Pharyngula

Posted by: donna | February 16, 2006 11:14 PM

What a fucktard. I'm so damn sick of the "math is hard" approach taken towards girls. But then, I was consistently pushed ahead in math classes as a teen and NEVER told it was supposed to be "hard". In the 70s, girls could do ANYTHING.

Hey, they still can. Don't ever let the fgucktards tell you any different.

Posted by: marky | February 16, 2006 11:22 PM

The "writing is the highest form of reasoning" line is so typical.
Cohen is such a moron he probably believes that Einstein couldn't do algebra either.
I'll stop here. There's just nothing to say to someone dense as a stone.

Posted by: Troutnut | February 16, 2006 11:25 PM

This quote from Cohen really caught my attention:

The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence.

I've got to call BS on that one. Does anyone here remember people in high school who were good at math but couldn't write?

When I was in high school 7-10 years ago, the people good in math and writing and history were all the same group of nerds who went on to good colleges. I don't remember a single one who did well in math and poorly in other subjects.

I think Cohen's trying to pretend that, because he doesn't possess their aptitude, they must not possess his. Otherwise they'd just be flat-out superior to him, and of course we can't have that! Every inept one-trick pony has to trot out this argument at one time or another.

Posted by: Lettuce | February 16, 2006 11:30 PM

Wow.

I'm not sure what else I can say… Wow.

Cohen's a hell of a typist, but not much of a writer.

Wow.

I can't imagine not having some understanding of algebra; Cohen's a marvel.

Posted by: larry | February 16, 2006 11:33 PM

Maybe if Dickie could put two and two together, he could have figured out that the Iraq war was pre-orchestrated, and that the evidence for it was false. He doesn't seem to have mastered his history courses, either.

Posted by: Carlo DiPietro | February 16, 2006 11:38 PM

What a dickwad. And I know he's a dickwad because I know what he's saying is absolutely, one-hundred percent false based on personal experience. I pretty much goofed off in high-school and did not pay attention in math class. I had the "math is hard and I'll never use it" attitude, which prevented me from making an honest effort at learning it at all. After I graduated I ended up playing a game of "catch-up" with mathematics, teachings it to myself with academic textbooks. It worked out in the end, but in retrospect I do wish that I had made more of an effort in high school, as I could've saved myself a lot of trouble.

Posted by: Michael Ralston | February 16, 2006 11:42 PM

Man. What gets to me is that I had mastered (well, basic, but still) algebra at the age of TEN...

... and the principle from algebra I use most often? The concept of ABSTRACT THOUGHT.

Is it strictly reasoning? Maybe not. But it sure as hell is the ability to deal with a concept without knowing everything there is to know about it.

Posted by: !!! | February 16, 2006 11:46 PM

The girl flunked algebra SIX TIMES. She wasn't going to be a scientist, a technician, a teacher, or an accountant in any case. And because of state requirements, she quit school altogether. But who cares, right? If you can't do math, then fuck you and who cares.

In any case, Cohen's sympathy for her hardly qualifies as some bullshit "math is hard" approach to girls. Did you (the genius behind that comment) even bother to READ the original article?

Since I finished up with calculus ten years ago, I've had absolutely no occasion or desire to use algebra, GREs excepted. I guess that makes me a talking sheep.

Posted by: craig | February 16, 2006 11:49 PM

I am completely tone-deaf when it comes to math, but that's something I regret, not something I'm proud of. I'm also totally tone-deaf to poetry (hmmm... could there be a connection?)... but you only have to listen to someone like Richard Feynman explain what math means to them to realize that you are missing out on something big, perhaps more so than a literally tone-deaf person does with regard to music.

Posted by: trueLiberal | February 16, 2006 11:51 PM

Sorry, but I think all of you should invest a bit more time in the humanities. If you did, you wouldn't be half as upset about this as you appear to be.

Talk about intolerance. The comments on this post win the cake. If this is the best an affection for Algebra can produce take it away already -- it begins to fester.

(And yes, boys and girls, this is a LIBERAL talking to you.)

Posted by: craig | February 16, 2006 11:54 PM

!!!, a proper resonse to someone who has tried at something and failed repeatedly and will likely never succeed might be "well, that's OK, you have other strengths..."

It's not a proper response to say to that person and tens of thousands of other impressionable young readers "Good for you! Anyone who is good at that stuff is a LOSER! A Geek! A Nerd!"

Posted by: loser | February 16, 2006 11:56 PM

Knowing algebra, I immediately see the discontinuous functions (mostly linear) that apply to the taxes I did this week. Deductions and all that. Yes, I used a computer to do them but knowing in the abstract what the functions were doing let me know how to plan ahead to maximize certain savings, something the software did a poor job at, and it is the highly praised market leader. I have zero training in accounting or tax law. It just clicked.

But bah, abstraction is useless I guess.

Posted by: kathleen | February 16, 2006 11:58 PM

why does anyone care if you are a self-described "liberal" or not?

Posted by: Ray Radlein | February 16, 2006 11:59 PM

As a first approximation, Algebra is simply the arithmetic manifestation of the Fourteenth Amendment; it is the notion that equal things should be treated equally.

I would be leery of anyone who could cavalierly dismiss either.

Posted by: Rick @ shrimp and grits | February 17, 2006 12:02 AM

All of you self-righteous math whizzes may mock this sentiment

I thought the subject in question was elementary algebra? I don't think anyone has a problem with Cohen feeling sorry for the girl, but that doesn't justify the fountain of bull that was the rest of his column.

Posted by: bitchphd | February 17, 2006 12:03 AM

The "algebra vs. the humanities" thing is false, anyway. I'm a humanities person, and in fact, I use algebra fairly regularly to figure things out.

Having said that, sure: if someone has repeatedly failed a subject and just cannot deal with it, yes--one reassures them that thay are not, therefore, doomed to a life of failure. On the other hand, I can't help but wonder if the poor girl in question might not benefit from a compassionate, skilled, and gentle teacher. I say this as someone who has taught adults with a long history of failure behind them how to read (and write).

Posted by: Alexey Merz | February 17, 2006 12:07 AM

A few of the careers that will be off-limits:

Market research;
Banking;
Surveying;
Architecture;
Industrial design;
Medicine;
Veterinary medicine;
Dentistry;
Machining;
Electronics;
Shipping/Maritime (beyond Able-Bodied Seaman)
Engineering;
Meteorology;
Aviation (beyond flight attendant);
Computer science;
Any career path requiring enrollment at Annapolis, West Point, or the Air Force Academy;
Any career path requiring enrollment in an MBA program that is not a complete joke;
Any [successful] career path that requires making projections about future expenditures of of capital;
Any career path that requires you to interact with, and be taken seriously by, people in any of the above careers.

Richard Cohen: too stupid to fart and chew gum at the same time.

Posted by: Michael Ralston | February 17, 2006 12:09 AM

It's intolerance to say that algebra really does do good things?
If so, then the Democratic "leaders" actions make a lot more sense - they're perfectly tolerant... including being tolerant of actions that are incompetant, immoral, or flat-out evil.

Posted by: Andrew | February 17, 2006 12:10 AM

So Cohen's argument seems to be "Algebra shouldn't be required for graduation from high school." I assume he's talking here about basic algebra, a class my brother and I passed in eigth grade and my sister passed in seventh. He's arguing that since not getting a high school diploma is bad, we should give diplomas to even those who don't pass algebra.

I feel that the same argument could be made about any class in high school. I don't use history in my everyday life, why not get rid of it? English? Nothing in my profession requires analysis of symbolism in literature, so why bother there? And on and on. At some point, we need to address the fact that a high school diploma should be indicitive of more than the ability to show up at 8:30 every morning. One of the many skills I'd hope students have learned is basic algebra - maybe they don't have to solve quadratic equations in their heads, but most students can use calculators in their classes these days anyway. If someone can't be bothered to put in the extra work required to pass a class they're struggling in, should they really get a diploma?

Posted by: Boronx | February 17, 2006 12:15 AM

It's not compassionate at all to lie to her about this, nor is it ridiculous that a high-school should demand at least a passing knowledge of Algebra to issue a degree, nor are either of things a requirement for a full life, whatever the heck that means.

Posted by: justin | February 17, 2006 12:25 AM

Hi, law student here. Guess what, math comes up...EVEN IN LAW SCHOOL. It turns out that you should have the basic reasoning abilities of a chimp if you want to do...y'know...anything. Seriously 2x + 3 = 9. If you have never had to use that level of reasoning...then you, my friend, are a monkey wrench. Not the mechanics, or contractors who use monkey wrenches and math in their jobs, but the actual tool itself. Hey, Richard Cohen is a tool...who knew?

