
A Group of American Teens Are Excelling at Advanced Math - selimthegrim
http://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/?single_page=true
======
j2kun
I am continually surprised by how many emails I get from teenage students
thanking me for writing my math blog.

On top of that, I try to occasionally make it out to high schools to give
guest lectures. I posted an example experience from one of these online [1]
and I am usually looking for other opportunities to do this sort of thing. I
think that if every math graduate student who is a reasonably good teacher
took a day or two out of every year to visit a high school math class, we
would see much more interest in math. Many of us (myself included) were not
particularly interested in math in high school and didn't discover the cool
stuff until college. So we were once the audience we'd be appealing to.

[1]: [http://jeremykun.com/2011/06/26/teaching-mathematics-
graph-t...](http://jeremykun.com/2011/06/26/teaching-mathematics-graph-
theory/)

~~~
Ntrails
The sad thing is that the cool stuff isn't even always complex. It's little
things, like going through how the quadratic formula is derived instead of
just telling someone to learn it by rote. Explaining differentiation with a
bit of the logic behind it instead of just teaching rules.

But at the same time - I know I'd have/did enjoy that stuff but maybe 60% of
my classes would have played up if a whole lesson was spent deriving and
exploring concepts without rote learning.

Being a maths teacher has to be pretty rough, especially given the number of
students who are openly hostile to it as a subject.

As an aside, I often think about my Religious Studies teacher who'd disparage
topics like Maths as being irrelevant after school. We'd never use them she
said. RS was vital to life success, Maths a pointless exercise. _It still
winds me up to remember_.

~~~
fluxquanta
>It's little things, like going through how the quadratic formula is derived
instead of just telling someone to learn it by rote. Explaining
differentiation with a bit of the logic behind it instead of just teaching
rules.

Once you get in the mindset of deriving equations, rote memorization becomes
insanely difficult, at least in my opinion.

During my last year as an undergrad majoring in physics I got a 4.0 in quantum
mechanics, but very nearly failed introductory chemistry (which I was taking
to fill a science distribution requirement at a liberal arts college), despite
many of the chemistry concepts just being edge cases of applied quantum
mechanics.

There was also the very embarrassing case of being called to the blackboard to
complete a problem in an elective course on number theory only to draw a blank
on what 9 times 7 was. I understood the solution to the problem itself, but
when the professor started giving me hints I had to admit in front of the
whole class that my issue wasn't with the number theory proof -- it was with
the multiplication table we learn as children.

~~~
jimbokun

      10 - 1 = 9
    
      9 * 7 = (10 - 1) * 7 = 70 - 7 = 63
    

I often do little calculations like this when I forget multiplication table
entries.

~~~
fluxquanta
As do I, but the pressure of the situation didn't help, especially when the
natural assumption of the professor/rest of the class was that I didn't
understand the much more "complicated" aspect of the proof and not something
most people take for granted as just "known" from elementary school.

------
anonymid
I was frustrated by this article because I find it taking for granted the idea
that math is only accessible to a small group of people - 'talented, gifted,
with an affinity for, confluence of specific abilities'. I find similar
language around programs like the Russian School, Brilliant and quite
obviously the 'gifted' programs.

Yet in this article they quote the following statistics:

\- High achievement in math: US 9% to SK 30% \- Ratio of high achievers
affluent vs poor: US 8 to 1, SK 3 to 1

These statistics communicate to me that half of all students are capable of
high achievement in mathematics. From my experience tutoring and visiting
classrooms of various grade levels and demographics, most students are capable
of the rich problem solving described in the article.

US education's biggest issue is social justice. We spend the least resources
on the children who need it most. It's funny to me that the closing of this
article suggests that it's time for the advanced mentors to step in to the
public education scene. What would a group of people that cater primarily to
the best-served students in the system have to say about how to help the
worst-served? What would they know about the obstacles faced by poor children
and parents; overworked, undertrained and unsupported teachers; and
underfunded schools?

~~~
jimbokun
"What would a group of people that cater primarily to the best-served students
in the system have to say about how to help the worst-served? What would they
know about the obstacles faced by poor children and parents; overworked,
undertrained and unsupported teachers; and underfunded schools?"

Hopefully they wouldn't get caught up in all that and just teach some math to
whoever's interested, regardless of income level.

