
The Unreasonable Ineffectiveness of Mathematics Education - ColinWright
http://www.refsmmat.com/articles/unreasonable-math.html
======
001sky
Math = Numeracy, logic, geometry. Those are the three reasons I learned math.
All three benefit from memorization. All three are practical. All three speed
up future thinking. All three are scalable. All three are intuitive. All three
are thinks you can't live without.

The reason why math is 'hard' is the same reason 'exercise' is hard. It takes
a combination of skill and practice (a/k/a discipline) to make it 'easy'. And
in a similar way to the endless "how to lose weight" fads, we see "how to do
make math easy," when <easy> is not 'in their nature'.

The main problem with math education is that it is falsifiable. Math teachers
can be measured, because math performance can be measured. This is why it
makes educators nervous. And, I suspect, why they mostly suck at teaching it.
They are the ultimate risk-averse sub-population. Subconsciously, 'educators'
<hate> the idea of accountability, because it is predicated on the notion of
potential failure. But the 'educational' establishement is <built> on the
foundation of unquestionable <authority>. so math is for these guys an
_existential threat_.

TLDR: To be good at teaching math, you have to be open to measuring your
failure, which makes people feel bad. Including the teachers.

~~~
thetabyte
No. No no no. Yes, arithmetic math does benefit from repetition and
memorization, is useful, and your comments on why getting good at arithmetic
is hard are spot on.

But math is so much more than arithmetic. Math is about learning to apply a
variety of available solutions and processes to solve a problem. Math is about
understanding relationships. It's why I get better at math in a combination of
my physics and programming courses than I ever did in algebra or calculus.

In fact, the biggest problem with mathematics education is that it is not
falsifiable. Measuring reasoning, logic, critical thinking, and problem
solving skills is almost as hard as teaching them. Writing a generally
applicable test that measures whether a teacher taught you to actually use and
solve problems with math is nigh-impossible, made worse that students (and
most of all, parents) don't want to be held accountable for problem solving,
because it's too fuzzy, or because you just "have to be smart". The fact that
real math skills are tough to teach and tough to measure is the problem, not
the reverse.

~~~
klibertp
"Math is about learning to apply a variety of available solutions and
processes to solve a problem."

Isn't programming about exactly the same things, only more entertaining,
because interactive? For example: <http://jeremyshuback.com/learning-math-
through-programming/>

~~~
eru
Yes, they are related.

Math is also interactive, if you do it with a friend.

------
edtechdev
One other suggestion: read some research on mathematics education. Look
through some of the proceedings of some of the recent RUME (research on
undergraduate math education) conferences, for example:
<http://sigmaa.maa.org/rume/Site/Proceedings.html> This book How Students
Learn (PDF can be downloaded for free) covers math education (as well as
history and science) <http://www.nap.edu/catalog.php?record_id=10126> it is a
sequel to the excellent (and free) book How People Learn:
<http://www.nap.edu/catalog.php?record_id=9853>

Students need a motivating context, a reason to learn mathematics (or any
topic). It's called situated learning (also situated cognition, situated
action) - with techniques like problem-based learning, challenge-based
learning, service learning, project-based learning, learning by design,
learning through games, simulations, modeling, programming, etc.

That's one side of it. Another is embodied learning. That's how we understand
math (and other) concepts. See for example work by Rafael Nunez
[http://vislab.cs.vt.edu/~quek/classes/aware+embodiedinteract...](http://vislab.cs.vt.edu/~quek/classes/aware+embodiedinteraction/papers/nunem99.pdf)
<http://www.cogsci.ucsd.edu/~nunez/web/FM.PDF>

~~~
wisty
OK, I know a bit about pedagogy, and a lot of it is crap. There's an awful lot
of relativism in most of it. Many of the people who teach teachers simply
don't care about what works in classrooms, because empiricism is an evil
capitalist plot (or something like that). When the Wikipedia page for
Education has gems like "Based on the works of Jung", you know you're not in a
field which cares about hard facts. Not that it's a real problem - the
statistics show that first year teachers are pretty poor (regardless of the
amount of pedagogy training they have), but they learn on the job and are
pretty good after about 2 years (unless they are just doing a year of teaching
to pad their resume, but that's another debate).

