
The Man Behind Common Core Math - danso
http://www.npr.org/blogs/ed/2014/12/29/371918272/the-man-behind-common-core-math
======
parfe
_It hit the mainstream in early 2014, when a dad in North Carolina posted a
convoluted "Common Core" question from his son's second-grade math quiz on
Facebook, along with a letter he'd written to the teacher. "I have a Bachelor
of Science Degree in Electronics Engineering which included extensive study in
differential equations and other high-math applications," he wrote. "Even I
cannot explain the Common Core mathematics approach, nor get the answer
correct."_

Lunch costs $14.45. You pay with a $20. If you calculate your change without
borrowing you just did common core math. The best facet of common core is the
amount of adults complaining they don't understand it. Rather than an argument
against, it is exactly an argument in support of teaching kids multiple ways
to think about math.

~~~
boobsbr
_If you calculate your change without borrowing you just did common core
math._

Borrowing?

~~~
parfe
Some random gis image.
[http://i.imgur.com/RvAUuPK.jpg](http://i.imgur.com/RvAUuPK.jpg)

Compare that to how you could solve the problem in your head.

.01 + .70 + 6.00

For my example I bet you'd think 5¢ + 50¢ + $5.00 to compute your change.

~~~
parennoob
Firstly, I think you probably mean +0.01 +0.70 +6.00

Also, when you say the +0.01 and +0.70 there, aren't you implicitly borrowing
anyway? It's just "easier" borrowing -- you say that 0.09 + 0.01 = 0.10, as
opposed to explicitly borrowing the 1 to the second decimal and subtracting
the 9. Similarly, you say that 0.30 + 0.70 = 1.00 instead of borrowing the 1
to the first decimal.

I can see why this makes mental maths easier, but I don't see that it is any
deep conceptual improvement over the borrowing. Is one of the goals of Common
Core to improve mental arithmetic? If so, then this makes sense. Otherwise,
unless you properly explain why the two are equivalent, and why the other
method is faster, it's more like a neat sleight-of-hand trick that might leave
kids slightly more confused about why it is "better" than the borrowing
method.

[Reference: Non-American, non-parent who knows very little about the American
education system, but has some friends teaching in it.]

~~~
parfe
Fixed, thanks.

All math solutions will be equivalent. And it isn't a parlour trick. It's
teaching kids to think about breaking down problems into smaller units and
composing a solution. The rote algorithms work, but training kids to execute
an algorithm won't help them understand.

The long form subtraction algorithm isn't a skill that carries over to
multiplication. Breaking a problem into smaller components, composing a
solution, and checking with your original estimate does carry over. And not
just multiplication but programming as well.

------
btilly
My children's school sent me a questionnaire on Common Core. They ended with a
comment, maximum of 300 characters. Here is what I told them:

 _Educational reforms usually result in an ambitious curriculum being
presented by underprepared teachers to unprepared students. And parents don 't
understand the homework and can't help._

 _For example, "New Math" ended with "Johnny Can't Add". I wish my kids
weren't victims of the current round._

I stand by that comment. Given how many failed reforms there have been over
time, how could these smart people not have predicted what has happened?

Right now we have a new set of standards. A new set of lesson plans. Every
teacher has been retrained to teach in a new way. We have new homework going
home with kids, which makes little sense to anyone. Kids learn to perform the
operations, but do not seem to be mastering the concepts. There is an endless
drum beat of positive messaging being sent home from schools. Parents that I
talk to are..shall we say..less than convinced.

This is about the worst kind of big bang upgrade that you could have.

~~~
21echoes
> Kids learn to perform the operations, but do not seem to be mastering the
> concepts

This is explicitly what Common Core is designed to fix -- Common Core is
designed to break K-12 math's traditional focus on rote arithmetic and instead
focus on learning math as abstract reasoning and multiple different solution
strategies.

That you would include this barb in your comment shows that you're more
arguing against the concept of changing standards, and not against Common Core
itself. That's not an indefensible position, and you do consistently argue
from that stance throughout your comment, but I fail to see how it's
constructive. The US is ranked ~30th in math worldwide -- obviously things
need to be changed. Perhaps there are better ways to change our standards:
what would you propose?

