
Why Do Americans Stink at Math? - theunamedguy
http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html
======
jimhefferon
I teach math. I am impressed that when you read these comments, very few of
them show evidence of having read the article.

The article is about experience with actual students, with ones who have a
real knack for the subject and would learn it despite what any teacher did,
and with ones who waver. There proves to be a better way, which the article
describes in various ways, including as "sense-making."

One of the problems here is that everybody has a pre-formed opinion and does
not seem to want to risk having to modify it with the evidence of experience.

~~~
whack
> _" One of the problems here is that everybody has a pre-formed opinion and
> does not seem to want to risk having to modify it with the evidence of
> experience."_

That's probably the most accurate description of HN comments I've seen. People
see a headline related to something they already have pre-existing beliefs
about, they read a few paragraphs just to make sure they're on point, and then
they jump straight to the comments to argue in favor of what they already know
to be true.

I'm willing to wager $10000 that a significant majority of HN commenters in
any thread do not read the article in full, and even among those who do, a
smaller minority actually post comments addressing the meat of what the
article is saying.

~~~
agentgt
_> I'm willing to wager $10000 that a significant majority of HN commenters in
any thread do not read the article in full, and even among those who do, a
smaller minority actually post comments addressing the meat of what the
article is saying._

I'm curious... did you read the article in full? I'm not saying you're wrong
but it would be funny if you didn't read it as well :)

One of the things I like about Scientific America is they have an Executive
Summary at the start of the article. So while folks may not have the details
they at least have the correct gist.

I skimmed the article. Do I have pre-formed opinions... I do. Would they have
changed after reading the article in detail ... they might have if there was
some hard evidence other than the obvious stat that the US is bad in math.

My question (I'm having my first child with in a month) is what do I do as a
parent other than be patient:

 _" Training teachers in a new way of thinking will take time, and American
parents will need to be patient. In Japan, the transition did not happen
overnight. When Takahashi began teaching in the new style, parents initially
complained about the young instructor experimenting on their children."_

My father forced my brother and I into Kumon. Kumon was hardly imaginative.
Did it work? I think a little bit.

Education techniques particularly math has changed so many times that it is
beginning to look like diet and exercises. We are all a little jaded so I can
understand the plethora of pre-formed opinions.

~~~
jimhefferon
> My question (I'm having my first child with in a month) is what do I do as a
> parent other than be patient:

You could look into how your local public school system teaches. Taking to the
people who teach there, for instance, is helpful. Expressing support for an
NCTM-like approach, if you find you do support it, would also be great.

> Education techniques particularly math has changed so many times that it is
> beginning to look like diet and exercises. We are all a little jaded so I
> can understand the plethora of pre-formed opinions.

I understand and as a person who teaches math, and teaches teachers too, I
feel the same impatience.

I want to know why we don't just go out and see, on actual students, what
actually makes them better at understanding and being able to solve problems.
Try different things and see what works. Review video tapes. Give before and
after tests, and focus groups, and see what the people in the class learn the
most from. Train teachers in the details of doing the job, as an engineer or
doctor would be trained in details.

The thing is, that's what the folks described here are doing. Have they got
the final answer? I doubt it, particularly as the impacts of tech is so little
understood even now. But they are making progress, at least it seems that way
to me. (If you are interested, _Building a Better Teacher_ is a source that
would give you more of an understanding of what the discussion is. This
article was part of the marketing people's plants for the book.)

~~~
bpyne
This comment is related to your muse starting with "I want to know why..." I'm
simply pondering and looking for feedback from someone who is actually a
teaching professional unlike myself.

"There [my comment: Finland], as in Japan, teachers teach for 600 or fewer
hours each school year, leaving them ample time to prepare, revise and learn.
By contrast, American teachers spend nearly 1,100 hours with little feedback."

This line took my notice. I have to wonder if their school systems are such
that teachers do not have to be in front of students 6 continuous hours daily
as my daughter's teachers do. (My daughter is in elementary school.) By the
time her teachers finish with students, attend after-school meetings and
grade, I can see there being precious little mental energy left for
professional development.

My friend Scott made a career change a decade ago. After being a software
developer for 22 years, he switched to teaching tech in a middle school. His
comment to me after his first year was that teaching is much more exhausting
because you have to be "on" 5-6 hours daily. If you're "off", students pick up
on it and reflect it. His opinion hasn't changed after a decade.

~~~
jimhefferon
My only comment would be that I find what your friend Scott finds. I don't
teach middle school, I teach in college, so my day is more mixed than his. But
my training was as a high school teacher and my wife is a high school teacher,
and I do find that her routine is exhausting.

I hear you about having little mental energy left. There are lots of intensely
dedicated teachers but it is unreasonable to expect that they will be on 24-7.
They get to have families, to have hobbies, etc., just like everybody else.
Just like engineers, police officers, and any other highly trained
professional.

(It is especially discouraging, for me, when someone writes a letter to the
editor seeming to assert that teaching is something women do so they get
summers off with their kids, kind of a hobby. Those make me cringe.)

~~~
bpyne
IMO a culture developed in the US in the past few decades - I would be hard-
pressed to pinpoint when but it's been within my professional life in IT -
that we should minimize any activities in a work environment that do not have
a direct tie to revenue. The result is that professional development is all
but non-existent unless you do it on your own time.