I've got a lot of respect for cognitive science though, and that seems to be
what you are recommending.

~~~
disgruntledphd2
Note that Jung was one of the first people to invetigate the use of words in
schizophrenia (in his thesis, as a matter of fact). Secondly, he created the
conception of extroverts and introverts that we typically use to describe
people today.

Seriously, go read some of the works of Jung before you sound off on his
issues. I did, and I was pleasantly surprised at just how sensible he was.

I completely agree that much of modern educational training is quite poor, but
take aim at (for example, the Myers Briggs or visual, auditory, kinesthetic
learning) rather than poor old Jung.

~~~
marshallp
Except the examples you've given like extroverts vs introverts are not
scientifically rigorous and the terms already existed well before him all
around the world in different cultures (outgoing vs shy/retiring etc).

~~~
disgruntledphd2
Statistics was pretty much in its infancy back then, how would you have
proposed he be scientifically rigorous?

Actually, if you could give me your definition of scientific rigour that would
probably help.

~~~
marshallp
Statistics was around then.

I consider science to be the art of making correct predictions. So you need a
hypothesis (in the form of equations or computer programs) that can be tested
on observations leading to correct predictions.

Extroversion/introversion might be scientifically rigorours by that definition
(they might have done quantitative studies) but I'm not sure Jung did those,
and even that it makes sense to create such a classificaton - people are a lot
more complex and I don't really see the need for use of such classifications.

That's a problem I see with psychology, sociology, economics, and other "soft"
fields. The quantification of things which are far more complex than the
simplistic models created to the point that they are essentially meaningless.
It's meaningless to quantify people into races or skin colors and that's about
the level that those sciences are at.

~~~
disgruntledphd2
Jung did his thesis in 1903. In 1903, regression had been invented, but was in
England and may not have spread very far from there. Fisher was 13, and had
not yet invented maximum likelihood and the application of statistics to
experimental design that we all benefit from today. Karl Pearson was working
on statistics, and had invented the chi squared three years previously. He was
in the process of generalising regression analysis in 1903.

Multiple regression (OLS) had not yet been invented. I'm not sure how you
expect Jung to have used an apparatus of statistics which really wasn't
developed (till Fisher) into a coherent whole when Jung would have been in his
forties, having already written a number of books.

Statistics in the sense of looking at populations did exist, but the whole
apparatus of modern statistics was developed in the early part of the 20th
century, concurrent with Jung.

I agree with your definition of science. Incidnetally, Hans Eysenck developed
a physiological test for extraversion/ introversion in the 1950's involving
the amount of stimulus required to become noticeable to a person. This has
been comfirmed by further research.

Speaking as a (soon to be) psychology PhD (all going well...) I would argue
that the "soft" sciences have the exact opposite problem, in that, jealous of
all the cool theories of the physicists they have attempted to jump straight
to the theory building without the benefits of hundreds of years of
observation.

I agree that models in the soft sciences are somewhat simplistic, but I
actually think that they're not simplistic enough. We (as a species) need to
figure out some invariants if we're ever going to do successful science on
people and the systems we create.

Back to Jung, while he didnt use the statistics that we would today, he did
spend an awful lot of time attempting to figure out why we are the way we are,
without resorting to sex sex sex (like the inimitable Freud). Personally, at
this point he's probably better read as a philosopher and student of human
nature, but he is well worth reading in that capacity.

That being said, he's an awful writer so it is a bit of struggle. Well worth
it though, in my opinion.

~~~
disgruntledphd2
Replying to myself as I believe we have triggered the algorithm for shouting
matches (though I don't believe either of us were shouting). Dangers of fully
automated approaches (black boxes), I suppose.

Funnily enough, I agree with you on psychologists and psychiatrists (to a
certain extent). We understand so little, and claim to know so much. Our
sample sizes and cultural range is quite poor (anthropologists are good at
this, but they tend to lack even a basic understanding of statistics). I do
believe that algorithmic approaches to predicting humans have potential, and
the reason I now work in the private sector is to get access to some of this
data as I believe that masses of data are the only way we'll get invariants to
form useful landmarks towards understanding of people.

I would note, however, that I suspect you are classing pychologists (or
cognitive scientists, as some of the hip american departments have rebranded
themselves) as therapists, which although a common misconception is about as
accurate as saying that computer scientists are software engineers (i.e.
sometimes, but its not a one to one relationship). Thanks for the discussion,
I enjoyed it.