Posted by: Shemp | February 17, 2006 12:30 AM

I was a lousy math student. I'm a good writer, but math (and, sorry to say, languages) was not my forte. But it's ridiculous to make a blanket statement urging others to drop it like a hot potato. This guy is just trying to push people's buttons. Well, here's one for ya, Richard-- you're retarted.

PS - That "trueLiberal" guy is a toady conservative troll. I've seen him on other boards.

Posted by: Siamang | February 17, 2006 12:36 AM

What is the Value of Newspapers?

Gabrielle, I understand that in your school, you are made to read the newspaper. And section A too, not just the TV listings.

Here's the thing, Gabriela: You will never need to read a newspaper. I have never once needed to read one and never once even rued that I haven't. You will never need to know -- never mind want to know -- what the dimwits on Capitol Hill do to make laws -- or something like that. Most of the important news can now be read on a computer or a fashion magazine.

Gabriela, sooner or later someone's going to tell you that newspapers teach reasoning, and foster a deeper understanding of the news. This is a lie propagated by, among others, hack newspaper writers. Newspaper writing, and especially op-eds, are the lowest form of reasoning. This is a fact. The proof of this, Gabriela, is all the people who work at newspapers and get paid to blather on without any resemblence to reality or facts, and except for George Will, can not write a readable English sentence.

Look, Gabriela, I am not anti-newspaper. It has its uses, I suppose. Fish need wrappers and puppies need to learn not to piss on the rug.

Maybe students should even be compelled to take the newspaper (maybe for a school fund drive to buy the school more VCRs), but you shouldn't have to read it. There are those of you, and Gabriela you are one, who know what it is like to stare at a newspaper opinion page until you have eyeballed a hole in the page and not understand a thing you're seeing .

I can cite George W., whose last name will not be mentioned, who never read a newspaper but when called to the board in geography class, located the Sahara Desert right where the Gobi usually is. He was off by a whole continent, but they elected him President anyway.

There are those of us who know the sweat, the panic, the trembling, cold fear that comes from reading Krauthammer, Coulter, or The Family Circus. It is like being summoned to your own execution.

I have lived a pretty full life since school and never, ever read -- or wanted to read -- a newspaper. I was lucky, though. I had graduated from high school and gone on to college. It's different for you, Gabriela. Reading newspapers ruined many a day for me. Now it could ruin your life.

I'm sure there's something about newspapers that you might be missing, but it's not worth the hard intellectual work and frustration. Plus your hands get inky, and well, that's unattractive on a lady. Don't you worry your pretty little head.

Posted by: Nan | February 17, 2006 12:43 AM

There is not one columnist worth reading in the WP op-ed page. Their editorial page is now neocon. They have wall to wall neocon columnists with idiots like Richard Cohen for "balance".

Posted by: Cass | February 17, 2006 12:46 AM

My algebra teacher in seventh grade only paid attention to the boys and even though we were the chosen few to take it a year early, some of us girls had trouble. I was one of them and I remain to this day deeply angry about being deprived of this very important and necessary step to higher education and higher thinking. It is necessary for both.

Posted by: hamletta | February 17, 2006 12:52 AM

I, too, am one of the many who have used algebra in the womanly art of cooking. In addition, figuring out how to cut a flounce not only requires algebra, but geometry!

That aside, Cohen fucked up here by aiming all wrong. His beef is not with algebra, but with the LA school system. This girl took algebra six times, and they couldn't figure out a way to teach her? Did they not try using its real-life applications, like cooking? I mean, that's pretty basic: 2 x 1 tsp. = X.

In addition, have they eliminated music education? Because musical training is a huge boon to the math-averse in helping them grasp mathematical concepts. A dotted-eighth and sixteenth-note pickup or a triplet...those are fractions in action. And music theory, hoo! I had to write in four voices and incorporate a given chord progression with no voices crossing. I did it all on paper, because we had no piano at home. And it always struck me how similar it was to quadratic equations.

Apparently there are studies that prove kids with musical training tend to do better in math. It certainly played out in my family. I was no math wiz, but I did better than my brother, who wasn't a musician.

Posted by: justin | February 17, 2006 12:53 AM

My coment above shouldn't be construed to cast aspersions on people with legitimate learning disabilities, but to say that you'll never use algebra is absurd. People with learning disabilties should get extra help in school so that they can learn the basics, like math, that will make them successful. And, incidentally, I was a double major: Physical Anthropology (science) and Classics (humanities)...guess what, they can inform each other. I would hope that a columnist at the WaPo would know that, but then again I hope I'll one day have a solid gold toilet.
(cleary, though, I was not a spelling major, my bad).

Posted by: Zeno | February 17, 2006 1:04 AM

Okay, so Cohen says he lives a rich and fulfilled life without math. Good for him. He feels sorry for a student who can't pass even elementary algebra. Sure, we all do. He then tells her algebra is worthless. Idiot. He's using her educational travail as an excuse to trash math. Sure, she's never going to become a scientist or engineering, but that's no reason to tell her "There, there, sweetie, it's all nonsense anyway. Forget numbers; only words count." Yeah, it's the poets that keep our modern society ticking along. Cohen is making a fool of himself. Especially with that unpersuasive anecdote that purports to demonstrate that math proficiency is the death knell of literacy. I'm a math teacher and my colleagues and I are plenty literate, so there!

Posted by: Ralph | February 17, 2006 1:15 AM

Well, I use algebra quite frequently, just as part of a rich understanding of the world around me. I think a person who advises kids to ignore math is just as bad as someone who buys them alcohol or cigarettes. He or she is diminishing young people's prospects for future appreciation of, and pleasure in, life's mysteries.

Posted by: anonymous | February 17, 2006 1:23 AM

Although Cohen seems to be unhinged due to a traumatic experience in Algebra, I think it's ok if some people are allowed to graduate without passing Algebra. If this girl tried six times and couln't make it, one has to look at the totality of her skills, and as a special case allow her to graduate if she has adequate knowledge of other subjects. What harm will come if that happens? To whom?

Posted by: r@d@r | February 17, 2006 1:34 AM

in my book, a kid who goes back and re-takes a subject they've flunked six times, without going out behind the gym and smoking a joint, or hanging out across the street from school with the heshers, is already six times more of a success than many adults. the most important lesson in life, bar none, is getting back up again. math or no math.

i was one of the "bad in math" kids. but my school and my teachers put in the effort and helped me get through. i'm now using math in studying certain elements of computer programming so i can get a better job than the one i had before.

i had a chemistry teacher who passed me by giving me a D- on a final exam i should have gotten an F on, because i wrote a poem on the back of the test about how science isn't everything. he told me this: "it was refreshing having a student who, while intelligent, wasn't bent on discovering the next element" - a salty remark directed towards the obnoxious over-achieving kids in the front of the class.

i think he also gave me a that D- because he was a fan of my band, and came and saw us play in the local nightclubs.

Posted by: Dan | February 17, 2006 1:57 AM

It's always nice to see someone so fundamentally useless to society grant the rest of us permission not to think.

I'll grant Cohen this, though: he does have the only job that I can think of that doesn't require math. Or any actual higher thought processes at all, for that matter. Being a pretentious, self-serving twat is easy; in order to operate a fryalator effectively, you at least have to know not to stick your body parts into the boiling oil.

Posted by: John C. Randolph | February 17, 2006 2:31 AM

Bible-thumpers, Marxists, "feminist mystics", eco-terrorists, and many, many other groups share this intense hatred of man's principle means of survival: his intellect.

Now, may we please put to rest the canard that anti-intellectualism is somehow the exclusive province of the right wing?

-jcr

Posted by: John C. Randolph | February 17, 2006 2:32 AM

Oh, and let me also mention how happy I am that Mr. Cohen didn't attempt to enter any profession where math is a requirement. I shudder to think what kind of damage he could have done.

-jcr

Posted by: Max Renn | February 17, 2006 2:38 AM

What a toad is Cohen, so warty, so immaculately green. I am a failed historian, and an educational research statistician. I am also a logician and symbologist. Fuck Cohen, and his dog. This column is a PERFECT representation of why Cohen is in fact an idiot on many issues. He can't fucking reason, he doesn't understand basic critical thinking, he's a complete a-logical operator. Ergh.

And algebra, logic, and symbology are foundational to almost all structured thought, used or not.

Posted by: outeast | February 17, 2006 3:41 AM

I received some advice which was not a million miles from this as a child, and yes, it caused me to make choices that closed off all doors to all science-related subjects of study. Though I've now become deeply interested in science I have never been able to recover the basic toolkit, making pursuit of a basic understanding of science very much an uphill slog.