The US is scrutinizing its education system right now. Unfortunately, we're
looking for simple answers and pinning blame on teachers when the problems are
more systemic. My neighbor is a visiting professor from Germany. His wife is a
teacher in grades 5-8 in Germany. My wife and I had dinner with them a while
back. They made the observation that blaming teachers took place in Germany
about 10 years ago. When all was said and done the problems were more
systemic, they were corrected, and the system is considerably better now in
their opinion. Hopefully we'll follow suit.

------
11thEarlOfMar
It's an interesting question when you consider that in at least two university
mathematics department rankings[1][2], the US holds 7 of the top 10 global
spots. One could argue that for whatever reason, many of the professors,
researchers and postdocs at those schools learned math in other countries,
but, if these lists are to be believed, the US does have the richest
mathematics knowledge in the world.

So two questions:

1) Why doesn't the preeminence of the US math knowledge appear to seep into
the primary and secondary school education?

2) If the primary and secondary education in the ROW produces such a high
level of capability relative to the US population, why aren't their
universities better represented in the rankings?

[1] [http://www.usnews.com/education/best-global-
universities/mat...](http://www.usnews.com/education/best-global-
universities/mathematics)

[2] [http://www.topuniversities.com/university-
rankings/universit...](http://www.topuniversities.com/university-
rankings/university-subject-rankings/2015/mathematics)

~~~
jomamaxx
"Why doesn't the preeminence of the US math knowledge appear to seep into the
primary and secondary school education?"

Because preeminence of top tier institutions (which are kind of global centres
anyhow) - has absolutely nothing to do with teaching math to the commons.

Here's a hint:

+++ Americans don't suck at Math +++

There's a very un-PC but very large elephant in the room that people won't
discuss.

\+ European American and Asian American 'testing scores' are actually pretty
good - and have been holding steady for a very long time. (Asians do a little
better). Nothing has changed.

\+ Latino American and African Americans fare poorly, but having been getting
better since we've been measuring by standards (i.e. 1950's-1970's).

Here's the trick:

\+ European Americans actually do better than Europeans - on average. \+ Asian
Americans to better than Asians - on average. \+ Latino Americans do better
than Central/South American Latinos \+ African Americans do better than
Africans.

The key correlating factor here is 'ethnicity'. 'Ethnicity' is the broad,
generalist predictor of educational outcomes. This definitely not 'race' and
it's not even 'IQ' (those things are plausible but controversial) - it's a
series of behaviours, social norms, examples, attitudes towards work, success,
access to services, social networks, mentors, role models, etc. etc. etc..

Educational outcomes (and crime stats, income stats) break down along ethnic
lines. In a manner of speaking - America can be thought of as 'four nations'
\- White, Black, Asian and Latino. Obviously - it's very crude and generalist,
and policy based on this would probably be racist - nevertheless - you pretty
much have to look at the data given this.

In the end: American test score results have more to do with the _changing
ethnic composition_ of the American population than they do anything else.
Again: White people and Asians in America have performed consistently he same
for decades. Teaching methods haven't changed much, students habits haven't
changed much - so the outcome is naturally consistent.

More economic prosperity, access to services and different attitudes + deeper
integration have meant Latino A. and African A.'s are doing a little bit
better - but because there are so many more Americans of those groups -
particularly Latino Americans - it changes the outcome of the 'average
american test score'.

Analyzing educational results does not make sense until you break it down
along ethnic lines. Once you do - it becomes crystal clear. It's the absolute
#1 most important thing about the educational data that turns 'paradox' about
educational investment (teaching has remained largely the same) and outcomes
into 'perfect sense'.

Unfortunately, it's so sensitive few will want to talk about it - for fear
that the general public equates educational outcomes to 'intelligence' and try
to strongly correlate ethnicity + race to this, which would be fodder for
racist/KKK types, which wouldn't really help the overall social situation in
America.

Anyhow - America is actually doing pretty well overall.

~~~
johncolanduoni
> European Americans actually do better than Europeans - on average. + Asian
> Americans to better than Asians - on average. + Latino Americans do better
> than Central/South American Latinos + African Americans do better than
> Africans.

I've always heard this explained as a sort of "selection bias". Since
immigration to the US (particularly for university education) is often seen as
desirable, the people who manage to pull it off tend to be above the mean. Do
you feel that explanation rings false?

~~~
JetSetWilly
> I've always heard this explained as a sort of "selection bias". Since
> immigration to the US (particularly for university education) is often seen
> as desirable, the people who manage to pull it off tend to be above the
> mean.

I think this is an explanation that could only be come up with by the
descendants of those who have emigrated.

Thinking here in Scotland, the people who emigrated were not necessarily the
most able or genetically superior somehow. Often, they were simply the most
desperate. People who were cleared off their farms by landowners, people who
had no other options available to them but to roll the dice and go abroad to
Canada or Australia or the USA.

Most folk don't want to emigrate, certainly not in the 19th century. It is a
last resort that you do if you are out of options. But perhaps the most
capable and able have other options to take advantage of?

~~~
ArkyBeagle
It's not clear that capability was that much of a factor. As the scion of
Scots emigrants from the 19th Century, at least the 20h century version of my
family was made up of bright capable people but hardly brilliant.

~~~
arethuza
It's pretty awful to read how people regarded the Highland Clearances, like
this from the _Scotsman_ :

 _" Collective emigration is, therefore, the removal of a diseased and damaged
part of our population. It is a relief to the rest of the population to be rid
of this part."_

[https://en.wikipedia.org/wiki/Highland_Clearances](https://en.wikipedia.org/wiki/Highland_Clearances)

~~~
ArkyBeagle
DNA has made for the possibility of a much less nasty world.

------
atemerev
The key to math education is practice. Even drilling, maybe.

