The Math Scam
Some of us
are good at math, some of us struggle merely to get through it.
good at it or bad, few of us will ever again use anything we learned
in calculus or trigonometry class ever again, not even once. After
graduation, few will even be able to recognize such general terms
as sine and cosine, much less be able to explain what they mean.
For those who
want to become engineers, scientists or economists, math is the
foundation of their careers. Its vital, not to be questioned.
For the rest
of us and I include technicians and medical workers*
among the rest of us math is, more often than not, a painful
and soul-breaking ritual that we are forced to endure if we hope
to have a decent life.
line is that lots and lots of math is supposed to prepare us for
work. Its supposed to teach us to think logically. Its
also supposed to help America compete against Asian Tiger economies
that are eating our national lunch.
may be mistaken. For many, if not most students, math education,
at least as taught in this country, is little more than a cruel
and expensive obstacle course designed to force large numbers of
them to fail.
this torture machine produces generations of Americans who graduate
utterly unprepared to tackle real-world studies.
the following sample problem that all students bound for higher
education are expected to understand:
the unit circle in the coordinate plane enables the extension
of trigonometric functions to all real numbers, interpreted as
radian measures of angles traversed counterclockwise around the
taken word for word from page 60 of the California Common Core standards,
is among the norms used by 45 states and the District of Columbia
to determine what every student should know. There are many, many,
more examples, all equally opaque.
somebody in 45 states and D.C. really thinks that all of us common
folk really, really, need to know how to traverse counterclockwise
around the unit circle or we wont be able to think logically,
as if mathematicians are known for their logical thinking. (Ted
Kaczynski, Paul Erdos, Lord Bertrand Russell, John Nash, and Sir
Isaac Newton come to mind all of them brilliant, all of them
mentally handicapped in various ways.)
During my career,
Ive written thousands of articles on subjects as varied as
boxing and physics, Ive designed software products that won
two Editors Choice awards, but Ive never had occasion
to traverse counterclockwise around the unit circle,
nor even to traverse it clockwise. Not once.
Nor did I ever
have to understand how the unit circle in the coordinate plane
enables the extension of trigonometric functions to all real numbers.
In fact, I dont even know what a unit circle or a coordinate
plane is, or why anyone would want to traverse one. Ive looked
it up, and I still dont know, other than the unit circle has
something to do with a radius of a circle being equal to one.
One what, no one says, at least not in English.
Im sure that some people actually need to know all about the
unit circle. I would include among them such truly and honest-to-gosh
smart people as scientists, engineers, economists and artillery
for example, needs to understand the unit circle. So does his wife.
Theyre both astrophysicists. They study the paths of comets
and asteroids, and how to send space probes to meet them, what is
known colloquially as rocket science.
like my brother his face is familiar to the millions who
like history of the planets shows may account
for 1 percent of the entire population. To that 1 percent, lets
add people whose work requires them to talk to scientists, engineers,
economists and artillery officers, and we may have another 1 percent
of the population. Lets add another two percent for people
who marry scientists, engineers, economists and artillery officers
and those who know how to talk to them. Lets also add another
percentage point for math hobbyists who are actually interested
in traversing the unit circle for its own sake and we have
a total of 5 percent, one out of 20.
being extremely generous.
The rest of
us, 19 out of 20, are force fed higher math for up to four years.
All college-bound students are required to pass three years of it.
Vast numbers drop out in frustration, others manage to barely get
by and swear that they will never enter a classroom again.
And a day after
our last finals, all of us who passed immediately forget absolutely
everything. Meanwhile, very, very, few of us are taught how
to use math to solve real-world problems, such as how to calculate
the amount of wood needed to build a house, or how much concrete
is required to pave a patio.
homeowner doesnt have much use for the unit circle, but knowing
how to buy just the right amount of materials, how to have it delivered
on time and how much it will cost down the line, would save a lot
of time and money.
not as important.
There are those
who believe that degrees are pointless scraps of paper. I disagree,
but Peter Thiel and others have a point: We force young people to
suffer obscure and useless subjects as a ritual because its
the way things are done, and the way things have always been done.
courses and thats what they are, obstacles disguised
as courses exist because our grandparents and great-grandparents
endured them, and if they learned to traverse the unit circle, well,
by jiminy, todays young whippersnappers had better learn to
do it as well. We may no longer be expected to learn Latin and Classical
Greek, thank Almighty Zeus, but the struggle with theoretical math
still holds a mystical, untouchable holiness among well-meaning
And yet very
few young people study computer programming in high school, and
those who do, dont learn enough to obtain an entry level position.
Think about it, 35 years into the PC age, and most kids put on their
blue caps and gowns without ever learning Boolean logic, conditional
loops, variables and arrays, terms that should actually mean something
to the average, reasonably educated person.
the starched-collared, monocle-wearing worthies who invented secondary
education curricula for the unwashed masses, back in the olden days
of bustles, shirtwaists, handlebar mustaches and buggy whips, didnt
think that practical subjects were as important as the skills they
mastered at their exclusive private schools such as translating
Ovid or Caesars Gallic Wars.
by 1900 times had changed. According to Professor Mark Ellis of
Cal State Fullerton, a specialist in the history of math education,
The turn of the 20th century was the first era of large cities
with diverse populations. Child labor was banned. Kids had time
to go to school.
was a vast increase in demand for secondary education, but the idea
that students born of farmers or immigrant shopkeepers should study
bookkeeping instead of Pericles Funeral Oration was difficult
for academics from privileged backgrounds to understand.
such as shop and home economics managed
to infiltrate the system. Boys used to learn how to saw lumber,
and girls learned how to cook. Perhaps, these days, boys and girls
should study both subjects, or at least learn how to operate a microwave.