It's my firm belief that most intelligent people who 'have a problem with maths' have that problem because at some early stage they failed to master one or more essential skills. Unfortunately, the education system is not well set up to recognize that and to take such people back and babywalk them through the basics - instead it's easier to pigeonhole people as 'not mathematically inclined' or whatever. The attitudes of people like this Cohen are symptomatic of that...

Oh, and 'reason even a little bit'? What's that about? As I understand it, one strength of algebra is precisely that it encourages you to think systematically - in the kind of way needed for, say, logic. You know - that little tool for reasoning. Gagh...

Posted by: tristero | February 17, 2006 4:25 AM

Among the many repulsive things in Cohen's essay is the setup of a false dichotomy between math and the arts, particularly literature. Let's not fall for it.

This is not a fight between the slide rulers and the snoots, the math kids versus the word folks. This scrap pits *anyone* who's educated against the proudly stupid.

I make my living in the arts, composing music and getting it performed. It is simply inconceivable to me that anyone would take Cohen's attitude, just as inconceivable as someone claiming that learning how to spot irony and metaphor is worthless. And Cohen's being doubly arrogant because his attitude fails to address any real issues in the tragedy of the poor girl who dropped out.

What a total schmuck.

Posted by: melior | February 17, 2006 4:36 AM

As Neal Stephenson notes in his recent trilogy, al gebra is another one of the inventions of those evil scary Arabs, and hence Mr. Cohen can't be bothered to dirty his beautiful, ugly American mind with it.

Posted by: crmj | February 17, 2006 4:44 AM

I especially like the bit where he says that computers can't write columns, obviously the highest human calling. I think he should be called on that. I bet it would be possible to devise a program to write one of those "got up in the morning and found the cat had been sick on the floor, woe is me" type columns. Any takers?

Posted by: Bob Mottram | February 17, 2006 5:09 AM

What a moron! This guy clearly doesn't have a clue about the modern world. As a software engineer I use maths practically every day, including what you might call "algebra", calculus, geometry, basic number theory and much more besides. These sorts of skills are what drives modern technology and modern economies.

Next time this guy buys something online, and a little lock symbol appears at the bottom of his browser, he's using algebra.

Posted by: Anonymous | February 17, 2006 6:06 AM

Gabriela,

Your boyfriend takes you to an intimate little restaurant that doesn't take American Express. You will have to pay your tab in cash. There's a 6% sales tax and you both agree that, unless the service really sucks, less than 15% for a tip is tacky. You have $250 between you. What can you spend on the meal?

MoonBat.

We have nothing to fear but fear itself. --- FDR

Be afraid. Be very afraid. --- BushCo

Posted by: Marion Delgado | February 17, 2006 6:16 AM

U da man. I like the sheep remark.

Remember, for today's optimates, freedmen and slaves don't need knowledge, it just confuses them. Hew wood, draw water, take your clothes off, missy - how many of those jobs need algebra? none. and that's why our economy won't be competitive, our nation godly, or our borders secure until every four-eyed freak with a science book in his home has his head staved in with a rifle but.

Posted by: Mike Nilsen | February 17, 2006 6:36 AM

This makes 'Yes, Virginia, there is a Santa Claus' look like rational, pragmatic advice. What a bonehead! Cohen should absolutely be fired for spouting this codswallop. Let the cries for his blood begin!

Posted by: atablarasa | February 17, 2006 6:38 AM

This may have already been mentioned, but not in the first half of the posts, anyway.

Algebra is the basis for everything mathematical. We teach arithmetics as a separate function, but 2+2=4 is algebra. Manipulating fractions is algebra.

The problem is that people hear "algebra" and see quadratic equations. It's likely that the girl knows a lot more algebra than she thinks she does. Cohen I'm not so sure about.

Posted by: Jonathan Badger | February 17, 2006 6:50 AM

A (little) bit of defense for Cohen: while he is wrong that math isn't useful, he's right that claiming that math "teaches logic" is a pretty bogus argument. Why is it that every topic that wants to justify itself falls back on the old canard "it teaches logic"? Latin teachers also like to claim that Latin "teaches logic"; heads of chess and bridge clubs say their favorite games "teach logic".

If you want to learn logic, take a logic course -- you can find them in any philosophy department. Take a math course if you want to obtain a useful tool for doing science and engineering. Take a Latin course if you are interested in learning about an ancient culture. Learn chess or bridge if you want to have fun.

Posted by: JayAckroyd | February 17, 2006 6:56 AM

For those complaining about readers not reading Cohen's article, you should look at the article he's referring to in the LA Times. (I assume; dead tree columnists don't hyperlink.)

This isn't about Gabriela's aptitude. It's about a critical failure in the US education system to teach artihmetic, and a critical failure to motivate children in elementary school to master basic skills.

Excerpts:

She knew she would face another day of confusion, another day of pretending to follow along. She could hardly do long division, let alone solve for x.

[snip]

Shane Sauby, who worked as an attorney and stockbroker before becoming a teacher, volunteered to teach the students confronting first-year algebra for a second, third or fourth time. He thought he could reach them.

But, Sauby said, many of his students ignored homework, rarely studied for tests and often skipped class.

"I would look at them and say, 'What is your thinking? If you are coming here, why aren't you doing the work or paying attention or making an effort?' " he said. Many would just stare back.

[snip]

George Seidel, devoted a class this fall to reviewing equations with a single variable, such as x -- 1 = 36. It's the type of lesson students were supposed to have mastered in fourth grade.

Only seven of 39 students brought their textbooks. Several had no paper or pencils. One sat for the entire period with his backpack on his shoulders, tapping his desk with a finger.

[snip]

But Gabriela didn't give Seidel much of a chance; she skipped 62 of 93 days that semester.

After dropping out, Gabriela found a $7-an-hour job at a Subway sandwich shop in Encino. She needed little math because the cash register calculated change. But she discovered the cost of not earning a diploma.

"I don't want to be there no more," she said, her eyes watering from raw onions, shortly before she quit to enroll in a training program to become a medical assistant.

Could passing algebra have changed Gabriela's future? Most educators would say yes.

Algebra, they insist, can mean the difference between menial work and high-level careers. High school students can't get into most four-year colleges without it. And the U.S. Department of Education says success in algebra II and other higher-level math is strongly associated with college completion

At some point, people become responsible for their own futures. But that elementary school graduates can't do long division is something that you can't blame the kids for. The failure that shows when a kid can't do algebra (won't even try to learn how to do algebra) has its seeds in allowing kids to not learn basic arithmetic. The algebra bar is where it becomes impossible to cover up that failure any longer.

Posted by: Luthien | February 17, 2006 7:04 AM

Just another example of the dumbing of America. Quest for knowledge: BAD! - Rampant acquisitive materialism, greed, ignorance, and narcissism: GOOD! This mantra is repeated over and over by our culture in so many insidious ways. It is leading us, as a country, over the cliff and into the abyss. Jefferson and the rest of the founding fathers would weep.

Posted by: theAmericanist | February 17, 2006 7:09 AM

Lord, you guys are arrogant.

I'm gonna speak up for Cohen (who, IMNSHO, was ruined as a writer when they gave him another 150 words to work with. When he had only 600 words in his second section column, it was a polished gem.)

"Writing maketh an exact man," seems to have been pretty much what Cohen had in mind.

What's the broad purpose of an education? It's to learn to read, to write, to think and to speak - in that order. Math is only a means to an end, folks: it's not the end itself.

You can argue that it is the most effective means, you can argue it is the essence of thinking: and when you do, you prove Cohen's point.

Cohen writes a newspaper column, on deadline. He found an excellent story about a kid who was evidently UTTERLY failed by her school system -- and half of the posters here announced that they're on the school system's side.

The other half missed Cohen's point. (which says a lot about your own education, that "learn to read" part)

Learning to THINK is the purpose of taking algebra (and, in fact, most high school courses). Clearly, this is not what this kid was getting -- and it's not what the school system demonstrated.

You guys really believe algebra is more important than history? (Yeah? Was it algebra -- or America, that invented citizenship. Explain why only those who can pass algebra can vote.) You find that the capacity to communicate clearly or listen critically is less useful than symbolic reasoning? You think YOUR experience of high school, college, your professions matter more than others? (Perhaps you should get out more.)

Cuz in this post and thread, I've seen more arrogance, more elitism, and more unchallenged ignorance, than in most political/cultural discussions I've been part of.

Generally speaking, algebra doesn't teach skepticism. Mathematics has an abstract quality, a sense that if the facts contradict the theory, it is the facts, not the theory, which is wrong. (Yeah, yeah, yeah -- I know that this turns science on its head, but remember what you're defending by attacking Cohen's column: a kid who flunked a class six times, which means she took it six times, and the school system couldn't find a way to graduate her: that's not an abstraction.)