Other fields deal with concepts more or less mapped to the real world. Physics
is about real world, more or less (right until you get to quants, then the
level of abstraction rises dramatically). Same goes for biology, and even
computer science in general. There, you can rely on words, which usually
convey meaning.

In math, you can't rely on words. You'll never understand even relatively
simple things like complex analysis or Fourier transform just by reading about
it -- words are never enough to transfer the knowledge to you. You need to
play with it, solve actual problems, understand in practice how various
"moving parts" are related to each other, and then accept the naming
convention (which is almost an afterthought, born as a mean of reference, not
as a way to describe things). Therefore, relentless practice and solving
abstract problems (a lot of them) is the only way to teach (or learn)
mathematical concepts.

Some teachers want to make math more accessible with bringing it "down to
earth", mapping mathematical concepts to more concrete problems. It is
theoretically possible, and I was a supporter of this approach until very
recently. However, math just doesn't work this way. Math is pure abstraction;
linking the abstractions to earthly affairs too early shuts down mathematical
thinking (creates biases that prevents applying mathematical insights to other
fields that are different from the one learned).

Mathematical abstractions cannot be transferred by words and formulas alone;
they need to be internalized by practice and drilling.

~~~
libeclipse
I disagree with this. I remember when I was in primary school and I was
confused about how to multiply decimals. At that level I didn't even know what
it would mean to multiply a decimal: how can you have 5, 0.2 times? I asked
the teacher and instead of explaining the concept properly, i.e. 0.5 is half
etc., I was just told to multiply the other way around, by adding up 0.2, 5
times - and do drills with that.

It's this kind of teaching that makes good robots and terrible mathematicians.
(Thankfully I'm neither the former not the latter.)

~~~
aswanson
That was a good way to teach you commutativity, though.

------
rdtsc
> Without the right training, most teachers do not understand math well enough
> to teach it the way Lampert does.

My high school math teacher majored in math and then got a certificate in
teaching. She wasn't a teacher who was told to teach math among other classes.
She knew all the advanced stuff (beyond what a high school curriculum
required), she was excited about it, she could explain things in various ways,
give analogies, was available after class to ask questions and so on. And that
is post-collapse Soviet Union full of corruption, poverty and other crap like
that. Surely if we can spend trillions of dollars on F-35 we can get us some
good math teachers...?

In this country I see a large disconnect between words "Oh kids are so very
very important, they are our future, they can't play outside too far because
they will be abducted and we care so much for them" and deeds: I see large
classrooms, not enough teachers, teacher are underpaid, not interested in
math. Funding comes from local property taxes so rich neighborhood get more
money, poor ones get less.

Another thing is I remember teachers were respected. Imagine how we react to
someone saying "Oh they are doctor. And then everyone nods, right, they are
very successful. Or lawyer, or works for Google and so on". Why isn't teaching
like that? My mom tells me someone back home thought she was a teacher,
because she at her age spoke some English. And she took it as a great
complement. In this country you tell someone you thought they were a high-
school teacher and they might get offended. Something is very wrong here...

As for making it more exciting -- initially I studies math by repetition and
it worked pretty well for me. I think works because kids are amazing at
memorizing stuff. Why not first take advantage of that? Starting them out with
set theory sounds all cool on paper that is not how humans learn.
Multiplication table, basic patterns, even operations are fine to memorize
first. Later on it makes most sense to introduce proofs, word problems (I
remember doing lots of word problems, our teachers were crazy for them) and so
on.

~~~
cocktailpeanuts
I don't know of any country where teachers are considered as elites. The
reason your mother took that as compliment is not because teacher is a high
social class occupation, but because being good at english is considered a
great skill in many countries. If you really had to compare, in most cases
people would feel more flattered to be mistaken as a doctor (or an engineer
who works at Google than as an elementary school teacher.

I know people will throw stones at me for this, but the reason teachers are
not the top 1% of the society is because functionally their job is a
commodity. (We're talking about elementary/middle/high school teachers, not
professors here).

It is not hard to find someone who knows high school math, for example. I'm
not discounting the fact that there are sometimes really outstanding teachers,
but the thing is, it's hard to objectively measure their performance since
their teaching talent is not directly related to how well their students do.
On the other hand, the "teachers" at universities are well respected since
their talent is not only limited to how well they teach but the quality of
their own research--the value is much easier to quantify.

~~~
hkmurakami
Afaik teachers are held in the same regard as doctors and lawyers in
Scandinavia.

~~~
dagw
Nope, at least not in Norway or Sweden. Or possibly only in the sense that non
of those professions are held in particularly high regard. And they certainly
aren't paid like doctors of lawyers.

Sure if you ask people, they respect teachers in the abstract sense that
they're people doing a very tough job for very little money, but it's hardly a
career people aspire to, and certainly most teachers I know will admit it was
their second or third choice that they kind of fell into.

------
nemo44x
Math is hard work. I was bad at math. I went to college a couple years after I
graduated high school where I made little effort to challenge myself. But
after figuring things out, at 20 I decided I wanted to do computer science as
I enjoyed some of the programming skills I picked up (C++ of all things!).

I was very unprepared for the math part of it and it was hard. I tested into a
remedial math level and when I looked at the CS requirement I knew that
wouldn't be a good way to start. So I bought a used math book and spent a few
weeks studying hard so I could get into a decent math placement so I could be
where I needed for CS. This was just the start.

I had a long road with a lot of frustration but I made it. I made it because I
never worked so hard at something up to that point in my life. There were
times I thought it was hopeless but I just continued to do rote math problems,
over and over again. And slowly the concepts started to sink in more and more.
But there was always the frustration of missing the little details and
forgetting a concept or not having enough experience honing a certain skill.
But if I kept at it, over and over again, I would learn it and it suddenly
became easy.

I was "bad at math". It would have been so easy to quit and try something
else. But I knew I wanted to not only pass my tests but really understand the
calculus and differentials, etc I had to do. And it was the best thing I ever
did for myself.

Not only does working so hard at something prove you can work hard and achieve
something but it shapes the way you see the world.

Math is hard. Some of us just have to work harder. People should realize that
failing is normal and if you keep at it you will eventually get it. For some
people it takes longer than others. I could never create math. But with enough
time I believe I could eventually truly learn anything because of this
experience.