~~~
btilly
_Common Core is designed to break K-12 math 's traditional focus on rote
arithmetic and instead focus on learning math as abstract reasoning and
multiple different solution strategies._

The fact that it is designed to do so does not mean that it succeeds in any
way. What I see is the replacement of rote arithmetic with the rote repetition
of formulaic statements that are not connected to actual understanding. This
is not an improvement.

 _That you would include this barb in your comment shows that you 're more
arguing against the concept of changing standards, and not against Common Core
itself. That's not an indefensible position, and you do consistently argue
from that stance throughout your comment, but I fail to see how it's
constructive. The US is ranked ~30th in math worldwide -- obviously things
need to be changed. Perhaps there are better ways to change our standards:
what would you propose?_

I would suggest incremental improvement, not revolutionary change. The
education establishment has a long history of revolutionary change, and knows
exactly how to go about it. This always turns out badly. The much safer way to
go is to incrementally improve, with constant feedback and repetition. It
doesn't feel day by day like progress, but it has much higher odds of actually
succeeding.

What our educational system has done is the equivalent of throwing out a major
software system, and rolling out a new one. Such big bang upgrades seldom go
well, and the larger the system the worse the disaster that follows. Even if
you can wind up in a situation where success can be declared, huge amounts of
damage are done.

------
jndsn402
IMO, the problem with the way Common Core has been implemented is that there
is a whole new analytical/critical thinking component that is bundled together
with math. But parents when parents think of math they think of computation,
arithmetic, formulas etc. Not 'explain why ancient calendars used 60-day
units' (actual question from my daughter's 6th grade curriculum, may be
misquoting a bit. The answer is because 60 has many factors).

I'm not saying it's good or bad to teach math that way, it was just not
communicated well and still isn't. Math has been replaced with math+critical
thinking. It's as if English class now also included Latin. Maybe good, maybe
bad, but it's a whole different class.

~~~
jwmerrill
It's hard for me to imagine a world view where adding critical thinking to a
subject might make it worse.

> It's as if English class now also included Latin.

I think a better analogy would be "it's as if English class now included
critical thinking." Or "it's as if Science class now included critical
thinking." Or "it's as if History class now included critical thinking."

All of those sound unambiguously good to me.

~~~
debacle
The math curriculum I was exposed to in school (relatively recently, by any
standard) always included critical thinking and was likely the subject that
involved the most critical thinking because it was the subject where critical
thinking was the most objective.