Math classes, in my experience, are designed and taught by people to whom math comes easily. They're not obviously intended to be useful, and when somebody objects, they get precisely the same arrogant "you're so ignorant" 'tude virtually every post in this thread reeks of.

And -- designed with that attitude, how is American math education working out these days? Got a high standard of high school math skills, do we?

A century ago, basic math classes were entirely focused on practical applications: what's the per bushel price of a rectangular wagon of thus and such a size filled with round bushels of something that costs so much per pound? (I gather kids of a century past knew how much a bushel of ears of corn or potatoes weighed.)

That was Cohen's point. For what this kid is doing, learning to THINK is a helluva lot more important than the abstractions of algebra. That she couldn't graduate is no reflection on her brains, her hard work, or her character -- but the school system's failure is a helluva reflection on its capacity to get it.

And this thread is, on yours.

Posted by: Julie Stahlhut | February 17, 2006 7:22 AM

Among all the subjects I learned in secondary school, algebra may be the one I use most in everyday activities. That's not just because I work in a lab, where I routinely mix reagent solutions in vastly different volumes. I constantly use seat-of-the-pants algebra to estimate volumes of ingredients while cooking, distances and arrival times while driving, and prices while shopping.

Yup, Gabriela can always use a calculator, and there's nothing wrong with that. (I use calculators and spreadsheets all the time in the lab.) I've seen college undergrads, though, who didn't know what to plug in to their calculators to solve simple subtraction problems. As always: Garbage in, garbage out.

Posted by: nathaniel | February 17, 2006 7:30 AM

Algebra is useful and for anyone to say otherwise means that they are not realizing when they use it in everyday life. Yes you will rarely see an equation 3x+4=15 in life, but you will use algebra. How about if 3 people are trying to split a bill? I had a girlfriend once who was trying to following a recipe that called for 3 pounds of beef and we had bought a 5 pound package, she was clueless as to how she could figure out how much to use. What if you have a half a tank of gas, can you make it to your destination?

Algebra also teaches logic skills, but perhaps in a way many people do not expect. Setting up equations comes into play all the time. Even if you have a problem that doesn't relate to numbers, the skills you learned in math can apply. Take all of these parts that don't seem related and then put them together in a manner that allows you to solve the problem.

Posted by: MissPrism | February 17, 2006 7:45 AM

OK, someone has said it now! And I'm going to disagree.

What a country "needs" is a different thing from how many paying jobs there are in a subject. History is vital, and so is algebra.

Posted by: JJB | February 17, 2006 7:52 AM

I don't know if anyone else has pointed this out, but for Cohen to debunk algebra with the following passage proves that he is in dire need of something or someone to clear up his own muddled reasoning (like a good editor):

"Writing is the highest form of reasoning. This is a fact. Algebra is not."

Is that supposed to mean that algebra is not the highest form or reasoning, or that algebra is not a fact?

Before we can reason, we have to learn how to think. It seems Cohen can do neither.

Posted by: JayAckroyd | February 17, 2006 8:04 AM

Americanist--

The reason that algebra is the sticking point is that there's no ambiguity about whether the answers are right. This kid speaks ungrammatically to a journalist for attribution. Dollars to donuts she couldn't locate the Gobi desert on a map, nor write a 600 word essay on deadline.

But the teachers grading her social studies and english exams can give her a passing grade because the evaluation is to some degree subjective. The educational failure isn't merely algebra. Algebra is a marker for failure of an entirely broken education system in her community. Parents are part of that as well--the LAT mentions a son of a Salvadoran immigrant who got through algebra with a tutor.

Cohen's solution--let the kid skip algebra--is the worst sort of treating of a symptom. The LAT article makes it very clear that Gabriela couldn't learn algebra because she didn't have a solid grounding in elementary school arithmetic, and that, apparently, there's no effective remediation.

But I am morally certain she doesn't have a solid grounding in grammar or english literature, either.

Posted by: Jeff Schmidt | February 17, 2006 8:11 AM

Re: theAmericanist

Cohen did find an excellent story, on that at least we can agree. Where I strongly part company with yours, and his, take on this is the direction he took the story. He was given an opportunity, as a communicator, to show us a failing in our education system. He could have examined the circumstances of her six-time failure. He could have offered solutions to her specific problem, and perhaps a general "math is hard" problem that continually plagues education.

But he didn't do that. Instead, he chose to write off an entire body of knowledge as unnecessary -- not just for this poor girl, but for EVERYONE. That's really, really stupid. Powerful stupid.

No one here is denegrating history, literature, music, or any other useful and necessary part of a well-rounded education. Cohen is the arrogant one.

Posted by: Dave S. | February 17, 2006 8:14 AM

Troutnut says:

When I was in high school 7-10 years ago, the people good in math and writing and history were all the same group of nerds who went on to good colleges. I don't remember a single one who did well in math and poorly in other subjects.

Same here, and I went to school 25 years ago.

Perhaps this guy went to Stereotype High.

Posted by: Steve LaBonne | February 17, 2006 8:29 AM

Gabriela, if you learn algebra well you might grow up to be a computer scientist who designs an AI program that can write better columns than Cohen. Not that that's a high standard or anything...

Posted by: MissPrism | February 17, 2006 8:33 AM

Kutsuwamushi, the "useful American education" quote is from Jefferson, not Cohen. I think we can forgive Jefferson being occasionally a little old-fashioned!

Posted by: deb | February 17, 2006 8:36 AM

Shame on you math bigots!
It's all about Gabriella, not the algebra. Unfortunately, Gabriella got the message that since she didn't pass algebra, she is a failure to be ever shunned by the college educated world. Now, that's a great message to give a kid!

The kid tried six times, it didn't take. We don't know why but the reasons could range from inept teaching, lack of ability, lack of effort, or just plain choking because she psyched herself into believing she can never learn algebra.

Sure, everyone should be required to take an algebra class, at least those who fail may know what they don't know, and once in a while, failure is a good teacher.

Perhaps Cohen's position has weak points, but I too see some compassion there.

BTW - most math teachers do not do a great job of showing students what's behind the curtain in math. Teaching to standardized tests will not improve that.

Posted by: Steve LaBonne | February 17, 2006 8:46 AM

It's absolutely true that Cohen's idiocy should in no way distract us from being outraged at the school's failure to help this poor kid.

Posted by: DouglasG | February 17, 2006 8:49 AM

The value of mathematics is very difficult to explain. This is especially true of someone who doesn't get it. Because algebra isn't attempted in most instances in until at least 8th grade, an aura grows around it that it is difficult. So, often what happens is that if someone finds it easy, they believe they have done something wrong and complicates it up. When I was a math teacher, I would see this a lot. So, the last thing mathematics needs is some ignorant blowhard reinforcing the myth that math is hard. It is easy! Everyone does it on a regular basis, but they just don't realize it.

You go to the store, you have $1. How many $.35 candy bars can you buy? That's algebra! You're 60 miles out of town, you're going 70 MPH, you know it'll be less than an hour to get to your destination. Why? You use algebra! You get paid $x a week. $y goes to rent. $z goes to utilities. How much do you have left? Algebra will tell you! This idiot most likely uses algebra EVERY DAY OF HIS LIFE and doesn't even know it.

So, instead of telling someone to perservere -- to keep trying, what does he do? He says it is just fine and dandy to give up. He was a quitter so wouldn't it be great if everyone gave up on things that were hard? Model American citizen that guy!

Posted by: Anonymous | February 17, 2006 8:53 AM

Writing is the highest form of reasoning. This is a fact. Algebra is not.

I'm a mathophobe because it was never seriously taught to me before seventh grade (which meant that I could never become a scientist -- just as well, I guess, as I'd probably be spending more time writing grant proposals than doing research), but guess what? If I was Richard Cohen's major advisor, and he was trying to write an English thesis paper that included that sentence, I would be boxing him about the ears.

I remember as a college student thinking that English thesis papers could be easily cobbled up with reams of Cohenesque bullshit. (My math sucked rocks, but my verbal skills were off the charts and had been since fourth grade, so I pretty much coasted to a B average through grade and high school, and was used to thinking of myself as pretty damned smart.) My advisor brought me up short with a comment to the effect that while my first effort would make a nice Op-Ed in the NYT, it wasn't backed up with FACTS. (And by facts, I don't mean throwing in bogus footnotes at random in the manner of Ann Coulter.)

So Gabriela, guess what? Despite what Mr. Cohen's telling you, you can't just coast on a verbal facility and expect to make a career out of it. The number of jobs open to people who use math is much bigger than the number of jobs where you can, like Cohen, get paid big bucks for making shit up.