~~~
yazaddaruvala
Congratulations!

I'm always disappointed when people say "some people just can't learn X".

It isn't that they cannot learn X, they just cannot learn it in the same time
frame, and they shouldn't be expected to!

~~~
nemo44x
I mean that's really the problem. For some reason we think things will just
make sense once we are taught the lesson and we try an exercise. But that's so
often not the case. Accept you'll never be the genius who creates new things -
maybe you will but put that aside. Focus on trying hard and committing
yourself. It doesn't matter if it's math or cooking food, the more you try it
and think of it and accept failure the better you'll be. Accept your limits as
a creator but never accept that you can't understand a concept if you spend
the time you personally need at it.

------
rabboRubble
In 4th grade, I got a C in math. During my teacher student grade review
meeting, my male teacher told me "it's okay, girls don't do as well at math as
boys."

Yeah, so there's this as a reason. I definitely wasn't a good student until
high school. I definitely had a bad teacher who gave me an excuse for _YEARS_
to accept bad results in math. My mother still bitches about that guy to this
day. I suspect I have a slight learning disorder that affected my ability to
process numbers. I mix 6/9s. 7/9s when transcribing numbers. Made homework
difficult. Once I got to the point where letters started replacing numbers in
homework, I went from a C student to an A student in math and was competing
for the top grade in my math classes. Once I learned that I could do the work,
I did the work and excelled.

I suspect that this type of bias affected more girls than just me, and these
discouraged girls affected US scores.

------
krapht
I found math class stultifying and boring until the focus switched from
learning algorithms for computation to doing proofs of relations and concepts.
Also I began to discover the actual applications for advanced math, instead of
learning it for its own sake.

I wish in hindsight that instead of taking endless years of calculus there was
a high school version of real analysis, and exercise problems rooted in real-
life to motivate the learning.

~~~
Merad
I didn't really get into math until calculus, personally. There was this
moment of realization that calc starts to describe the real world, opening up
the ability to do all kinds of useful and interesting things. I ate up calc
1-3 and differential equations, even though I have no real use for them today.
OTOH, my brain apparently just is not equipped to deal with proofs, either in
mathematics or comp sci theory. They were always an enormous struggle for me.

~~~
chrismealy
Me too. I loved the story problems in calculus. I felt like I had learned a
secret magic spell. Unfortunately I never get to use it in real life.

------
wirrbel
One very interesting thought I read about:

Modern math classes tend to be very applied. I.e. the primary objective is to
get the student to be able to solve real world problems with math. (A farmer
sells 3 potatoes for a dollar. How much do 8 potatoes cost?). There seems to
be some indication however, that abstract math is more accessible to some
children, especially if they aren't supported by parents during their
homework, etc. Because of this real-world to mathematical-world translation
step. By exploring ways to make math more accessible, "friendly" and useful,
teachers might actually make it harder for students to pick up math.

This is an interesting thought for me, because I tutored kids in math who were
not doing good in school. I kind of ended up with a typical scheme to get them
from "risk of failing the class" to Bs and occasionally As.

First I would introduce a a few techniques (equation solving in every case and
the mathematical topic of their class - logarithms, binomial terms, etc. -
also) and then give them very simple drill exercises. And a lot of them that
we would solve together. I.e. simplifying exponentials $exp(3) * exp(5) =
exp(8)$ etc. I always made sure that they were able to solve these drill
exercises eventually, and they were all able to, because they picked up the
scheme.

As a next step, I gave them the applied problems their teachers would ask them
to solve, and made it into a translation problem. I.e. I explicitly told them
that this was now just a translation. They could often identify with this
because they self-identified often as language persons ("I like the literature
class best", or "I like french class most"). I wouldn't ask them to solve the
translation result right away. But they often just naturally did because it
was not so different from the drill exercises.

Point is, I do not at all understand why I was needed for this. The teachers
consistently failed their students in class, by not providing them with the
very basic math skills and confidence that they needed to solve more complex
problems.

~~~
chrisdbaldwin
> The teachers consistently failed their students in class, by not providing
> them with the very basic math skills and confidence that they needed to
> solve more complex problems.

Finding a good math teacher in America is difficult because the good math
students rarely become teachers.

------
yazaddaruvala
One word: Football.

One of my friends graduated with an engineering degree from MIT. I once asked
him if he could have traded that to be better at Football, would he? His
response was that if there was even a remote chance he was good enough to play
in the NFL he would have traded education for that chance.

Humans innately crave fame, and the lack of scarcity that is perceived to come
with it. The USA has sadly, and unknowingly groomed that romanticism of fame,
towards consumables (this might be the long term effects of Capitalism).
Rather than grooming that romanticism of fame towards
research/intelligence/creation (the renaissance).