------
atratus
I have looked over some of the common core material given to both early grade
school and middle schoolers and its very clearly attempting to teach abstract
reasoning. There is alot of word problems that ask how to decouple a concept
from the concrete values calculated in a previous step. Most people from older
generations are not going to see the value in this... parents (and teachers)
need to know there is much more to math than arithmetic

~~~
ploxiln
Isn't it much easier to just use "x" and "y" instead of strange terms like
"subtraction stories"?

I always did quite well in math, but sitting there at the back of the class
messing around with stuff at the end of the book, I found that teachers tried
_so damn hard_ to make the content _easier_ , and in the process made it
harder. I could figure out how what they were saying corresponded to the
material, because I already knew the material, but could not see how anyone
else would understand it. Few did.

That said, "Common Core" is probably fine, as usual the implementation quality
is just much more important than any particular methodology. (just like
"object oriented programming" etc).

------
cabinpark
I think the greater problem is not with the standards (which I know nothing
about) but with who is teaching it. I have talked to people who are elementary
school teachers who know nothing about mathematics, yet they are given the
task to teach it to children. They have little understanding of why the
mathematics they teach is important and useful. If you don't give children a
solid foundation in their formative years, they will always struggle with
mathematics.

------
bane
The real problem is that Common Core tried to do several things in order to
improve rankings against countries like South Korea. But instead of doing the
things which high ranking countries have shown do actually produce high-level
results, they put together an almost completely untested curriculum, then
rolled out it out everywhere.

There's not really any evidence that the approach in Common Core will improve
student's math achievement scores, and lots of evidence that it's been an
abysmal failure. Instead of confused students ignoring the subject, we now
have confused, frustrated, miserable students, a generation of which will now
hate mathematics more than the one that came before them. The only thing CC
has achieved is in alienating an entire generation of students from the
critical skills of math.

The article makes the argument that the absurdity of the implementation of CC
is a result of local standards overriding a national, well thought out program
and that the CC creators are powerless to fix things. I call hogwash. Set up a
textbook certification program: publishers have to pay some nominal fee to
these guys to review the book and give it a seal of approval that "yes, this
book fulfills what Common Core intends". Use that seal as a quality signal,
books without the seal should be considered next to garbage and books with it
are assumed to be better.

They should also have written their own reference K-12 curriculum, providing a
gold-standard example of what it should look like. Publishers can license that
curriculum and publish it unmodified or they can license it and add (but not
subtract) chapters to handle local requirements.

That these things weren't done, on what's supposed to be a national
educational reform that was "a lot of work" boggles the mind.

It reminds me of various specification-by-committee standards that are all
over the tech world. They're laid out in document somewhere, with no reference
implementation and no certification that some other implementation really is
compliant and we end up with a decade of lost time while every developer tries
desperately to get their image to line up just right in half a dozen different
browser rendering engines, or get their query to work right in a dozen
different SQL standard databases to work the same.

------
mzs
I'm a parent and I've overall been very happy. In math it's very simple for a
kid to get hung-up on one simple thing and then they have this hole and cause
things build on previous knowledge later things are now trouble as well.

For example one of my children could not factor in the way I was taught with
the trees, but another way was presented and it totally clicked for her. For
one of my sons he could not do long division in the manner I was taught, but
another method worked for him instantly. He showed me and I even liked it,
cause I remembered how hung-up I had been about getting the correct digit at
each step myself.

I also like how it seems to have this component about reasoning. To many
people math is arithmetic, but it really is not that. The problem is that
there are kids where requirements were different. So for example now a third
grader is supposed to have memorized multiplication table, but there were
schools that never did that before. Or a sixth grader is now already supposed
to have done some geometry, but the school only did it in 8th grade or HS
before. There is no route to fill in the gaps during this transition in many
schools it seems.

------
malandrew
One of the biggest problems in changing anything like this is that it requires
extra effort from teaches to completely "retool".

Anyone who has ever spent anytime teaching knows that when you first start
out, you have to figure out a lot of stuff when teaching a new curriculum, but
by the time you've taught the material 2-3 times [0], you start streamlining
things and getting more efficient. The time you spend retooling almost always
comes out of your personal time. i.e. from hours beyond the 40-50 hour work
week.

After you know a curriculum well, you end up with more personal time.
Introducing new standards, means a new curriculum and a new curriculum means a
lot of unpaid personal time from teachers if you want them to really adopt it
and teach it well.

I just don't see a new curriculum working well unless it comes with the notion
of paid extra-time that you know teachers will have to put in to succeed with
the new curriculum. It doesn't have to be a lot, but simply 5-10 more hours
each week and a bonus equal to 10-25% of their salary to make up for the
additional time would probably work. The only key would be that there needs to
be a way to measure that teachers are putting in the extra time to really
learn the new curriculum and apply it instead of collecting the bonus for
putting in the minimum effort.

At the end of the day, it you don't budget both time and money to learn any
new curriculum, it's either going to fail or be met with resistance from
teachers who feel like they already have a system that works for them and
their students.

[0] either in the same semester or school year because you teach multiple
groups the same material or after 2-3 semesters or school years of teaching
the subject to one group at a time

------
pm90
Firstly, I would love to hear what tokenadult has to say about this.

Moving on, I think the article mentions the problem of getting good textbooks.
This has always been a huge problem, I think. In India, there is a trinity of
syllabi: one recommended by the Federal (Central) Govt. (CBSE), one by a
consortium of private schools (ISCE) and each individual state's syllabus. So,
a school does not have the independence to create its own curriculum, it has
the choice of adhering to these 3 systems. It does have the independence of
choosing textbooks; however, there are also officially prescribed books, and
many teachers teach from them only because they cover things that are often
asked in the standardized tests.

So, I don't know if it does good to have just one system, and not give schools
access to more options.

------
sputknick
Does anyone know: is their a difference between "Common Core" the method of
teaching, and "Common Core" the idea that all students across the nation
should be held to one standard?