~~~
hdctambien
> teach some math to whoever's interested

But in public school you have to teach math to _everyone_. Any they aren't all
interested.

~~~
wallflower
One of my teacher friends taught 6th grade math. In his classes, he had to
account for 4th through 8th grade math skill levels. Those with 8th grade
being Khan Academy-style motivated learners.

------
mixedmath
I've taught a summer program in number theory for high school students for the
past several years. Each summer, my classrooms fill with high school students
that are intrigued by the idea of math and extremely capable. That is nice and
inspiring, and generally more rewarding than when I teach calculus classes to
university students during the school year.

But my program is prohibitively expensive, and I'm acutely aware of the fact
that when my students return to their high schools, they will almost certainly
return to lackluster curricula. There are exceptions, of course. My summer
program is filled with a far-above-average percentage of students attending
private high schools.

The fact remains that students who attend the summer program are introduced to
interesting math with no guided way to continue their exploration. Sometimes,
students with supportive schools end up scheduling a self-study with some
supervision from a high school teacher or counselor; I've been asked to help
set up and guide self-studies, and I know at least a few of them have been
successful. In my experience, this has been the best outcome for my students
continuing exploration of advanced math. I'm not sure what this says about
math and American high school education.

~~~
VLM
"But my program is prohibitively expensive"

Why? Just curious if there's any brainstorming to be done.

Also expensive relative to what? Some people think Kumon is expensive. My kids
did it for a couple years. Its about $100/month. Its very popular among
immigrants who make a whole lot less money than I do. Of course Kumon isn't
"real" math because its very drill -n- kill (which is why we quit, more or
less)

~~~
mixedmath
> Why? Just curious if there's any brainstorming to be done.

I'm afraid that I don't know about the actual costs. There are several classes
offered, and though students only take one at a time, they sometimes link a
few and stay for up to 8 weeks. It's a pretty large board-at-the-university-
for-x-weeks style summer program.

I'm an instructor, and I don't set prices. I also understand that there is a
non-negligible cost to house and feed a student for a month. But program costs
each student about $6000 dollars. I think that's enough to be called
"prohibitively expensive," although I'm not sure how to compare these things
really.

------
shmageggy
The example problem they give is pretty neat, but they don't mention the (IMO)
interesting part of it. After sketching out the answer, I was suprised that
the height you gain is _independent of the size of the underlying circle_.
That certainly suprised me, as my intuition was that the height you would gain
would shrink as the underlying circle grew -- after all, you'd be adding a
constant length to an ever growing value. But the answer only depends on the
amount of length you add, so the problem has the same answer whether it's the
earth, the sun, or a proton. Neat!

~~~
poshenloh
Thanks! :) We were really thrilled to post the problem.

Our rope question from expii.com/solve is a multi-layered math puzzle. If you
haven't seen it before, the answer is often quite surprising: a human can walk
under the circle even though the 710 inches of extra length are shared over
the whole earth's circumference. Basic human intuition produces the most
common answers, which are the bacteria or the ladybug. This helps to
illustrate the purpose of math: to help us reason to determine the truth when
basic intuition fails. If basic intuition were always right, then we wouldn't
need math!

If you had seen the puzzle before though, you would already know that the rope
lifts high, because it lifts by 710/(2*pi) inches, which is 113.0000095...
taking us to the second layer of math embedded deeper in the problem. That is
remarkably close to a whole number, which is surprising because pi is an
irrational number. This means that pi is very close to 355/113, which brings
us to the topic of Continued Fraction representations of irrational numbers,
and amazing rational approximations of pi:
[https://en.wikipedia.org/wiki/Mil%C3%BC](https://en.wikipedia.org/wiki/Mil%C3%BC)

So, this problem hits at both basic and advanced levels. :)