Even local to the film industry, almost 100% of 10 year olds want to grow up
to be Brad Pitt or Salma Hayek, not George Lucas or Stephen Spielberg[0]. Even
fewer want to be the writer.

Even local to football, everyone knows the names of the player that caught
that hail marry, got that big hit, recovered that fumble. Few know the names
of the people who create those plays.

Only in recent years have the masses truly started to recognize
creators/intelligence with the title famous (Gates, Jobs, Zuck). But again for
the wrong reasons, i.e. for their money. Even artists Picasso, Beethoven
(adored for generations) have only truly been appreciated by the aristocracy,
i.e. the rich and "mathematically" acute.

Which way do you suspect the causal link lies? Are we first intelligent,
therefore we appreciate the intelligent? Do we first appreciate the
intelligent, therefore we become intelligent?

[0] I mean no disrespect to Brad Pitt or Salma Hayek, or actors in general.
Good Actors need to be extremely intelligent, but this isn't why they are
adored. I'd argue this part of them is even sadly shunned by the media and
populace.

~~~
totalZero
MIT has a pretty good football team.

[https://youtu.be/XnVcaHMsYqM](https://youtu.be/XnVcaHMsYqM)

------
tomc1985
If they would teach kids to _play_ with math (or any form of knowledge, for
that matter), and not just run through 10,000 rote problems, maybe we'd rank
better.

Especially word problems -- most of them felt like they were written for
students wearing intellectual blinders... if you had any modicum of relevant
knowledge outside of the lesson oftentimes word problems were impossible to
solve

~~~
increment_i
Could not agree with you more. Another thing I've noticed anecdotally is that
many of the math teachers in the secondary system in North America do not have
a broad understanding of math themselves. Math is given the most rote
treatment of all the subjects, and I suppose this is understandable given the
abstract nature of math.

But students are never told why they should care about abstractions in the
first place, which is unfortunate. Many high schools simply refuse to speak
the students' language.

I suspect this will change in this century. IMO, if a high school really
wanted to be progressive, they would totally reform their math curriculum to
include more exposure to applied math and computer sciences. Young folks
should be using math to build their own Instagram or Minecraft clones that
they can deploy to their devices that VERY DAY - using the concepts they've
been introduced to in mathematics.

~~~
sjg007
Not sure how math helps you deploy instagram clones. I mean set theory, logic,
computable functions but that's a big stretch.

~~~
rprospero
I would argue that every instagram filter is merely a linear algebra problem.

~~~
sjg007
true.. nice example.

------
pessimizer
Looks like the answer is buried at the end: "Finland, meanwhile, made the
shift by carving out time for teachers to spend learning. There, as in Japan,
teachers teach for 600 or fewer hours each school year, leaving them ample
time to prepare, revise and learn. By contrast, American teachers spend nearly
1,100 hours with little feedback."

------
saretired
Some of it is cultural: Americans don't want their kids to have too much
homework, in many cases they don't want to help with homework or are unable
to; they want a silver bullet. Some of it is lack of qualified teachers, and
part of that is the way public schools are funded from the local tax base--do
it cheaply as possible. Some of it is political pressure to dumb things down
so that students can be graduated from HS before they reach the legal drinking
age. Some of it is the rise of the education ``experts'' who always have some
new…silver bullet (Feynman had a lot to say about such experts after reviewing
math textbooks for California in the early '60s). The new math came about as
an almost hysterical reaction to Sputnik, when, in fact, the U.S. had plenty
of highly qualified scientists and engineers who just happened to get beaten
to the punch by the URSS. But no, the math curriculum had to change into some
kind of Bourbaki for tots, meanwhile in fact the Soviets were teaching math
the old-fashioned way--nice cognitive dissonance there. There are a lot of
factors, and I don't see any magical way of improving curricula, getting
better teachers, requiring more homework, etc.

------
ausjke
The new SAT etc now puts more weighs on reading comprehension and make math
less important, which further weakens the willingness to study math, so the
Asians(who are traditionally better at math) will not dominate the SAT high
scores. As a country this will only make math education much worse, it should
be another way around, otherwise, you can not compete in the STEM field, which
is crucial for future.

~~~
ausjke
[http://www.usnews.com/education/best-global-
universities/sea...](http://www.usnews.com/education/best-global-
universities/search?subject=engineering&name=)

Chinese Tsinghua Univ beats MIT to take the top seat at USNews for
engineering. I think this is the second time in a row.

As far as I know, Chinese universities took the best students without
considerations of gender at all. They do have AA for races but it is minimal.

USA is moving towards to AA-for-school-and-workplace, I hope this will make
more people happier with high self-esteem, in the meantime you lose your
competitiveness quickly.

------
danharaj
Put 100 mathematicians, math educators, and policy makers into a room and ask
them to come up with a good mathematics curriculum. They'll come out with 101
proposals. That's not a problem, really. Mathematics is not merely about
mathematical substance, but also mathematical process (the two are intimately
related), and not just process, but the process of discovering processes.
Curricula, standards, directives, are all substance. Policy makers want to put
their name on a thing, a substance and give it to everyone else and hope that
process develops... somehow.

I think you have to contextualize mathematical in the broader problem with
american public schools: they're awful, awful places for many students
including me. I ended up studying higher mathematics in college and still
study on my own for my own pleasure (and I get to apply some really high
powered ideas to programming once in a while which grants a satisfaction that
lingers). I think my math education could have been advanced 5 or even 10
years if public school weren't such a soul-crushing stultifying nightmare of
procedure and compliance.

~~~
yorwba
> (and I get to apply some really high powered ideas to programming once in a
> while which grants a satisfaction that lingers)

Mind sharing what some of these ideas are?