Posted by: PaulC | February 17, 2006 8:53 AM

Cohen really is an idiot.

Actually, algebra in the sense of solving for an unknown can come in handy (for budgeting and other kinds of quantitative planning--in high school I was pretty obsessive about calculating minimum grades needed on remaining exams to keep my course average above a certain amount). It is that true for most purposes you're rarely going to get anything beyond a linear equation in one variable, and it's also true that you can actually solve for unknowns by trying lots of possibilities on a spreadsheet. Note, though, that anyone who can make up a spreadsheet is still using symbols to represent undetermined quantities, so without any exposure to the concept of algebra, you won't even get far in using something like Excel.

If Cohen isn't just sleepwalking his way through life, I assume he does some kind of quantitative reasoning--for instance when deciding what kind of house he can afford if nothing else. My suspicion is that people who claim that algebra is difficult and not useful are probably not great quantitative thinkers either. I'm not really sure how people like that make it through life. A series of hunches or feelings about whether something will work out, then a surprise at an occasional disaster or unexpected windfall? Why would you advocate that anyone eschew particular mental tools?

Posted by: Anonymous | February 17, 2006 8:59 AM

What are the objects of an useful American education? Classical knowledge, modern languages, chiefly French, Spanish and Italian

I think it's interesting that he singled out those three languages. All three are members of the Romance family and are quite similar to each other, and while French and Spanish (especially Spanish) can be very useful, Italian isn't exactly on the top of the list of "practical" languages to learn unless you're a fashion designer.

So why learn those three? Learning languages from different families would teach you much more about language, and give you a more well-rounded language education. For example, you could learn Spanish, Japanese, and Arabic.

Or maybe you could choose three languages that would be very useful in the field you're interested in. If you're interested in literature, maybe that would be French, Russian, and Ancient Greek.

It seems to me like he's repeating old-fashioned notions of what a proper education is (after many of the values these notions are based on, at least regarding language, have been discarded by modern scholarship), rather than thinking about what a student would learn the most from or find the most relevant. I dunno, it seems pretty conservative to me.

;)

Yeah. I took German because it's the language of chemists, or was until recently. (Though again, my abysmal math put paid to that career path.)

How bad am I at math and logic? It takes me fifteen minutes to solve a beginner-level sudoku. I admit it, I'm an ape with shoes. :-)

Posted by: Emanuele Oriano | February 17, 2006 9:13 AM

To all the commenters disparaging Italian: keep in mind that the quote was from Jefferson, writing in the late 18th century. At the time, not knowing Italian would have been worse than not knowing French today, as a LOT of fundamental texts of philosophy, history, literature, political science, and so on, were only available in the original Italian. As to science, Galileo Galilei was born less than two centuries before Jefferson.

Italy has always been a laboratory of the Western world; and it should be noted that it continued to be a laboratory throughout the 20th century (e.g., Fascism in politics; countless movements in arts; and right now, a media mogul as Prime Minister and a renewed assault from the Catholic Church against the secular State).
The greater availability of high-quality translations is what makes knowledge of the Italian language less necessary; but a knowledge of Italian thought remains very useful.

Conflict of interest disclosure: I am Italian.

Posted by: crackpot | February 17, 2006 9:20 AM

Studies have shown that music education produces better performance in other academic areas, such as math. The point is, it's hard to say that algebra, or any other subject, doesn't influence your brain in seemingly unrelated areas, but that's the "liberal" arts approach. Can't have our brains all polluted by such liberal concepts as "logic" now, can we?

Posted by: BBOCK | February 17, 2006 9:26 AM

Let me say, I really hate math. I wasn't very good at math in school. I took Algebra, Trig, Geometry, physics, chemistry, etc. And of all of those things, I have used algebra and geometry. And my passing knowledge of biology and chemistry and physics has made watching cooking shows and PBS more informative and educational for me.

But I have to say the most asinine thing this guy said was when he talked about never needing algebra. He's a writer, so maybe he doesn't need it. But if you work in business, you need to understand how to calculate things. If you want to do any computer programming, you need to be able to understand the concept of algebraic order of operations. This moron probably thinks that 2+3x6=30, when anyone who has passed algebra probably knows that it's 20. Why does that matter? A lot of people have to work with Excel for business. You have to enter the formulas according to algebraic order of operations, or you get the wrong results. It's a very common problem. Algebra and Geometry teach a lot of important skills: ability to follow a procedure, the concept of variables and solving a problem with unknowns, the concepts of simplification and cancellation, etc. These concepts can and should be used in everyday life.

The second most asinine thing Mr. Cohen said was that he makes his living from typing. No, he makes his living from writing, albeit poorly. A friend of mine never took a typing course and I can't watch her type because it drives me crazy. It's hunt and peck, whereas I rarely look at my fingers. But she's an excellent writer. And she types pretty well for a hunt and peck typist. Keyboarding skills are not the most important thing about being a writer. Being able to express yourself clearly, and having something worth reading is far more important. Sadly, Mr. Cohen had nothing intelligent to say, and he said it poorly.

Posted by: Dan S. | February 17, 2006 9:29 AM

One specific point - and speaking as a literacy teacher and not a mathematician:

"this whole philosophy of math education that focuses on "math in the real world" . . every single textbook I've seen that uses this approach is an absolute piece of shite. There's a good reason for this -- the interesting thing about math is not its use in the real world, but rather in the way it teaches one to think logically, find patterns, and become comfortable with abstraction."

It shouldn't involve a neglect of the aspects you discuss, but a bridge to them, so that more students cross over, and those who don't get to the other side at least go further, rather than being stuck on the bank, staring at the river . . . Think of every time you were able to move on to a better understanding of something in science (politics, history, etc.) through somebody using a familiar example, etc.

More generally:
Hopefully we can all agree that the article Cohen leeched off of brings up very real and important issues - pedagogical, social, etc. - and his reply, however well intentioned, went way overboard into broadbrush stupidity. Part of the problem is pretty simply - we don't give schools the resources they need and then ask more and more of them.

"Last fall, the school scheduled 17 classes of up to 40 students each for those repeating first-semester algebra . . ."
Great. You take kids who have already failed the subject once and put them into extra-large classes. Yes, that's a formula for success! But smaller classes now - to say nothing of the last 8 years, and extra tutors/resource people, and etc. - that would cost money! (although that's being considered). The article is really quite good - everybody, go and read it.

Given that high school graduation is a practical necessity, do we insist that everyone reach a specific (albeit low) level of proficiency, even though at this point many students realistically are not going into any of the careers mentioned - do we try to give everyone a sort of sub-college prep education? Or do we give up on entire groups, with the predictable crappy consequences (on the individual and collective level)? There are all sorts of creative and innovative ways to attempt that first option - but you can't do it on the cheap.

"

Posted by: nerpzilla | February 17, 2006 9:34 AM

theAmericanist - Actually, the "invention" of citizenship goes back at least to the Greek republics. It is a simple fact that the United States did not invent citizenship.

There are a lot of things the American System did invent (or more accurately, put theory into practice, check out Jean-Jacques Rousseau's Social Contract, for instance), however the citizen was not one of them.

Posted by: DAS | February 17, 2006 9:46 AM

It is true.

Someone making a living spouting (ideally) informed opinions about things political and the like need not use algebra in his/her work. Not directly, at least.

However, in order to understand large numbers, aggregate behaviors and other things about how a mass society works, you need to be comfortable with statistics and statistical inference. In order to have a solid grasp on such things, you need to know some calculus and linear algebra, which require knowledge of good, ol' middle-school algebra.

If our pundit class never did understand algebra, it's no wonder they seem to have so little clue as to how the economy works or doesn't work, how different actions by our leaders will affect the livelihoods of the masses, etc.

Posted by: Dan S. | February 17, 2006 9:48 AM

"Anon: my source for the math is the test which it was required for all high school graduates in Iowa in the 1890s."

I think you just made Anon's point here. High school grad in 1890 (let alone 1870) meant something a bit different from what it does today. That's a major part of the real issue being obscured by Cohen's harmful silliness. In a very simplistic sense - try to get everyone ready for non-selective state school/2 year college, or tracking? But that is really is way too simplistic.

Oh, and what was that study that argued people had trouble detecting nuances - sarcasm and so on - in e-mail, etc.? : )

Posted by: Steve LaBonne | February 17, 2006 9:53 AM

DAS, I'm not sure I agree even with:

"Someone making a living spouting (ideally) informed opinions about things political and the like need not use algebra in his/her work. Not directly, at least."

