17% to 58. You
don't want an answer - just a working method. A lot of people can't do this on
paper, but that's okay because we have computers to do that stuff. Lots of
people can't add 17% to 58 using a computer. I find that a bit scary.

Going on to the example: I'm pretty stupid; I've often said that I am hopeless
at math. I found that single example really easy to understand. I've not had
any exposure to similar examples. I don't believe the author is actually
baffled by the example. Perhaps a book might help?

[http://www.robeastaway.com/books/maths-for-mums-and-
dads](http://www.robeastaway.com/books/maths-for-mums-and-dads)

> What on earth are number bonds? What are partitioning and chunking? And why
> does my child look blank - or have a tantrum - when I demonstrate long
> multiplication? This book is for mums, dads and grandparents who want to
> help their primary school children or grandchildren with maths. To do so,
> many parents find they need to overcome their own rustiness and also to
> learn the strange new methods and terminology. Throughout the book are
> games, puzzles and examples of amusing ways in which kids ingeniously 'get
> it wrong'.

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blkhp19
While I agree that one example is not enough to grasp the concept for most
people, I think that the "counting up" method is actually better because it
shows kids what is going on in subtraction.

The borrowing method that I learned growing up doesn't make much sense. You
just follow the rules with no real reason.

I'm in my third year of college and only just learned why the borrowing method
works - and I only learned it because I had to start subtracting numbers in
different bases for my MIPS assembly class.

~~~
seanflyon
Perhaps the counting up method makes it easier for most kids to grasp the
underlying concepts. The borrowing method can also teach kids the underlying
concepts and follows nicely from addition as it is the inverse of "carrying
the 1".

> You just follow the rules with no real reason.

This is the real problem here. We should not teach our kids to memorize a set
of rules but to understand the concepts. When I was in school I had a rule
that I would not memorize rules that I did not understand or formulas that I
could not derive. I would probably be faster at arithmetic if I had memorized
my multiplication table like I was supposed to, but I think that rule served
me well.

~~~
adamtj
When you're in 2nd or 3rd grade, it's more important to learn the mechanics of
subtraction than to understand why it works. Kids at that age need to fill
their brains with facts so that they have the raw materials for developing
understanding when the are more mature and more able to understand.

In this case, borrowing is more compact and efficient. That makes it faster
and easier, both on paper and in your head. If you write out the borrowing
method as verbosely as this counting-up method, it's almost as easy to
understand. However, that's not important in elementary school and shouldn't
be done. The counting-up method has the disadvantage that you _can 't_ write
it more compactly.

Students who learn the counting-up method will be hobbled in algebra: they'll
be wasting their limited brainpower on the mechanics of subtracting the hard
way when they could be using an easier method and devoting more brainpower to
learning the concepts of algebra.

Of course it's important to understand how subtraction works, but by the time
you get to algebra, that should be easy. Anybody who is uncomfortable in their
ignorance can either just think about it, or ask a teacher. It's not hard.
Just note that 325 = 300 + 20 + 5. Then line everything up and go. That
understanding isn't worth a lifetime of pain.

~~~
seanflyon
I think that understanding basic concepts is foundational. It not only gives
you an understanding you can build off of, but also teaches you how to think,
how to approach a new problem. You say that kids need to fill their heads with
facts, but I think they should fill their heads with concepts that they
actually understand. Simple concepts that they understand, not facts, are the
raw material for developing more complex understanding when they are more
mature.

I realize that I cannot prove what I just said, so perhaps I stated it too
strongly. It's possible even, that what I claim is true for some children and
what you claim is true for others. I know that an emphasis on understanding
has served me well, and that an emphasis on rote memorization has worked
poorly for several people I know.

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warmfuzzykitten
Perhaps more disturbing than the author's inability to understand a simple
procedure in a third-grade math text is his attempt to cast Common Core as
part of an overarching conspiracy of corporations and (of course) government
to turn our little ones into docile robots. This is what a nut case looks
like.

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daltonlp
The first two paragraphs illustrate a huge problem with US math education,
which pre-dates common core, but is reinforced by it.

That problem is the false belief that numeracy is improved by learning
different ways of looking at number operations. (i.e. four ways to subtract).

Our child's second-grade teacher (a very good teacher) has a poster
illustrating 7 ways to subtract. Seven ways, no exaggeration. This poster is
older than common core.

Students learn math just like they learn to kick a ball. By practicing. Learn
one way to subtract, and practice it really really well. Or learn two ways,
and practice each way really, really well. Learn more ways if you want, but
practice each way really really well. Most math curriculums assume that
learning multiple ways is equivalent to (or better than) practicing one way.
They don't require the repetitive practice.

As comments have pointed out, the common core standards don't explicitly
require this multi-way approach. But the CC standards compound the problem by
requiring students to _explain_ concepts in order to demonstrate mastery.
Completing lots of subtraction problems with a low rate of error doesn't
count. You must _explain_ , in order to understand. And if you _really_
understand, shouldn't you be able to explain different approaches?

I would say no. Or at least, not yet. I don't want a third-grader explaining
how to subtract unless they can also finish 50 subtraction problems in a row
without pausing to struggle. And if they get the problems right? Good job, you
get an A. Wonderful, let's skip grading the explanation because that is
subjective as hell.

TL/DR: The article rightly points out a crap way to teach math. Common core is
not totally to blame, but it makes a bad problem worse.

~~~
scarmig
Which programmer would you rather hire: the one who memorized a particular
algorithm but has no idea how it works, or someone who can develop it from
first principles and enlightened judgment?

There's no strong reason to glorify one particular subtraction algorithm over
another, especially since the actual use case for it is relatively rare.

~~~
daltonlp
Full agreement - any subtraction algorithm is fine, as long as it's well-
learned (which takes a non-trivial amount of practice).

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hyperair
I wouldn't fault Common Core. I'd fault the textbook. That little page on
counting-up subtraction didn't make sense to me either, so I went to
Wikipedia, read this shorter snippet[1], and understood it immediately. That
textbook's just crappy.

[1]
[https://en.wikipedia.org/wiki/Subtraction#Counting_up](https://en.wikipedia.org/wiki/Subtraction#Counting_up)

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jeff303
This is what one implementation of Common Core looks like