There are many interesting ways to teach math through multi-layered puzzles
which have something for everyone, no matter where you are in the experience
spectrum. Our goal is to provide these for free, disseminated over the
Internet. :)

~~~
shmageggy
Ahh, I had assumed you had chosen that length because 2*pi is close to 6,
which easily divides into 60 feet. But this is way cooler. Very neat!

------
lintiness
"The No Child Left Behind Act, which shaped education for nearly 15 years,
further contributed to the neglect of these programs. Ignoring kids who may
have had aptitude or interest in accelerated learning, it demanded that states
turn their attention to getting struggling learners to perform adequately..."

teaching to population averages will prove disastrous to our long-term growth.
thank goodness we have private institutions to pick up the slack where massive
bureaucratic oversight often (so often) gets it wrong.

~~~
JoeAltmaier
I'm glad private institutions exist too. But remember you can only get the
education you can afford. Since brilliance is not necessarily related to
parents' income, private education is a poor substitute for efficient, timely
public education.

~~~
wastedhours
Exactly - that's why things like
[https://www.teachforamerica.org/](https://www.teachforamerica.org/) have to
exist. It's a socio-economic issue that's holding back talent in developed
countries across the world, where parental income directly impacts on academic
success. Considering the imbalance is so pronounced in-country, it's a real
shame...

~~~
douche
I applaud Teach for America for the effort, but I'm not sure that's really
that successful. I graduated with more than a handful of people that went into
TFA, and around 90% of them burned out hard after a couple years. Most of them
had no teacher training, and, really, no cultural context for understanding
the cultures they got dropped into. Inner city ghettos, Cajun Bayous, and
Appalachian hollers are a different world than white-bread East Coast
suburbia.

I think if you want to fix the disadvantaged areas of the country, you've got
to reverse the brain-drain that's sucking the best and brightest people out of
these communities. Decentralizing the economy would be a good first step.

~~~
wallflower
The deeper problem with TFA is that by hiring TFA teachers they are literally
ensuring 100% turnover in 2-3 years since TFA teachers do not usually stay
past their 2-3 year assignment in their placement areas. There are a few who
do stay, however, as a pure numbers game, it is not enough. Also, you can
Google (or Bing) away for stories of how TFA teachers are given inadequate
training and special-needs students (or worse, disruptive students) are put
into their classrooms.

Up the Down Staircase is a lightly fictionalized novel about teaching in the
1960s in a public school system. Bureaucracy, parents (or lack thereof),
funding, burnout. Almost 60 years later, many of the same fundamental problems
still exist.

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

------
dineshp2
The fundamental problem of education in public schools and its ineffectiveness
is not being addressed.

It's great that many of these extracurricular clubs and institutes exist to
impart advanced education to interested students. But it does not solve the
underlying problem.

~~~
dominotw
>The fundamental problem of education in public schools and its
ineffectiveness is not being addressed.

If it so ineffective, how come americans win so many nobel prizes, have
thriving high tech industry ect

[http://graphics.wsj.com/which-country-has-the-most-nobel-
pri...](http://graphics.wsj.com/which-country-has-the-most-nobel-prizes/)

~~~
dineshp2
You cannot conclude that the current school education is not
ineffective(effective) just by looking at the number of Nobel Prize winners.

The USA is lagging behind many countries in key areas( especially STEM
fields).

Anyway the point I was trying to make was that, these extracurricular
initiatives are great, but it cannot be a solution to a poor public school
system.

~~~
dominotw
>The USA is lagging behind many countries in key areas( especially STEM
fields).

Lagging how?

Test scores are not a good way to measure the "lag", imo.

~~~
dineshp2
There is lots of research which suggests that the USA is indeed lagging behind
in STEM fields. K-12 does not prepare students well enough when compared to
many Asian and European countries. The numerous research articles are a Google
search away.

Another indicator is the lack of sufficient skilled workforce in STEM fields
in the USA. This forces many tech companies to hire from abroad.