~~~
danharaj
Lately I've been experimenting with comonads to structure stateful code. The
idea is that a comonad describes the interface for a state machine, and you
can convert any comonad in Haskell into a monad transformer which acts as a
restricted form of the state monad. The state monad describes expressions that
can arbitrarily manipulate a state of some type. The monad you derive from a
comonad does not have direct access to its state, the comonad describes all
the allowed manipulations and queries.

This is all described and implemented here:
[https://hackage.haskell.org/package/kan-
extensions-5.0.1/doc...](https://hackage.haskell.org/package/kan-
extensions-5.0.1/docs/Control-Monad-Co.html)

In particular, the type:

    
    
      data CoT w m a = CoT { runCoT :: forall r. w (a -> m r) -> m r }
    

Let's unpack this. The following type represents a state machine whose nodes
are labeled with a continuation demanding an `a` and executing an effect:

    
    
      w (a -> m r)
    

The forall quantification in CoT means that it does not care what the result
value is. It will take a state machine, manipulate it for a bit, produce an
`a`, pick a continuation from the state machine and execute it.

That's a lot going on! I don't have time or space to explain how this is
actually useful but here's a handy approximation:

\- `w` is an interface

\- `w s` is a model labeled with a value of `s` for each state it can occupy.
These labels are a sort of view.

\- `CoT w m a` is a controller that can manipulate a model and compute in some
effectful context.

High powered MVC. The upshot is that because we're leaning on Functors,
Monads, and Comonads there are extremely well behaved and natural composition
operations. For example, `fmap` allows us to change the view of a model by
applying a pure function. The fact that `CoT` is a monad means that we can run
controllers in serial, as well as combine our controller languages in sensible
ways. The fact that `w` is a comonad means we can reason about the behavior of
models equationally. This lets us transform, compose, and compare models with
mathematical precision.

This is a project I only seldom work on in my spare time. I have already
applied it to writing GUI's and game logic to good effect but I'm still
exploring the design space regarding reactivity and temporal behavior. This
has led me to reading the mathematical literature pertaining to products of
comonads/sums of monads (they're dual).

------
58
Might it have something to do with this?

[https://www.washingtonpost.com/local/education/majority-
of-u...](https://www.washingtonpost.com/local/education/majority-of-us-public-
school-students-are-in-
poverty/2015/01/15/df7171d0-9ce9-11e4-a7ee-526210d665b4_story.html)

I'm no fan of the American education system, having suffered through it a full
12 years, but I have to believe it's not the primary cause here. Math is hard,
and near impossible if you're stressed. I excelled at math, despite relatively
boring math curricula. Why? Because I wasn't stressed as a kid, my family was
stable and did not suffer from any serious physical and mental illness, and
one parent always made enough money so that the other could stay at home
throughout my entire childhood. I had an enormous advantage, and most all of
the kids I knew through advanced math classes and math competitions had a
similarly charmed existence.

~~~
WillPostForFood
This article debunks the Washington Post claim about a majority of kids in
public school being in poverty.

[http://marginalrevolution.com/marginalrevolution/2015/01/no-...](http://marginalrevolution.com/marginalrevolution/2015/01/no-
a-majority-of-us-public-school-students-are-not-in-poverty.html)

~~~
pessimizer
By failing at reading comprehension. There's a vast difference between public
school students and school-aged children. In Chicago, only 10% of public
school students are white[1], with a 45% white population[2] (for example.)
Conflating the two things seems almost willfully deceptive.

edit:

[1] [http://www.cps.edu/About_CPS/At-a-
glance/Pages/Stats_and_fac...](http://www.cps.edu/About_CPS/At-a-
glance/Pages/Stats_and_facts.aspx)

[2]
[http://www.census.gov/quickfacts/table/PST045215/1714000](http://www.census.gov/quickfacts/table/PST045215/1714000)

~~~
WillPostForFood
What's wilfully deceptive is pointing to one city and claiming it is relevant
to national statistics. The WP Article assets a majority of public school
students IN THE US are in poverty, that is objectively false. So the reading
comprehension problem isn't with the article I cited.

~~~
58
The WP article isn't really central to my point -- that outside factors have
more to do with poor math performance than anything happening inside the
schools. I worked in a public school as a tutor for kids slightly behind their
grade level (not with the kids who were really struggling) and I have plenty
of anecdata from that experience. Kids with drug-addicted parents, kids with
parents in prison, kids not having enough food at night, medicated kids, obese
kids, a kid who had to move mid school year because his house was shot up in a
driveby, etc.

------
HarryHirsch
Since no one has brought up "Nix the Tricks" yet, here's the link to the
ebook: [http://nixthetricks.com/](http://nixthetricks.com/)

Foreigners are likely unaware that these are the algorithms routinely taught
to US students in math class. There are no formal proofs, no emphasis on
making sense - the only purpose is to have something memorizeable to have
students pass the next test (and possibly the No-Child-Left-Behind test at the
end of the year). There is no generalization, no focus on understanding. When
you tell an American kid at university level "this is why concept XY makes
sense" they don't understand why you might say this, they are only interested
in the algorithm and the solution (and passing the next test, of course).

Small wonder that anyone exposed to that curriculum sucks at math and on top
of that us turned off the subject. It's like Feynman in Brasil!

------
yanjuk
I taught my two kids long division in about ten 40-minute sessions spread over
5 days. I sat with each child as we learnt the procedure. To begin with I held
the pencil and asked questions, then the child took over the writing and I
monitored to fix mistakes until finally the task could be performed/practiced
solo.