------
bearmf
I will present a somewhat controversial point of view here. The problem with
math education lies as much with teachers as it does with students.

If you have students that cannot understand basic formulas and memorize them,
you are not going to teach them abstract concepts. Concrete math is much
easier than abstract math for the vast majority of people. I cannot really
believe the stories about people who are supposedly talented at math but are
not engaged enough by the school curriculum and consequently fail at the
tests. School level math is very easy for anyone with some aptitude for math.
Anyone who fails it will probably have even greater difficulties with abstract
concepts behind it.

That gifted students are not stimulated enough is the real problem. Math
classes for gifted children is probably the only solution. Something like
Stuyvesant High in New York City but on a wider scale.

As for better math education in Singapore and Taiwan, well, they do have
better students than most US public schools. Both genetics and culture play a
role here. Asian people have both higher average IQs and higher average
conscientiousness. Their teachers are able to teach math at a higher level. US
could surely learn from them, but not every school could use their techniques.

~~~
guylhem
I disagree. The current perspective of IQ and ethnicities show that while
there might be slight differences, they are dwarfed by the differences in the
education process.

If you want another example besides Singapore, look at french math textbook
for highschool students - with nth derivatives, etc.

Here's the first link googles gives me - something that a finishing highschool
student, around 17 years old, is expected to do if he is enrolled in a
"scientific" curriculum. (basically there are 4 curriculums - scientific,
economic, literary (humanities), technical (vocational))

[http://maths54.free.fr/terminal/ch7_der_fonct_comp/cours_cha...](http://maths54.free.fr/terminal/ch7_der_fonct_comp/cours_chap7.pdf)

~~~
bearmf
I do not want to discuss race/national IQ differences, this is a sensitive
topic and does not really belong here. I am quite sure individual IQ
differences are not controversial though and cannot be "dwarfed" by good
educational processes.

The French textbook looks reasonably rigorous but as you say it is intended
for "scientific" students. Thats basically what I was talking about in my post
- you need to select for gifted students before moving on to complex math (not
that derivatives are particularly hard if you do not have to prove theorems).
In US I believe differential calculus belongs to AP Calculus high school
classes. No idea about their level but content on the internet looks similar,
maybe less rigorous.

~~~
guylhem
FWI, I do not believe in IQ. The evolution of scores alone makes me think
there is a confounding variable. Students should just study what they can get
money from and they are interested in.

In France, there are 4 curriculum of approximately similar sizes - at least
when I did my studies. There is no IQ selection.

There is no selection either based on being "gifted" or not - you just get a
curriculum matching the job you said you were the most interested in, if you
basic grades are enough (i.e. if you persistently had below average grades in
math, you might not be enrolled in a scientific curriculum)

"scientific" students makes 25% of the students - I'm not sure it can be
compared to the situation in the US unless 25% of the students go in AP
classes.

[The other curricumulum also have decent math, only slightly less theoretical
or more into specific domains, such as arithmetic or geometric progression
mathematics (for economy and some BTS vocational studies)]

Edit : Enrollment trends are shown in <http://quanti.hypotheses.org/631/>

red is humanities

blue is economics

green is scientific

[apparently vocational studies are gaining ground, and humanities are
declining, a good thing considering the job market]

~~~
lutusp
> FWI, I do not believe in IQ.

As stated, this is a meaningless claim. Do you mean you don't believe in the
accuracy or social value of of IQ testing, or don't believe that IQ exists as
a measurable quantity, or don't believe in the practice of ranking people
based on intelligence?

~~~
guylhem
Sorry, I should be more precise.

First, I don't believe that IQ exist as a measurable quantity - IQ is too many
things thrown together in a single bad. Tests group together various things
which may be handled by different subsystems in the brain. If there is
something called IQ, it's an aggregate.

Anyway, if there was such a unique quantity, actual data shows a progression
of IQ scores in time - therefore if the tests are considered accurate and
unbiased, it must be a "quantity" that can evolve based on the society a
person lives it. It should then be considered not as a value, but as a
function depending on a variable called society.

I do not know if studies have tried to measure the accuracy of repetitive
measurement in low education adults enrolled in a learning program. If there
are such studies and if they show inconsistent result (ie any change of IQ),
then IQ should be considered as a function of 2 variables : f(society,
personal experience).

Now, even if we consider that at a time t it could be accurately measured and
that societal bias could be removed, considering how other qualities (such as
determination, work ethic, consistency, creativity, competitiveness...)
influence the outcome of any human activity, it seems foolish to rank people
based on just one quality - especially if we don't know the other values, and
their individual ponderation in the end result.

This ponderation could also be different depending on the activity, and IQ
provide an absolute advantage in some activities (rhetoric?), but say
determination would give an absolute advantage in other activities
(startups?).

I prefer to say I "don't believe in IQ" because it's easier to say that way
than giving this long version.