~~~
kaitai
Common Core is a set of standards
([http://www.corestandards.org/Math/](http://www.corestandards.org/Math/)).

I don't think there is one official way of teaching that is "Common Core."

The texts currently labeled Common Core are mostly copy-and-paste remixes of
existing material.

The exams labeled "Common Core" are unfortunately similar. They don't test the
standards as written. For math, a discussion at
[http://www.washingtonpost.com/blogs/answer-
sheet/wp/2014/11/...](http://www.washingtonpost.com/blogs/answer-
sheet/wp/2014/11/30/a-dissection-of-common-core-math-test-questions-leaves-
educator-appalled/) . Unfortunately, a theme seems to emerge of Pearson tests
written to test Pearson materials, some of which have a "Common Core" label.

------
Strilanc
> _As powerful and influential in reshaping American classrooms as the
> standards could be, they don 't include lesson plans, or teaching methods,
> or alternative strategies for when students don't get it._

That seems like a really serious flaw. Did the teaching community at least
make and share their own?

~~~
ashark
That's what consultants are for.

The typical cycle for curricula, teaching strategies, and/or discipline plans
in schools:

1) OMG the kids aren't learning better change everything!

2) District, state, or both pick some new system and pay some consultants and
various companies a bunch of money.

3) Administrator presents plan to teachers: Here's the new system. Half of
it's not finalized yet. Should be done in a year or two. We're not
implementing some parts of it because they make me uncomfortable. The old way
is stupid and sticking to even the parts of it that work well for you will
result in my making your life miserable and eventually trying to fire you.
You'll need to re-write all your lesson plans to conform to the new system.
Here's a mountain of new paperwork for you. No, you can't stop filling out any
of the old paperwork.

4) A couple years pass

5) Goto 1

~~~
acdha
A few years ago, a veteran teacher told me his version:

1\. Introduce a new test with an unfamiliar blend of questions, new style
questions, etc. but don't give teachers extra time to actually receive updated
textbooks, update their classes, etc.

2\. Start giving the test to students immediately before they have any
experience with the new format

3\. Use the result low test scores as proof that things were really bad before

4\. As everyone gains experience with the new system, attribute rising scores
entirely to the brilliance of the new model. Give bonuses to district / state
officials.

5\. Once scores plateau at roughly the previous levels after a few years,
start talking about repeating the process. At no point should you seriously
consider tackling the structural problems preventing holding perennially
under-performing groups back.

------
duckingtest
If I were to design a school program from the ground up, I would teach
programming just after reading & writing. The best way to learn math is to try
to make a program that solves specific problems.

~~~
EliRivers
_The best way to learn math is to try to make a program that solves specific
problems._

An often reasonable way to ensure that you can mechanically apply a problem
solving technique (which is related to, but absolutely _not_ the same thing as
understanding the maths) is to make a program that does it. Trying to learn
maths by programming it is a terrible idea.

Just this morning I've been looking at Riemann's geometry; learning that
through the medium of writing a program to "do it" would be painful. I don't
even know what it would mean to write a program that "does" Riemann's
geometry. I suppose I could write a program to apply some equations, but
that's not learning the maths at all. That's automating some equation solving
and it teaches me nothing about the maths.