~~~
douche
To make a reasonable comparison to the United States, you'd have to lump a
European country in with a third-world developing country to get the same
level of racial and cultural heterogeneity. People always try to compare the
US to Finland, when Finland has less population than New York City and the
demographics of New Hampshire.

Tech companies hire abroad because it's cheap, not because there is a real
skill deficit.

~~~
dineshp2
I don't how you would take into account all possible factors to make a perfect
comparison, but objectively looking at the research and data available on this
topic, it's clear to me that the USA is lagging in STEM fields.

Some tech companies do hire from abroad because it's cheaper, but there is a
real skill deficit in STEM fields and there are just not enough skilled people
available to recruit. This has been openly acknowledged by the tech companies,
universities and the Government.

The question is not whether the USA is lagging in STEM, it is what should be
done about the fact that the USA is lagging in STEM fields?

~~~
dominotw
> but objectively looking at the research and data available on this topic,
> it's clear to me that the USA is lagging in STEM fields.

I did some googling around this but all the research uses test scores to come
to that conclusion.

I would like to see some other methodology.

~~~
wallflower
While imperfect, test scores provide some context for comparison.

The being said, back in 2013, this article was widely shared. It demonstrates
that you can teach STEM ways of thinking (e.g. CS), starting from early
elementary grades. It does not have to be a AP-level course.

[https://neil.fraser.name/news/2013/03/16/](https://neil.fraser.name/news/2013/03/16/)

------
mojoe
Reminds me of the math program that Jason Roberts is providing to a group of
younger students in Pasadena. If you've never heard the TechZing podcast I'd
recommend it: [http://techzinglive.com/](http://techzinglive.com/)

------
HiroshiSan
"Nearly everyone in the accelerated-math community says that the push to
cultivate sophisticated math minds needs to start early and encompass plenty
of thoughtful, conceptual learning experiences in elementary and middle
school."

What hope do I have to study advanced math when I've begun to teach myself in
my mid 20's?

~~~
adventured
A lot of hope. Your brain is still incredibly capable of uptaking new skills
at a high rate in your mid 20s.

Your brain starts to slow down around 25-30 years of age or so, based on the
major studies I've read. Eg:

[http://time.com/63500/brain-aging-at-24/](http://time.com/63500/brain-aging-
at-24/)

Per that, the drop between 25 and 40, is only around 15%.

Becoming better at learning, and wiser in how you spend your time, can offset
some of the cognitive decline that comes with age versus the raw capability of
youth that is perhaps more squandered due to lack of wisdom.

------
poshenloh
I think that excellence in math is actually in everyone's reach. The main
questions are why and how to reach it. :)

The article surveys the field of enrichment programs and activities, many of
which are available only to people in certain areas. I've witnessed the
immense local impact of those outreach efforts, while visiting Math Circles,
high schools, and academic competitions around the country. The people who
lead those events (mostly after-hours or on weekends) are an incredible bunch,
and many of them do it out of their passion for the subject.

However, I think we would all gain if we could engage everyone in
math/science, no matter where they live. The success of these programs shows
that interesting content increases interest! The Internet allows us to level
the playing field, and scale the impact of free educational resources to the
world.

I was once at a math education conference where groups were pitching ways to
develop math talent. These programs sometimes need financial sponsorship from
governments or foundations, so that they can remain accessible across
socioeconomic lines. On the second morning of the conference, I suddenly
thought: how much money does our public school system spend trying to teach
soccer each year? (I don't think it's much.) It seems that many students
achieve fairly high levels of proficiency regardless.

Of course, there is still much value in funding the current math education
efforts, but that made me think about whether significant gains could come
from finding out how to communicate educational content in the most engaging
way. That would take a page from the startup playbook (optimizing for
engagement).

So, I got my hands dirty. I launched a startup (expii.com) to crowdsource and
rate free interactive lessons in math and science, to quantitatively evaluate
an organized collection of these resources, distributed at scale across the
world. The objective is to turn every smartphone into a pocket tutor,
delivering the most engaging lessons produced by the combined creativity of
the world.