In this one-on-one practice approach misconceptions are eliminated quickly at
the start. It could not easily be replicated in a large group. Instead the
approach in the article seems to be about groups of people identifying each
other's misconceptions. Either way the effectiveness lies in avoiding bad
habit formation.

If you look at YouTube each method of arithmetic has variants and you can pick
the one that looks best. e.g. I chose a method of multiplication with
consistent placing for the carries which reduced error considerably over what
I was taught at school.

------
droithomme
People keep saying Americans stink at math, americans don't understand
science, americans are ignorant, etc.

And yet at the same time we have these sorts of track records:

[http://www.popsci.com/us-dominates-at-sending-stuff-to-
mars](http://www.popsci.com/us-dominates-at-sending-stuff-to-mars)

It's not just Mars or the moon, or decades ago, the US also is where most
operating systems and software and CPUS are conceived of and designed. As well
as countless other things that people who are so ignorant would not reasonably
be expected to be able to do.

~~~
tmerr
I agree USA has an impressive track record for space exploration and is at the
forefront of computing, but that seems like more of a reflection of our
economy and top talent than overall math literacy. Ideally we would have the
best of both worlds: good high school education, and a good economy, but for
some reason the former lags behind.

------
daodedickinson
Well, a lot of people came to America hoping they would need math less.
Americans stink at it because they feel they don't need it and when they feel
otherwise it will be too late. It's easy enough to encourage seduction too
math as the article suggests, but the real challenge is somehow blocking out
more and more distractions (other options) when you can't reduce them because
freedom and democracy are national ideals. Math can be interesting but how do
you keep it more interesting than video games when you don't have a culture
willing to regulate them as harshly as South Korea or China? How do you keep
people from following Howard Hughes and having fewer friends, staying mostly
home, and watching an astonishing amount of recorded video? Howard Hughes was
hardly someone who could do nothing with math, but there are a lot of pitfalls
in America to which the schools are blinded or can't do anything about. How do
the schools, with such little authority, reduce problem behavior AND help
something more difficult and at least supposediy more healthful fill the void.
This is the problem with the democratic subject that Plato described: in
democracy so many behaviors must be acceptable / not disqualifying for power
and respect that people cycle through a great diversity of them. This is far
more a pressing issue than whether teachers already trying to teach math do it
this way or this other way: if they still have to compete with more and more
cell phones and games and other entertainments and Babel, they will get
diminishing returns.

~~~
daodedickinson
To put it more succinctly, when you have this American phenomena often labeled
"ADHD", whatever you think is really happening there, education must be viewed
in light of the whole attention economy of the child's life.

------
jason_slack
I am 39, American, white and I am taking a math class at my local college. I
am the oldest person in the class by far. I get A's, so do a few others. Most
get C's.

I do every homework problem. I do variations of the homework problems. I spend
at least 6 hours outside of our class time (3 hours) doing the math.

When we have tests the Instructor gives us problems that are not like the
homework where she can see if we can evaluate and apply the concepts to things
we haven't yet seen.

------
madengr
Americans who need to be good at math, are good at math. If you don't use it,
you lose it.

Hell, I'm an EE, so I'm probably one of those who would be considered "good at
math" (at least by layman opinion), yet I may do at most a couple of integrals
a year. I'm mostly just doing basic algebra on an RPN calculator. Though I did
ace all that EM theory, random proceses, etc in grad school; do I use the math
behind it? Rarely.

------
njharman
Can't read article, paywall or adblock or something.

Is it because our popular culture ridicules being good at math as nerdy?

Is it because almost every american can name at least one sports or pop singer
who makes multiple millions but probably has never even heard of a
mathematician let alone be able to name one.

The root cause is we don't value math as a society. Until we do, we won't
spend the effort needed to figure out how to teach individuals better.

~~~
mgr86
text dump: [http://ix.io/1AfP](http://ix.io/1AfP)

------
hackermailman
Japan times wrote a response to this article:
[http://www.japantimes.co.jp/community/2014/11/23/issues/teac...](http://www.japantimes.co.jp/community/2014/11/23/issues/teaching-
quality-lesson-quantity-may-key-japans-top-math-marks/)

Not mentioned is the Japanese preschool system:
[http://www.ernweb.com/educational-research-
articles/mathemat...](http://www.ernweb.com/educational-research-
articles/mathematics-teaching-in-japan/)

"Seventy percent of all children attend preschool for three years. Young
children are gradually trained in important school-related behavior,
practicing routines that will be used throughout elementary school."

"Two traits pervade the culture and are taught by both parents and teachers:
effort and persistence."

------
rhapsodic
Here in America, we call people who excel at football "heroes", and people who
excel at math "nerds".

------
joe_karn
As far as I'm concerned, higher national IQ, more discipline in the classroom
and possibly a longer school day is why America 'sucks' at Math compared to
Japan. May be more of one and less of another, and let's not ignore the
negative relationship between mean class IQ and the frequency of disruptions.
This is only up to a point - potted plants have very low IQ but aren't
disruptive, but like American students they also suck at maths. Anyway, I can
say to nytimes, without reading the article that panflutes and sandals can
only help America's children so much.

------
whoops1122
American dont stink at Math, American stinks at training kids in general, you
cant give too much home work, kids need time to play, and the Chinese kid in
China is at school till 9 pm constantly doing and practice math. yeah, an avg
American kid is not going to be as good as avg Chinese kid.

However, the top 3-5% of the American kid is going to be just as good if not
equal to their Chinese counter parts.

In China, education made all kids above avg regardless if you are below or
above intellectually. In America, an idiot is going to be an idiot, and a
genius will take that step to be a genius.

------
naveen99
The funny thing is addition and multiplication are black box operations for
most software people (non-ee) also. I wish some analog stuff was included on
those books like nand to tetris: [https://www.quora.com/How-do-I-create-a-
circuit-from-basic-c...](https://www.quora.com/How-do-I-create-a-circuit-from-
basic-components-R-L-C-that-gives-me-an-adder-and-a-multiplier-of-two-analog-
signals)

------
anexprogrammer
_Everyone_ believes they are bad at maths, so they are. It applies just as
much to the UK. My youngest believes this strongly, yet when we were quizzing,
or helping with homework, she didn't seem to find it too hard, just believed
it so. She certainly didn't get those beliefs from home!

Looking at my kids maths lessons, especially in late Junior, so much effort
was spent to actually _hide_ the maths that I wonder they learnt anything!