~~~
lutusp
> I prefer to say I "don't believe in IQ" because it's easier to say that way
> than giving this long version.

Yes, but for this subject, saying it that way is completely uninformative, to
the degree that it's misleading. It would be like saying Harry is not now
beating his wife -- it leaves too many questions unanswered.

------
tokenadult
Once again ColinWright graces the front page of HN on a weekend by submitting
a story on mathematics education. The blog post submitted here, by an
undergraduate physics major at the University of Texas at Austin, prompted me
to read some of the author's other writings. The author's perspective on the
importance of mathematics as a tool for understanding physics immediately
reminded me of some good reads by older authors on physics. "How to Become a
Good Theoretical Physicist" (HTML title "Theoretical Physics as a Challenge")
by Nobel laureate Gerard 't Hooft

<http://www.staff.science.uu.nl/~hooft101/theorist.html>

lists essential knowledge that everyone should possess who desires to advance
theoretical physics, and included in that knowledge is much mathematics. There
is a whole book, The Road to Reality: A Complete Guide to the Laws of the
Universe by Roger Penrose,

[http://www.amazon.com/The-Road-Reality-Complete-
Universe/dp/...](http://www.amazon.com/The-Road-Reality-Complete-
Universe/dp/0679776311/)

that is marketed as a book about physics but includes a huge section reviewing
secondary school mathematics as an essential background to physics.

The blog post submitted here has a title that is an homage to the article "The
Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene
Wigner in Communications in Pure and Applied Mathematics, vol. 13, No. I
(February 1960).

[https://dtrinkle.matse.illinois.edu/_media/unreasonable-
effe...](https://dtrinkle.matse.illinois.edu/_media/unreasonable-
effectiveness-cpam1960.pdf)

People who know physics have long been delighted to find in physics
applications for the mathematics they learned in mathematics courses without a
hint of how useful the mathematics would be. The blog post author, however,
goes beyond that perspective to urge, "Let’s think of mathematics in the
abstract. Mathematics, at its most basic, is a very simple set of very well-
defined rules. The rules describe the behavior and interaction of certain
completely imaginary objects. Upon these rules, mathematicians have built
others." And that brings to mind Paul Halmos's article (with its intentionally
provocative title, an example of Halmos's spicy style in expository articles
about mathematics) "Applied Mathematics Is Bad Mathematics" Halmos, P.
"Applied mathematics is bad mathematics." Mathematics tomorrow (1984).

[http://books.google.com/books?hl=en&lr=&id=FcgB818WA...](http://books.google.com/books?hl=en&lr=&id=FcgB818WAQgC&oi=fnd&pg=PA193&dq=paul+halmos+applied+mathematics+is+bad+mathematics&ots=p0vNtw9Mxt&sig=VcLMDtZX26VSaeMCse4wPqjyzcs)

Halmos claims that mathematics is interesting and beautiful whether or not it
has an apparent application.

Other replies already posted to this submission have helpfully mentioned the
issue of empirical tests of what method of teaching mathematics may best help
young learners appreciate (and later apply) mathematics. I have been deeply
interested in cross-national comparisons of educational practice since living
overseas beginning in 1982. In those days, one way in which school systems in
most countries outdid the United States school system, economic level of
countries being comparable, was that an American could go to many different
places and expect university graduates (and perhaps high school graduates as
well) to have a working knowledge of English for communication about business
or research. I still surprise Chinese visitors to the United States, in 2012,
if I join in on their Chinese-language conversations. No one expects Americans
to learn any language other than English. Elsewhere in the world, the public
school system is tasked with imparting at least one foreign language (most
often English) and indeed a second language of school instruction (as in
Taiwan or in Singapore) that in my generation was not spoken in most pupils'
homes, as well as all the usual primary and secondary school subjects. At a
minimum, that's one way in which schools in most parts of the world take on a
tougher task than the educational goals of United States schools.