~~~
duckingtest
>An often reasonable way to ensure that you can mechanically apply a problem
solving technique (which is related to, but absolutely not the same thing as
understanding the maths) is to make a program that does it.

What "problem solving technique"? There's no algorithm you can mindlessly
remember and use it to create algorithms. Making a program that solves the
problem is the highest possible understanding.

>I don't even know what it would mean to write a program that "does" Riemann's
geometry

That's because it's an abstraction, not a problem to be solved. In the same
way you can't write a program that 'does' functional programming, you can only
program in a functional way.

Well, I guess writing an AI which can solve problems in Haskell would be an
exception. I bet you couldn't remember its code and execute it in your head,
though.

------
jwmerrill
The common core Mathematics standards are available for anyone to read here:

[http://www.corestandards.org/Math/](http://www.corestandards.org/Math/)

I would encourage anyone who is really interested in this issue to spend some
time reading, or even skimming just a few sections. I find the standard is
generally quite readable (conceding that it's a non-trivial commitment to read
more than 1 grade level, but then again, there's a lot to know about math...)
and I also tend to agree with many of the ideas in it.

I've been disappointed, but in hindsight not very surprised by the anti-
intellectualism in the public response to the common core. I'm more surprised
to see similar anti-intellectualism here. I expect better from you, HN!

It's true that the common core places more emphasis on critical, analytical,
and sometimes even abstract thinking than the "traditional" math curriculum
(whatever that is...). But as people who read hacker news, doesn't that sound
good to you?

It's also important to know that the Common Core standards are a set of
expectations, and that's actually all they are. They are not worksheets or
standardized tests. If you see a bad "Common Core" worksheet, it is a bad
response to the Common Core, but it isn't actually the Common Core itself. If
you want to criticize the Common Core itself, choose a part of the document
above and criticize it. Or failing that, criticize the process that led to its
creation and dissemination. But criticizing a few oddball problems is not a
powerful argument.

My own criticism-in-hindsight is that the Common Core is trying to do two
things at once. Maybe it would be succeeding better if it only tried to do one
of them at a time.

The first is to provide a nationally standardized set of grade level
expectations. Many people have an interest in this goal because it makes it
easier to prepare teaching materials for a large group of students, and to
compare education effectiveness across regions. In an alternate world, this
could have been done descriptively instead of prescriptively. The standards
could have simply described what was happening in the largest fraction of the
country's classrooms.

The second goal is to improve math pedagogy in the U.S. and bring it up to the
best international standards, including tying math more strongly to critical,
analytical, and abstract thinking skills. This is a prescriptive goal.

If the standard was a process, we could have started with 1, and moved to 2
incrementally. But I suggest this only half-heartedly, because I think 2 is a
great goal, and I think the Common Core (as a document) does a pretty good job
of it.

Now to be clear about my own biases:

I don't have any children (school age or otherwise). If my first exposure to
the Common Core was seeing my child assigned problems that looked unfamiliar,
unimportant, or even that I didn't know how to do, I'll concede that I might
have reacted negatively too.