Innumeracy like Cohen's is a major part of the reason why the press is unable to report in a meaningful way on Bush's disastrous fiscal policy and the steady stream of lies used to "justify" it.

Posted by: minimalist | February 17, 2006 9:56 AM

Not much I can add at this point, except:

If writing is "the highest form of reasoning" and Cohen is such an intellectual ninja, why was he one of the few sentient beings to actually fall for Colin Powell's dog-and-pony show at the UN? He actually took that bullcrap as proof that Iraq had WMDs. Nobody I knew fell for that: not humanities majors, not scientists, not even those dumby dumbhead mathematicians.

Every few weeks Cohen writes something that either bends over backwards to kiss the buttocks of the right wing, or something simply mindbendingly stupid. I find myself agreeing with George Will more often than I do with this supposed "reasoning liberal", because at least Will writes about something he knows about (baseball) from time to time.

I've said it before, I'll say it again: Cohen is either the dumbest human being to ever wangle a spot on the WaPo Op-Ed page, or he gets kickbacks for playing the liberal Uncle Tom for the right-wing elite. Maybe he even gets invited to some of their parties, as long as he wears the gimpsuit.

Posted by: MissPrism | February 17, 2006 10:06 AM

I find it strange that the person banging on about how illiterate we math spods are is the one who resorts most to capital letters for emphasis. Not to mention the incessant LOLing.

Posted by: JY | February 17, 2006 10:11 AM

Americanist-

invent:
"To produce or contrive (something previously unknown) by the use of ingenuity or imagination."

Citizenship was not a concept that was previously unknown at the time of the founding of the USA. The founders of the USA could not, therefore, have invented it. Perhaps they resurrected the notion, but certainly did not invent it.

Furthermore:

citizen:

1. A person owing loyalty to and entitled by birth or naturalization to the protection of a state or nation.
2. A resident of a city or town, especially one entitled to vote and enjoy other privileges there.
3. A civilian.
4. A native, inhabitant, or denizen of a particular place: "We have learned to be citizens of the world, members of the human community" (Franklin D. Roosevelt).

Under these four common definitions of citizen, there were multitudes of citizens extant elsewhere at the time of the founding of the USA.

Posted by: W. Kiernan | February 17, 2006 10:16 AM

See, Gabriela, if you don't know algebra, then it's impossible for you to understand tax rates; and if you work for a living but you don't understand tax rates, why not vote for the nice man in the flight suit? And if you vote for him, then Richard Cohen, who has a considerably fatter income than you probably ever will have, gets another nice fat tax cut at your expense.

Posted by: CCP | February 17, 2006 10:23 AM

So I think we can all agree that algebra is useful knowledge; that it's good to "make" people learn algebra.
Organic Chemistry on the other hand...

Posted by: marky | February 17, 2006 10:30 AM

In case no one has already done so, let me point out yet ANOTHER part of Americanist's
INCREDIBLY STUPID rant which reveals his
STUPEFYING IGNORANCE (do the caps help? thanks). He writes that mathematics can't teach skepticism. I disagree completely.
Speaking as an actual mathematician, not a WaPoo wanker, I can say that a mathematics background has made me immensely more of a skeptic than I would otherwise have become. When you see how simple mathematical arguments can have flaws, even after multiple checking, you get a very strong sense of human fallibility. When it comes to more complex problems in math and science, only in very narrowly defined problems can one make accurate statements.
Without a mathematics background, how does Cohen expect to evaluate supply-side propaganda? I have in mind the infamous Laffer curve. Anyone with a science background would dismiss the use of the Laffer curve as a policy instrument out of hand, but Cohen will have no clue. What about Powell's speech? Again, if you have a math/science background, you really doubt that such a precise description of elements in a photograph can be accurate, for instance.

In the famous Two Culture model, the verbal side has lost---decisively---but they don't know it. Quantitative reasoning is the engine that moves the world today. As a matter of fact, I think that the sloppy thinking of historians, and the faux precision of reasoning in the humaninities, ruins people for participation in public life.
I love history and literature, by the way---I just wouldn't want anyone making or considering policy decisions to rely on a humanities background alone.

Posted by: anonymous | February 17, 2006 10:34 AM

Inadvertently Cohen is making a good point about the lack of recognition and rewards given to people who do the heavy lifting that produces real goods and services in the country. The only recourse that these people have is to make a shitload of money like Gates or the Google founders. Otherwise these nerds do their own thing, living in dark cubicles of corporate America that pays much more to 6 feet blonde male MBAs whose main skills involve populating pre-programmed spreadsheets than to the people who actually design planes and computers and cars and software programs.

On another note, Washington Post should fire Richard Cohen for betraying so much ignorance about what 'reasoning' is.

Posted by: Dan | February 17, 2006 10:36 AM

As a waiter, I often needed to use algebra -- to back out the tax for someone who presented a tax exemption card, for example.

As a restaurant manager, I used algebra in my liquor, food, and staff calculations, estimates, and predictions -- especially in relation to anticipated sales.

As a baseball fan, where statistics rule, algebra has been a great tool in looking at the numbers in new ways.

As a web project manager, algebra helped with cost estimates and resource planning.

As a technical writer, algebra helped me understand what the programmers and developers were doing and translate it to layman's terms.

I've held a wide variety of jobs and interests, and have always found algebra useful.

And I was an English and Philosophy major.

Posted by: Steinn Sigurdsson | February 17, 2006 10:39 AM

Cohen should contemplate how the column reads if "arithmetic" and "algebra" were interchanged with "english" and "history". Then he might not be so smug.
If he can understand the concept. One of these abstractions.

Posted by: Timothy | February 17, 2006 10:41 AM

Siamang, that was the most hilarious retort to Cohen that I've read yet. Brilliant!

Posted by: Dan S. | February 17, 2006 10:47 AM

ahrg, typing too fast . . .

Posted by: Keith G | February 17, 2006 10:50 AM

If you're going to demonize the other side of the argument with vague Nazi references, it's more impressive if you spell it right--it's "�ber alles", or "ueber alles", if you don't want to bother with umlauts

And you actually mean "fluent", not "fluid", but what the hell--just so long as you're making a great living with that awesome humanities training, that's what's really important.

Raven, as far as vague Nazi (tongue-in-cheek) references, I was sarcastically responding to the ad hominen attacks against Cohen I saw up thread.

As far as my lack of German spelling skills, I'll cop to that. Knowing my weakness, I tried to find an online citation:

Im ersten Bereich "Alles ?LIS"

My bad, I guess.

I meant fluid, as in

Marked by facility, especially of expression: easy, effortless, flowing

Seig Heil, baby! :)~

Posted by: Timothy | February 17, 2006 10:54 AM

jkubie,

I think learning basic algebra in high school is not too much to ask. It is a valuable skill no matter your chosen field of work. I think the thing that bugs me the most about Cohen's column is that he uses his national exposure and influence to rail against math, instead of using that influence to call for improved math curricula, teaching standards, improved tutoring options for struggling students, etc. No, just get rid of it all. Don't require it. Nevermind the long-term societal and personal impacts of poor math education.

I think you would have written a far better column, because you at least recognize that things could be improved. Cohen just says to hell with it.

As an atmospheric scientist, I'd love to see more earth science taught in high school. One issue though - earth science is basically applied physics and chemistry, so you gotta know that stuff first. Perhaps the physics and chemistry curricula could be improved, and feature more discussion of things like real-world applications in earth science, etc. But ultimately, the basics have to be taught before specialized instruction can begin.

Posted by: nerpzilla | February 17, 2006 11:00 AM

I'm confused. The Greeks didn't have real citizenship because they had slaves and excluded women. The framers, on the other hand...

Posted by: Kenneth Fair | February 17, 2006 11:04 AM

One further note on the Americanist's assertion about the "invention" of citizenship: He is evidently unfamiliar with the history of Iceland, which operated as a free state without a king from at least 930 CE, the date the Icelandic parliament (the Althing) was formed, until 1262 CE, when it joined the Norwegian kingdom. The system was made up of an alliance of chieftains, but unlike in other feudal systems, the people could decide which chieftain to support.

Posted by: Joe Shelby | February 17, 2006 11:05 AM

Franabanana: I think this girl probably *does* know how to do all of those things and doesn't realize its algebra she's doing. again, a failure of most math classes is to try to teach it too much in the abstract first (rules and derivations) and THEN use the word-problem to try to apply that knowledge. This is even more the case in geometry.