It was on my second stay overseas (1998-2001), that I became especially aware
of differences in primary mathematics education. I began using the excellent
Primary Mathematics series from Singapore

[http://www.singaporemath.com/Primary_Mathematics_US_Ed_s/39....](http://www.singaporemath.com/Primary_Mathematics_US_Ed_s/39.htm)

for homeschooling my own children, and I browsed Chinese-language bookstores
in Taiwan for popular books about mathematics as my oldest son expressed an
avid interest in mathematics. I discovered that the textbooks used in
Singapore, Taiwan (and some neighboring countries) are far better designed
than mathematics textbooks in the United States. (During that same stay in
Taiwan, I had access to the samples United States textbooks in the storeroom
of a school for expatriates, but they were never of any use to my family. I
pored over those and was appalled at how poorly designed those textbooks
were.) I discovered that the mathematics gap between the United States and the
top countries of the world was, if anything, deeper and wider than the second-
language gap.

Now I put instructional methodologies to the test by teaching supplemental
mathematics courses to elementary-age pupils willing to take on a prealgebra-
level course at that age. My pupils' families come from multiple countries in
Asia, Europe, Africa, and the Caribbean Islands. (Oh, families from all over
the United States also enroll in my classes. See my user profile for more
specifics.) Simply by benefit of a better-designed set of instructional
materials (formerly English translations of Russian textbooks, with reference
to the Singapore textbooks, and now the Prealgebra textbook from the Art of
Problem Solving),

[http://www.artofproblemsolving.com/Store/viewitem.php?item=p...](http://www.artofproblemsolving.com/Store/viewitem.php?item=prealgebra)

the pupils in my classes can make big jumps in mathematics level (as verified
by various standardized tests they take in their schools of regular
enrollment, and by their participation in the AMC mathematics tests) and gains
in confidence and delight in solving unfamiliar problems. More schools in the
United States could do this, if only they would. The experience of Singapore
shows that a rethinking of the entire national education system is desirable
for best results,

<http://www.merga.net.au/documents/RP182006.pdf>

but an immediate implementation of the best English-language textbooks, rarely
used in United States schools, would be one helpful way to start improving
mathematics instruction in the United States.

The blog post author begins his post with "In American schools, mathematics is
taught as a dark art. Learn these sacred methods and you will become master of
the ancient symbols. You must memorize the techniques to our satisfaction or
your performance on the state standardized exams will be so poor that they
will be forced to lower the passing grades." This implicitly mentions another
difference between United States schools and schools in countries with better
performance: American teachers show a method and then expect students to
repeat applying the method to very similar exercises, while teachers in high-
performing countries show an open-ended problem first, and have the students
grapple with how to solve it and what method would be useful in related but
not identical problems. From The Teaching Gap: Best Ideas from the World's
Teachers for Improving Education in the Classroom (1999): "Readers who are
parents will know that there are differences among American teachers; they
might even have fought to move their child from one teacher's class into
another teacher's class. Our point is that these differences, which appear so
large within our culture, are dwarfed by the gap in general methods of
teaching that exist across cultures. We are not talking about gaps in
teachers' competence but about a gap in teaching methods." p. x

"When we watched a lesson from another country, we suddenly saw something
different. Now we were struck by the similarity among the U.S. lessons and by
how different they were from the other country's lesson. When we watched a
Japanese lesson, for example, we noticed that the teacher presents a problem
to the students without first demonstrating how to solve the problem. We
realized that U.S. teachers almost never do this, and now we saw that a
feature we hardly noticed before is perhaps one of the most important features
of U.S. lessons--that the teacher almost always demonstrates a procedure for
solving problems before assigning them to students. This is the value of
cross-cultural comparisons. They allow us to detect the underlying
commonalities that define particular systems of teaching, commonalities that
otherwise hide in the background." p. 77

A great video on the differences in teaching approaches can be found at "What
if Khan Academy was made in Japan?"

<http://www.youtube.com/watch?v=CHoXRvGTtAQ>

with actual video clips from the TIMSS study of classroom practices in various
countries.

~~~
Evbn
Why did you open with an ad hominem and ad datum reference?