That's a big project. In the meantime, while the content is crowdsourcing, I
also am broadcasting interesting nuggets of math each week at expii.com/solve
(again free). These deliver the same topics I talk about in person at middle-
and high-school math enrichment events around the country when I visit them to
give guest talks:
[https://www.youtube.com/watch?v=9sxVgJ_wPaM&feature=youtu.be...](https://www.youtube.com/watch?v=9sxVgJ_wPaM&feature=youtu.be&list=PLqv4sKOD1bsUoSs-
SbzlA2BE1tML4A33u)

My thought process is that if I'm taking the time to develop the materials to
deliver to only 200 people at a time, then we should harness the Internet to
scale the distribution to the world, while also packaging the content in a fun
way, to show to the mass audience why math is actually a very interesting
subject. :)

Ultimately, I think that the global project to build interest and excellence
in math is an enormous task, which needs the insight and hard work of a great
multitude of people, and a diversity of ideas and approaches. Thanks to
everyone who is pitching in on this mission! :)

------
dominotw
what a strange thing to subject your kids to, shame on these parents.

Has anyone done any studies on what these 'math wizards' end up doing in life.

I grew up in Indian community where this kind of stuff was the norm, many of
my friends won regional championships but __none __of them do anything
remotely related to math now. Instead of associating math with magical
patterns that explain the world, they now associate it with stress
/anxiety/competition.

Please don't do this repulsive stuff to your kids, read Richard Feynman's bio
and see how his parents inspired him to like math/science/world.

~~~
sdenton4
The sort of thinking in Feynman's bio is what drives math circles, though.

I taught at a math circle for a few years; we did 'looking at awesome stuff'
for two thirds of the year, and competition prep for one third of the year.
Different kids came for different parts, but will came out smarter for the
experience, I think.

------
dzdt
TLDR : American public schools suck but there is an increasing number of
extracurricular math programs that help talented kids learn advanced problem
solving skills. Mostly only well-educated and well-off parents get their kids
into these programs. That kind of sucks, and there are marginal efforts to
reach out to poorer students. But the real story right now is, if you have
kids in public school, their math education sucks and you might want to look
into extracurricular options -- there are lots out there.

~~~
rayiner
The difference between "good schools" and "bad schools" is much more about the
kids that go there than anything about the school itself. You're seeing this
starkly in D.C. where gentrification in certain neighborhoods is shifting the
student demographics from 90% low-income to 20% low-income over just 4-5
years. Test scores are shooting up, but it's not like they fired all the
teachers and hired new staff at twice the salary.

American schools are fine. Our problems are social. For example, the U.S. has
the second-highest rate of single-parent families along with one of the
highest gaps in PISA scores between single-parent and two-parent households:
[http://educationnext.org/international-look-single-parent-
fa...](http://educationnext.org/international-look-single-parent-family).

The U.S. also has a larger fraction of children in the lowest income
distribution than comparable countries: [http://www.epi.org/publication/us-
student-performance-testin...](http://www.epi.org/publication/us-student-
performance-testing). Accounting for that eliminates a lot of the supposed gap
in U.S. student performance:

> If U.S. adolescents had a social class distribution that was similar to the
> distribution in countries to which the United States is frequently compared,
> average reading scores in the United States would be higher than average
> reading scores in the similar post-industrial countries we examined (France,
> Germany, and the United Kingdom), and average math scores in the United
> States would be about the same as average math scores in similar post-
> industrial countries.

~~~
venomsnake
Aren't schools financed by local property taxes in US. And the rich parents
pay more in taxes and there is more resources in the system.

Also well off parents could help school in other ways.

~~~
lintiness
teachers in bad / poor areas in the states aren't paid less than teachers in
the "good" areas. cps for instance, chicago public school teachers are among
the best paid and worst performing in the country.

~~~
ryanhuff
I didn't know the teachers were the ones earning the grades. See the posts
above that cite what happens to re-gentrified areas, where the social-economic
make-up of a school changes but the teacher make-up does not.

~~~
prostoalex
You're implying teacher quality and school financing are irrelevant, and yet
every conversation about public schooling in the US brings those arguments up.