I feel it should go the other way around (as that's how we discovered it in the first place) -- give the problem, the application that needs new knowledge you don't already have, and then show where the new lesson or "rule" answers the question in the way that what you already know doesn't. and last, show the derivation of it (if it applies) to "prove" that it works in all cases, not just the original example.

at least, that's how i'd try teaching for those not mathematically inclined. for those going into a math field, the derivation approach is more important because it forces the student to learn to create new algorithms and rule out logical directions that while accurate, don't go anywhere. this is all essential in applying higher maths to physics, chemistry, and computer science.

Posted by: jbark4 | February 17, 2006 11:19 AM

Cohen's article is definately teh suck, but I'm going to have to stick up for typing class a little.

I don't know how any of you 'hunt and peck'-ers made it through college :)

Posted by: Dan S. | February 17, 2006 11:20 AM

jkubie is pointing us in an interesting direction. Forget about beating a stupid horse - what do y'all think high school science education should look like?

Posted by: Dan S. | February 17, 2006 11:23 AM

"I don't know how any of you 'hunt and peck'-ers made it through college :)"
Very, very slowly.

By my senior year I had managed to evolve a sort of weird half-arsed quasi-touch-typing that was more efficient than plain hunting and pecking, but not by all that much.

Posted by: Charles | February 17, 2006 11:38 AM

I reflected on comments by Walt, Deb, and others that Cohen's response was "compassionate."

I think Walt et al. are wrong and, frankly, blind.

If Cohen had been genuinely compassionate, he would have made his response privately. He makes good money and could afford to hire a tutor for the young lady. No one with the intelligence to pass a history class or an English grammar class is incapable of learning algebra. Many people, including a very bright lady dear to my heart, are emotionally paralyzed by it and they need someone who values them as a human being to show them how to play this game called math.

Cohen is, I believe, not at all compassionate. Having failed at an endeavor, he seems to want others to fail. He is using his position to legitimize failure.

The man is so insubstantial that it's amazing there are even a few people who can't see through him.

Posted by: Torbjorn Larsson | February 17, 2006 12:05 PM

While I'm a bit divided about early algebra studies since they are fairly repetitious, they do indeed help to teach abstract reasoning.

It's somewhat akin to music; either you can do it or not. Music ability or abstract resoning seems to support abilities in other areas.

And both can be fun.

Posted by: PaulC | February 17, 2006 12:15 PM

As someone who disagrees with Cohen (see above) and does find algebra useful on a regular basis, I would have to add one thing. Assuming some people really have some kind of conceptual block that makes it impossible for them to learn mathematics, I don't think that makes them "bad people" any more than being tone deaf, dyslexic, or physically uncoordinated would. Nobody can be expected to be good at everything.

However, I wish such people would stop insisting to me that math is unimportant or useless. You can get by without reading too, but so what? I never learned to play a musical instrument. In retrospect, I wish I had, but I don't go around telling people who did that they wasted their time. Some people get great satisfaction out of playing the pianos. Others enjoy the kinds of problem solving--sometimes useful, sometimes not--that can only be carried out effectively with algebra. These are both worthwhile activities, and kids should be encouraged to pursue them while their minds are young and agile.

Evidence from other industrial countries suggests that more people can be taught math competency than you might assume based on the poor performance of American schools. Thus, relatively few people can really use the excuse that it's too hard for them. Saying that "writing" is a "higher" form of reasoning is just a post hoc rationalization. People of normal intelligence can do both up to a certain level of competence and they have plenty of time to learn how to do both.

Posted by: waltw | February 17, 2006 12:28 PM

There's a myth here that somehow an academic gift is somehow proof of one's elevated status in the cosmos. I have conversations with traditional Calvinists who think this way, as certainly the Algebra Ueber Alles crowd seem to have a similar thought pattern. It really doesn't matter if I agree with an unproveable thesis like this. Maybe you can quantify your essential superiority with statistics showing higher income levels, or a lower incidence of morbidity. Who knows? I wouldn't be surprised, but you guys would still be essentially Republican, mocking those with lesser gifts as somehow deficient. The ugliness of your elitism has a political component, but it is the underlying motivation that betrays your agenda. Preen all you want. Not all people are equally gifted, and the more conscious among us can appreciate that.

Posted by: PaulC | February 17, 2006 12:34 PM

waltw:

There's a myth here that somehow an academic gift is somehow proof of one's elevated status in the cosmos.

Posted by: Steve LaBonne | February 17, 2006 12:37 PM

waltw has it bass-ackwards. The problem with the educational "system" that failed Gabriela is that it suffers from much the same delusion as he, and excuses its failure in terms of "gifts" or lack thereof in the students. Math-phobia is in considerable part an artifact of execrable teaching, just as getting serious about training elementary teachers to teach reading more effectively would result in a remarkable decrease in diagnoses of dyslexia. (I know the residue would not be zero in either case but it would be very meaningfully smaller, resulting in a large number of improved life outcomes.) We know these things can be done better because they are done better in a number of other countries.

Posted by: theAmericanist | February 17, 2006 12:49 PM

LOL -- y'all keep demonstrating what you claim to lament.

Dan asks me: "Are you saying that algebra is useless to her life..." No. (Dunno how you could have read that into what I wrote.) I suppose Cohen was, though I suspect it was intentional hyperbole.

So I am really impressed how few folks posting here can actually READ -- which is why it comes first in the sequence "read, write, think and speak". Reading is a bit more than you guys think it is.

The meaning of "citizen" is a case in point. The word has a precise definition and, used precisely, it does not start with what the citizen owes anybody else -- which is why the bullshit dictionary definition cited above is WRONG, or at least misleading.

But of course, to catch onto that, you have to actually know how to read a dictionary (or generally, several), and then -- guess what? -- to write precisely for the meaning you want to communicate.

LOL -- in fact, it is typical of the mindset that confuses math with thinking (not to mention the kind of dogmatic that typifies liberalism) to cite a dictionary as proof of anything.

It's generally in writing that you confront how bad most dictionaries are, though reading widely can do it too.

Likewise, Nerp isn't so much confused, as refuted and won't admit it: To "produce", the first verb in the definition of "invent" somebody cited, denotes creating an object, not defining a concept. The ancient Greeks, the Vikings in Iceland, these were all essentially TRIBES. There are zillions of examples of tribes, basically extended family, cultural and linguistic groups, which recognized a rough equality.

But -- if you use the term precisely (you math guys have remarkable difficulty with precision), that's not "citizenship". Let's have a show of hands -- is what they have in Saudi Arabia "citizenship"? How about China?

The modern concept of citizenship is an American invention: "all men are created equal...", so that rights are not granted by governments, which are established "to protect those rights, deriving their just powers from the consent of the governed".

That is almost wholly absent from the Greek and Roman concept of citizenship. To the extent it's there at all, the dynamic was precisely the opposite of the American experience: toward less, not more.

Nerp -- being evidently somewhat less literate than he brags of being numerate -- seems to have missed what the American invention of citizenship PRODUCED -- which is why I cited Jordan: unlike every other example, the United States was founded on a universal proposition, which folks came from all over the globe to take us up on: that's the American invention of citizenship.

Very practical, too -- unlike this discussion. But then, you guys are such practical thinkers, having been educated in algebra.

I'll defer to folks who know better, but it seems to me that the approach I saw in the math part of the Iowa high school graduation test from the 1890s made more sense than the problem assigned to 15 year olds cited above -- which, by inference, lots of you guys seem to endorse: an unintelligible abstraction practically calculated to confuse folks. Somebody said it's so hard to communicate how valuable math is?

I got news for you: if you can't explain it to a kid, you probably don't understand it yourself.

Put it this way: you'd teach far more math skills, including algebra and calculus, if every single problem involved real folding money, real coins, the price of gas in the tank, the miles per gallon of the car.

I got a cousin whose paradigm math problem was figuring out the most efficient routes trucks could take, with the variables being the cost of fuel, and how far they could travel between gasing up, empty and full. (An empty truck is cheaper to drive, but you make no money on it. A full truck costs more to drive, but profitable: how much gas is left in the tank when it delivers its load?)

That was practical enough it got him a job buying and selling debt denominated in different currencies (which was profitable enough that he bought his own island).

But what really impresses me is that his math skills were also sufficient to see through the Long Term Capital Management -- a triumph of 'algebra reasoning', that damn near wrecked the global economy.

Posted by: Julie Stahlhut | February 17, 2006 12:51 PM

There's a myth here that somehow an academic gift is somehow proof of one's elevated status in the cosmos.

Maybe someone, somewhere, is saying that, but as I read this thread, the consensus is that an "academic gift" isn't the question. Maybe not everyone has the time, inclination, or academic "giftedness" to get consistent As in advanced math classes, but when an increasing percentage of kids can't manage C minuses in Algebra I within five or six tries, something is systemically wrong with the educational environment.