Instead, theyre cramming math, yet falling even further behind
Latin and Classical
Greek are now out of fashion, praise Jove and all the others. A
few might want to study these languages so that they can name new
species of slugs and jellyfish. (These days, dinosaurs are mostly
given Chinese names.)
law still requires three years of higher math, including calculus
from anyone who wants to go to the University of California or Cal
State to study marketing, public administration or even history.
mean that that there are any monocled, pointy-bearded men and pince-nez
wearing women out there eager to paddle the daylights out of nineteen
out of twenty students with wooden rulers for failing to traverse
the unit circle. Far from it. Their modern incarnations, such as
Gerardo Loera, executive director of curriculum and instruction
of the Los Angeles Unified School District, mean well. They just
dont get it.
be as embarrassing to say I cant do math as it
is to say I cant read, Loera says, which
would make sense in a perfect world. I still believe that
math skills, such as critical thinking and problem solving, will
transfer to other areas and are important even for liberal arts.
Even if students dont take any more math.
a fine and decent man who proved remarkably open and generous with
his time, couldnt cite any facts or figures to back up that
belief. I asked him if calculus and trigonometry are useful in,
and admitted that I cant cite any research that higher
math helps journalists.
why Asian countries seem to be eating our lunch appears to be an
understanding of a basic fact of the human brain: Only so much stuff
can be forced inside.
So they teach
math from staple-bound booklets less than a hundred pages long.
Only the most important topics are covered, but students are given
time to actually understand them. Contrast those books to the dangerously
heavy bricks California students are forced to lug home every day,
and skim through because theres no time to really understand
whats in them.
in teaching mathematics admits that the situation is ridiculous
and self-defeating. According to a famous paper by Prof. William
H. Schmidt of Michigan State University, the math curriculum in
the United States is a mile wide and an inch deep.
in math education that Ive talked to, including Cathy Seeley,
a past president of the National Council of Teachers of Mathematics,
agree with Schmidt: High schools are trying to cram too much into
too many topics in too little time, the teachers have to move on
before the kids have time to absorb anything, the lessons are so
abstract that they mean absolutely nothing, and in the end, the
students will forget absolutely everything.
claim that the problem isnt topics Singapore students,
we are told, study more math topics than American students and do
better on standardized tests.
is an island city state. It has a small, rigorously conformist and
highly disciplined population that accepts a single-party dictatorship
without complaint. Singapore also famously produces university graduates
who havent the slightest idea where babies come from. Even
worse, chewing gum is illegal there.
It is also
one of the countries whose students are expected to brutally cram
for admissions tests. Once admitted, Asian students find that university
studies are less rigorous than they are in North America, hence
the vast numbers that come here for post-secondary education.
There are those
who still believe that narrowing math standards in high school
and adding flexibility to the system will cause California
and the rest of the country to go to hell in the proverbial hand-basket.
These should remember that American high schoolers have been doing
poorly, by international standards, for decades, yet our universities
are still the envy of the world.
I would never
say that higher math is only for nerds, or that it is unnecessary
for those interested in fields that build on its foundations, nor
would I ever say that students shouldnt know what trigonometry
is, and why Newton invented calculus.
of frying their brains trying to traverse the unit circle counterclockwise,
perhaps students should be given a year of natural history. Instead
of trying to solve useless, abstract puzzles, they should try to
plot the orbit of a Mars probe, or how much energy would be required
to send an asteroid hurtling to Earth to wipe out the dinosaurs.
Or how scientists were able to use math to analyze regular mutations
in DNA, proving that we are all descended from a single woman who
lived some 200,000 years ago.
Or how King
George III used calculus and astronomy to test the first practical
longitudinal chronometer. (Yes, King George was the villain of the
American revolution, but ancestors of most Americans arrived on
this continent in reasonable safety, and at a much lower cost, because
that very odd King was able to prove that the longitudinal chronometer
actually worked and convince others that it did.)
find these examples more interesting than anything in the Core Curriculum.
They might not be able to traverse that unit circle counterclockwise
when they were finished, but they would know a few more things that
they might remember past prom night.
and nurses dont need higher math. Perhaps some doctor might
like to throw a quarrelsome hypochondriac from a window and calculate
the time it takes him to land that would be higher math.
But in the real world, they mainly need to know the metric system
and be able to keep its infernal decimal points in the right place.
They have too much to learn about the infinite frailties of human
anatomy to be bothered with traversing the unit circle. Try asking
your surgeon a trig question, and you might as well be speaking
Latin or Classical Greek, but he or she is still required to learn
higher math as a way of demonstrating an intelligence sufficient
to remove an appendix.
with permission from CalWatchDog.