~~~
matthewhall
I love math and I think I'm pretty good at it

~~~
anexprogrammer
OK, not everyone, but it seems to be the subject that people are most likely
to claim to be terrible at. Schools don't help by sucking all the fun out of
it.

Was always my favourite subject, but that was despite school rather than
because of.

------
andrewclunn
If you convert our scores to metric it's not so bad.

------
dimino
I've latched onto this as my explanation for why English students are worse
with math (English counts numbers weirdly, but Asian languages do math within
their language to perform counting):

[http://www.wsj.com/articles/the-best-language-for-
math-14103...](http://www.wsj.com/articles/the-best-language-for-
math-1410304008)

------
SixSigma
Because they don't spell it as Maths, obviously.

~~~
mc32
We spell it the same, we just abbreviate it differently.

------
shams93
I think it is related to our refusal to embrace the metric system, kids at a
young age get thrown off by our archaic system of measurement.

~~~
geomark
I've wondered about that. The imperial system is positively awkward. What
about other countries that also use the imperial system instead of metric? Are
they also behind?

~~~
tomc1985
The UK uses their own screwy imperial units for some measures

~~~
Frogolocalypse
Not really. You still go to the shops and buy things in litres and kilograms,
and their entire construction industry is in metric. The only commercial
product that isn't in metric, funnily enough, is beer and cider. I guess
getting pissed people to change proved harder than everything else.

~~~
anexprogrammer
...and milk is always pints. An _awful_ lot of products come in imperial sizes
but metric labelling - 454g jars of jam etc.

Timber sometimes gets called 2x4 even though it's 50x100, but that seems less
common now.

Oddly just about everyone still uses feet and inches for their height. I hear
kilos more and more often for weight, I don't think I've ever heard cm for
height in the UK.

~~~
Frogolocalypse
> ...and milk is always pints.

Returned milk is (you know, in dem bottles). But milk you buy in the store is
1L, 2L, etc.

> Oddly just about everyone still uses feet and inches for their height.

True. Probably because of the recognition of the 6' centering measurement.
People know that if you're 6', that's kind of the cut-off for what is referred
to as 'tall enough'. Over that, you're generally 'tall'. Under that, and
you're average height.

~~~
anexprogrammer
Not in any supermarket I've been in, 4 and 6 pints are the commonest. Maybe us
northerners aren't trusted with metric milk yet!

Only time I see litres is some of the niche brands (like Cravendale and
branded organic) in bigger supermarkets, or 500ml in corner shops and some
garages. So they can charge more. Presumably people compare 2l price with 2.3l
/ 4 pint instead of £/l.

------
ArkyBeagle
It's an anecdote, but...

Guy I went thru undergrad with went to a high school where the 10th grade
algebra class requires naming the principle to be applied for each step in a
problem, as if it were a proof.

This is painful. But he'd learned algebra properly. I hadn't. His math grades
were much better than mine for a long time.

------
macawfish
I hear Americans all the time _telling themselves_ that they are bad at math.
These are my friends and family. I tell people that I'm into math. >50% of the
time the first thing someone says is "I'm bad at math."

------
vog
In contrast to this, note that in International Mathematics Olympiads,
pupils/students from the USA are quite good:

[http://www.imo-official.org/](http://www.imo-official.org/)

~~~
johan_larson
Oh sure. The _best_ education in the US is awesome, possibly the best
anywhere. But the average is pretty sad, particularly compared to the rest of
the first world.

------
fspeech
Math is the lingua franca of sciences. It should be taught like a language as
well. In our elementary schools we don't have teachers dedicated to teaching
math. Instead we have teachers who are afraid of math themselves.

------
graycat
I'm an American, and I don't "stink at math". I will compare my math SAT and
GRE scores with any nation in the world. Similarly for my Ph.D. dissertation
in applied math and my peer-reviewed, published papers in applied math. Opps,
those paper were already reviewed as "new, correct, and significant" according
to international standards.

Next, uh, I do have some opinions about the NYT, e.g., their track record on
getting and publishing good, correct information. Hint: That opinion could not
go much lower.

------
kristopolous
Where's our Dr Seuss of math?

------
meira
Because you don't use math while watching TV and Reading FB newsfeed all day
long.

~~~
danharaj
Subscribe to the right fb feeds and you would

------
tgarma1234
Because there are a thousand other things you can do that are worthwhile and
there is no anxiety to be perceived as "smart" in the way that math requires.
Just party on and network and land yourself in a start up. You can pay someone
else to do the math because the real money is in MAKING DECISIONS.