~~~
WildUtah
_Ad datum_ means "to (toward) the given (item)." You probably meant _ad diem_
, "to the day (or date)."

------
bmuon
I disagree on the premise that math is tought in the wrong way. Repetition is
a very important part of learning so learning to use mathematical constructs
is just as important as learning to know how to build them. Also, people don't
naturally think in abstract terms, many learn from example first, interpolate
and then gain an understanding. Humans are more inductive than deductive. So
at the very least it's not that the current education is wrong, but that it
needs to add the teaching of another skill.

Like another poster says, the topic requires research. Teaching to think in
abstractions isn't easy.

------
peripetylabs
I don't recall ever wondering "why" I would ever "need" mathematics. I just
always enjoyed it. To me, trying to convince students why they should enjoy
mathematics (just because we do) seems like a good way to make students
miserable.

Is mathematics education really failing because it doesn't produce _many_
mathematicians?

~~~
ams6110
I think this is the real issue. A small fraction of people are fascinated by
mathematics and enjoy it. The idea that there is some specific way to teach
mathematics that will ignite some spark in a person who doesn't inherently
have it I believe is false.

------
davidkatz
This is indeed a serious problem. An interesting startup that is trying to
address it is <http://www.mathalicious.com/>. They give math teachers lesson
plans which tie math to things that students care about - 'is Kobe Bryant a
better shooter than LeBron James?'. Things like that.

From my own experience, I was pretty bored with Math in high school. Through a
series of coincidences I started reading some popular physics books, which led
me to study Physics and re-discover Math as an incredible tool.

~~~
Tycho
A pattern i see a lot is that people develop and interest in maths outside
what their school was doing. Maybe we need to shift the onus onto individual
children and families to foster interest in maths, regardless of how the
schools teach it. It doesn't really matter how well you prepare the food if
people don't have an appetite.

~~~
Evbn
You say that parents should take a role in their children's intellectual
development? Then what am I paying property taxes for?

~~~
lutusp
> You say that parents should take a role in their children's intellectual
> development? Then what am I paying property taxes for?

Let me ask another question -- do you really want to avoid having to provide
an intellectual context for your children's life experience, and assign that
responsibility to governments instead? Doesn't that sound dangerous? I shall
resist quoting historical examples in which governments became the primary
source of ideas and intellectual content for a new generation.

------
quinndupont
This article really should reference Kirby's excellent article about a non-
Platonic concept of mathematics, which, in arguing that the _writing_ of
mathematics is necessary for the doing of mathematics. On this view,
mathematics education is a necessarily in scriptural activity.

Kirby, Vicky. "Enumerating Language: "The Unreasonable Effectiveness of
Mathematics"" Configurations, 11, 3 (2003).

------
7952
A few years ago I read an article [1] about a school teaching maths by
pretending that the process was magic in Harry Potter. Perhaps what children
and adults lack is a sense of imagination of how to apply concepts.

[1]
[http://news.bbc.co.uk/1/hi/england/nottinghamshire/7094593.s...](http://news.bbc.co.uk/1/hi/england/nottinghamshire/7094593.stm)

------
j2kun
Interesting mathematics can be taught in high schools. In fact, I've tried and
had some wonderful results. See my account of it here:
[http://jeremykun.wordpress.com/2011/06/26/teaching-
mathemati...](http://jeremykun.wordpress.com/2011/06/26/teaching-mathematics-
graph-theory/).

------
orangeduck
Great article. The lego air plane analogy is very accurate. It is certainly
true that maths has lost some of its mysticism in early education but I think
perhaps telling students that "maths is a set of abstract made up rules
governing an imaginary universe" might alienate them just as much as before.

------
Heliosmaster
great article, very well written with many agreeable points. But I doubt that
the teaching of mathematics can be easily subverted into a better one, mostly
because there is plenty of people that do not care enough: they think "math is
hard and sucks" or simply do not care about knowing the alphabet of the
knowledge. That's why at the University math is taught the good way, because
there almost everybody is genuinely interested in the subject.

~~~
kiba
Math is hard and sucks because we are forced to do tedious and time consuming
calculations by hand. Even with a calculator, it's still painful.

I basically cringe at khanacademy everytime they forced me to do this.