I do have a physics Ph.D. (i.e. math background), I do think and care a lot
about how people understand math, and I do work on a software tool that tries
to help children think about (part of) math more powerfully.

~~~
zaroth
The issues with Common Core as I've read are a lot bigger than a few oddball
problems, or under-developed worksheets or testing. The problem is apparently
instead of taking these core and mostly trivial concepts and finding ways to
actually make them intuitive, in the name of "critical thinking" we've created
this theater-of-the-absurd approach like what you see discussed above.

I don't have much personal exposure to "Common Core", but I've found when all
the implementations turn out as shit, the blame usually lies with the
specification.

My personal opinion is that a lot of this overloading on processes and bizarre
approaches to presenting problems (and don't get me started on the form of
homework assignments and tests) is because we're out-pacing the natural
cognitive developmental process. For example, take the sample chapters that
were on the front page a couple days ago from "Math from [Age] 3 to 7" [1] you
can see a very interesting approach to building math skills. But even in that
case, the author is rushing developmentally advanced tasks which are more
likely to result in frustration and giving-up than engagement and learning.

Fundamentally, most learning does not occur while a teacher is speaking. The
more absurd lengths the teacher goes to "explain" some concept, the less
likely any child is to actually learn it. The more foreign the concept is by
the time the kids get home, the less likely it is to be mastered.

I have a daughter in Kindergarten, but fortunately not one that follows CC. I
just spent some time reading through /Math/Content/K/ on corestandards.org.
Most of it is, IMO, complete trash and not at all aligned with how kids in
kindergarten _actually learn this shit_. As a "spec" it's writing is sloppy,
poorly defined, and highly ambiguous. If this is the starting point, I'm not
at all surprised the resulting lesson plans are worse than nothing.

I also spent some time reading /Math/Practice and it struck me how all these
things that CC is presenting as "Standards for Mathematical Practice" are not
at all how children conceptualize mathematics, or cognitively approach the
task of solving a math problem. Many of the stated practices are directly
contrary to how children will naturally want to approach and solve a given
problem, and I can imagine exactly how teachers faced with "instilling" these
practices would get to exactly where we find ourselves.

[1] -
[http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf](http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf)

~~~
jwmerrill
> I just spent some time reading through /Math/Content/K/ on
> corestandards.org. Most of it is, IMO, complete trash and not at all aligned
> with how kids in kindergarten actually learn this shit. As a "spec" it's
> writing is sloppy, poorly defined, and highly ambiguous.

I respect that you took the time to read the document, but your criticism
isn't very specific. Are you bothered by the fact that it uses words that
aren't appropriate for Kindergartners to describe what they should know? Or
that it says what they should know, but not always how to teach it?

I think the "spec" analogy is a good one. The goal of a spec is to lay out
requirements, not implementation. Same idea here, which strikes me as the
right choice.

The actual expectations are to know a few things about counting, numbers, and
shapes. That seems developmentally appropriate to me (admitting that I don't
have much recent experience with kids this age).

What do you think Kindergartners should know?

Re: the practices part, these same practices are mentioned at every grade
level through high school. I agree that the practices sound way too advanced
for Kindergarteners, but the goal is to get students to do them well by the
end of high school, not by the end of Kindergarten.

~~~
zaroth
A specific accounting of that would be several blog posts long I think, it's
quite hard to get specific without cherry-picking particularly bad parts.

I continued to read through 5th grade math curriculum, and really I think it's
completely the wrong approach for how children should learn the material. It's
hard to summarize everything I dislike about it in just a few sentences.
Mainly I think the process should be much more natural. This isn't something
that really has to be taught, through 5th grade at least it all comes
naturally in the right environment. So the approach is backwards; it's not
'here are the list of skills which should be taught and mastered at each
grade' it's here are the ways we foster learning over this 6 year period.

The whole approach of setting these micro-goals, the whole thing is far too
low level. When a spec starts at such a low level, it becomes a prescriptive
checklist, not a spec.

------
elberto34
The way you improve test scores and increase America's economic
competitiveness is to understand that higher IQ students will learn faster and
more efficiently than lower IQ ones, and then by grouping the students
accordingly. Instead of wasting billions trying to get everyone up to speed,
let's devote more resources to those who demonstrate talent, while those who
cannot keep up are encouraged to pursue vocational work. Hence, we see that
that the problems facing our educational system cannot be lessened by throwing
money at it with reckless abandon, but by better understanding human
biological differences and how these not only effect learning, but economic
outcomes. I don't want to make this a partisan issue, but what we observe is a
leftist denial of human cognitive differences and a denial of the significance
of these differences as the culprit. Better teachers, new technologies, and
new curriculum can only go so far; for progress to really be made we need to
stop being in denial of human biology as it pertains to IQ and learn to face
these sometimes uncomfortable but inescapable realities head-on.