~~~
j2kun
Mathematics is not about calculations. That's exactly the problem with math
education, that the people designing the curriculum don't accept that.

~~~
Evbn
You seem to be unaware of how curriculum has been designed in recent decades.
The current "Where's the Math" protest movement is complaining that the
curriculum is devoid of calculation.

------
marshallp
There's a few problems with the article. The rules argument he makes could
instead be made for the more useful field of computer programming.

Also, the reductionist paradigm is dead. It worked for finding laws of physics
and some chemistry, but otherwise, in the most useful fields of today, like
biology/materials/chemistry (high throughput methods), computer vision, search
engines etc. the automated creation of hypotheses through machine learning is
winning out.

Conrad Wolfram gives a talk about the need for math education reform
<http://www.youtube.com/watch?v=60OVlfAUPJg>

He uses the term mathematics, but completely removing that term and replacing
it with computer programming and machine learning should be done. They sound
cooler and this step will remove all the baggage and ill-will mathematics has
in society. That way, all mathematics teachers can be simply removed from high
schools and colleges and replaced with computer programmers. Estonia is one of
the few enlightened places on this subject with their introduction of
programming as mandatory from year 1 in k12.

Almost the entire high school drop out rate can be attributed to maths
teaching, and their is no solid empirical proof of it's utility over
programming (the practice of "science" hasn't been applied to "maths" itself).
<http://en.wikipedia.org/wiki/Mathematical_anxiety>

The same argument can be made for a number of other subjects, such as
chemistry (why teach the periodic table?), languages (we have google translate
and should taxpayers be funding this unproductive activity), and others
(everything should be reexamined in light of search engines and instant
information access).

The only useful subjects in k12 are probably

\- computer programming, including machine learning/statistics

\- physical education,

\- communication (reading/writing/public speaking/socialization)

\- general studies (trivia like history, geography, astronomy),

\- personal finance

\- physical crafts (3d printing, woodshop, cooking)

~~~
defen
From reading your HN comments, you seem like the kind of person who has a
small axiomatic set of principles, and then attempts to fit the world to those
principles. Without going into the merits/demerits of that approach, I'd at
least like to point out that it occasionally leads to absurd conclusions -
such as replacing language courses with Google translate. Do you really think
that Google translate is a feasible way to converse with someone in a foreign
language? Or, for translating literature? Here is the opening paragraph of War
and Peace, computer translation vs human. Note that Google translate assumed
the whole thing was French, and left the Russian parts untranslated, so I had
to manually translate the Russian words. Italics represent words originally in
Russian.

Google translate:

Еh, my prince. Genoa and Lucca are only appendages of, _the manor_ ,
Buonaparte family. No, I warn you that if you do not tell me that we have war,
even if you allow yourself to overcome all infamies, all the atrocities of
this Antichrist (my word, I think) - I do you know more, you are no longer my
friend, you are no longer _my faithful servant_ , as you say. _Ну, hello,
hello_. I see that I frighten you, _sit down and talk_.

Richard Pevear and Larissa Volokhonsky translation:

Well, my prince, Genoa and Lucca are now no more than possessions, _estates_ ,
of the Buonaparte family. No, I warn you, if you do not tell me we are at war,
if you still allow yourself to palliate all the infamies, all the atrocities
of that Antichrist (upon my word, I believe it) - I no longer know you, you
are no longer my friend, you are no longer _my faithful slave_ , as you say.
_Well, good evening, good evening_. I see that I'm frightening you, _sit down
and tell me about it_

~~~
marshallp
Is it the responsibility of the taxpayer to fund the education for the leisure
activity of the upper middle classes (speaking with foreigners or reading
translated literature).

The education system that exists today (k12 + college) is a McReplica of what
aristocratic people of earlier centuries considered fit for their children
(who would never actually need to work). We're living the enviousness of the
middle classes of a century ago (this same principle applies to the
McMansions). It has no relation to what a more perfected reality could be.

With respect to google translate, I think we'll see a lot of improvements. I
expect to see human level performance within 5 years (it's a "let the
computers run long enough" + "enough data" problem).

~~~
defen
What about countries where English is not the native tongue? Surely learning
it can have huge advantages.

~~~
marshallp
Yeah, I totally agree, in non-english speaking countries it's completely
justifiable (until human-level language translation comes around).