Primary and secondary education shouldn't be selecting for "elites" -- they should be equalizers in the sense of optimizing everyone's future opportunities (rather than "equalizers" in the sense of "a race to the bottom"). Someone who drops out of high school to work in a fast-food place is hardly having her opportunities optimized. And it's not the cosmos that are doing this to her.

Posted by: Linnaeus | February 17, 2006 1:07 PM

Most people here have said enough of what needs to be said, but I'll throw in my two cents anyway.

I understand what Cohen was trying to do, but I don't agree with how he did it. I struggled mightily through mathematics, but I recognize its value - in both the abstract and concrete senses - and Cohen's apparent dismissal of algebra was poorly worded, to put it mildly.

This comment, I thought, was particularly astute:

Part of that failure is that math is often mis-used in schools as a way to filter students, so that students who fail at it acquire a visceral hatred for the subject, not so much because of its content as because of the way it has been used to tell them they're dumb.

Agreed. My personal experience with math instruction involved a lot of people, both teachers and fellow students, who simply had no time for me when I didn't "get" the concepts as quickly as they did. I think the cultural authority of science and mathematics implies, in the minds of some, that if they don't perform well at such subjects, they're simply not smart people.

Because of Cohen's myopia, you get responses like this:

In the famous Two Culture model, the verbal side has lost---decisively---but they don't know it. Quantitative reasoning is the engine that moves the world today. As a matter of fact, I think that the sloppy thinking of historians, and the faux precision of reasoning in the humaninities, ruins people for participation in public life. I love history and literature, by the way---I just wouldn't want anyone making or considering policy decisions to rely on a humanities background alone.

I understand what the commenter is getting at, but I think this is a false dichotomy. The "two cultures" concept is about bringing together forms of knowledge, not about creating intellectutal hierarchies. The idea was to argue for the inclusion of science in a general intellectual culture, and Snow was critical of those who dismiss such inclusion. It's not about who wins and who loses.

Perhaps, because I'm an historian, that one irked me a little. No, policy decisions shouldn't rely on one kind of intellectual background exclusively, but I don't know of anyone who actually argues for that. I certainly wouldn't agree with that approach.

In teaching history, I often see sentiments similar to what Cohen suggests with respect to math: "Gee, I'm not going to use this," "This isn't like science or math, where you know the answer and it doesn't change, etc." While it's true that the epistemology of my field has a subjectivity to it that wouldn't be appropriate in the sciences, that's because the questions I deal with are of a different nature and can't be answered (purely) scientifically.

I do agree with the general sentiment voiced here. Cohen had an opportunity, and he dropped the ball in an embarrassing fashion.

Posted by: Steve LaBonne | February 17, 2006 1:15 PM

Do I really need to point out that compounding is, yes, an ALGEBRAIC concept??

Posted by: anotheranon | February 17, 2006 1:29 PM

nerpzilla: you mean our framers didn't have black slaves who weren't citizens?

the longest currently existing, uninterrupted democracy, with citizens, is Switzerland. it's been continual since the 1300's. they didn't always allow women to vote but they didn't have slaves, either.

Posted by: PaulC | February 17, 2006 1:38 PM

I understand the need for knowing geometry, and I thank good fortune almost every day that I took 4 quarters of Statistics in college, but I have never understood the value of Algebra.

This is also the key idea that Fibonacci (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html) transferred to Europe from the Arab world that in no small way fueled later advances in Western science.

I suspect what you're saying is that the algebra you learned is so second nature that you didn't even notice you were using it when you studied statistics. Sadly, someone who did not absorb introductory algebra would be ill-prepared to learn any later math that involves formulas more complex than a few basic arithmetic operations.

I agree that learning particular algebraic techniques--e.g. completing the square to solve quadratic equations, or applying the quadratic formula--may turn out not to have direct applications for many people later in their lives. But the basic principle that you can represent relationships between unknown quantities symbolically has such a wide range of applications that trying to do without it is effectively going to cut you off from progressing in any area requiring quantitative analysis.

Posted by: dAVE | February 17, 2006 1:47 PM

things I use math for(not related to my job):

mixing drinks
cooking
mixing cleaning solutions
figuring out how much lumber/flooring/etc. I need to buy.

--

There was a customer where I work (a tile store). He has been asking for a week about getting an additional 800 square feet of a tile from Spain. I started getting freight rates, etc. Anyway, today he says he actually needs 1550 square feet!
Furthermore, this whole thing started because he miscalculated the first time and didn't buy enough to begin with. So, do you need math? YUP!

Posted by: P J Evans | February 17, 2006 1:52 PM

Flunked algebra six times? Did anyone stop to think, somewhere before that point, that she might not have any math skills beyond '1+1=2'? I suspect that Gabriela was simply passed on through many of her elementary school math (and probably other) classes, because it was too much trouble for the schools to provide the help she needed. (Add that the LA schools have been dysfunctional in many ways for many years.) (Yes, I have seen this sort of thing. My nephew had bad math teaching in elementary and high school, and had real trouble with basic math in college, when he had to pass a required class.)

Posted by: Alexey Merz | February 17, 2006 2:07 PM

Colin,

one of my most mathematically literate friends was taught new math in the early 70s, by teachers who, apparently, actually understood it. He loved it, too. My teachers did not understand it, and I disliked it rather intensely; luckily for me, my electrical engineer dad spent a lot of time re-correcting my exercises. I think that many teaching methods can work, but that if the teacher does not understand what is being taught, all is lost.

Posted by: marky | February 17, 2006 2:24 PM

Linnaeus,
since I'm a math type, I have trouble reading sometimes, but it didn't seem to me that you disagreed with my observation about quantitative reasoning trumping "literary" reasoning.
By the way, I think the Snow divide is inaccurate; I think the proper distinction is between numerate and innumerate people---Cohen being self-identified as part of the latter group.

I have a challenge for Cohen and his defenders: Do they think that those who formulate public policy in economics, the sciences, environmental policy, etc., need know no algebra?

Posted by: Dianne | February 17, 2006 2:25 PM

"As such, it would have worked just as well if my calculus class had been taught in French."

Is it completely wrong and elitist of me that my first thought was "Cool! I wish my calculus class had been taught in French." In my case, it would have made French, which bored me to tears, more interesting.

I'm also tempted to add a joke here about the dread al-Gebra terrorist cell and its instruments of math instruction, but I'll refrain. Someone else has probably already done it.

Really, anyone with a normal or higher IQ and no learning disabilities can learn basic algebra if they are taught it reasonably well and haven't been completely convinced by the propoganda that they can't and never will be able to learn it. Why didn't someone get this poor child help after she failed algebra for, say, the second time. A person who failed once might be able to make it if they wake up and concentrate. A person who has failed it twice clearly needs more help. That doesn't mean that she can't learn it, only that she needs more help than she is likely to get by sitting in a class listening to a teacher give the same lecture she failed to comprehend five times before.

Posted by: RavenT | February 17, 2006 2:30 PM

no idea what you're talking about, PZ; I'm a total pussycat :).

Posted by: MissPrism | February 17, 2006 2:37 PM

About the al-Gebra terrorist cell: the word is indeed Persian in origin, and comes from a book by al-Khwarizmi (whose name became "algorithm").

Posted by: mothworm | February 17, 2006 2:44 PM

I don't like the use of standardized tests as an excuse. The state graduation tests and other state proficiency tests, with no exceptions that I'm aware of, are pitched at a very minimal level of competence. A school that cannot bring most of its students to even that level is a bad school, and shooting the messenger won't improve it.

I don't know that it's the level of knowledge required that is the problem, but that "will this be on the test" is the only criteria for what is taught in the classroom. We're teaching the kids to pass a test, but not to integrate knowledge.

Posted by: TexasLib | February 17, 2006 2:50 PM

I looked up the original article. The girl dropped out of school and went to work at a Subway making $7 an hour. It takes a lot of persistence to try a class over and over and over again, 7 times, but eventually it just beat her down.

My mother had a similar time with math. Algebra wasn't a requirement when she graduated, and math was the only class in High School that she made under an A, at a time when grading standards were a lot tougher. She had one required math class in college, trigonometry, which took her 3 times to pass, and she admits she only passed it because her teacher went easy on her after she swallowed her pride and begged. She passed with a D, the only time as an undergraduate she made a grade less than an A. She spent 45 years teaching English at high schools and could probably say she never used algebra or trig as an adult. Is there anyway American society would have been better off if she'd been forced to drop out of high school and go to work making minimum wage the rest of her life?

I'm mom's opposite. I ended up with a master's in math and though I'm not in a math-related job, I still use algebra frequently. I use trig all the time when I'm woodworking in my garage. But I also taught and tutored a lot of people as a grad student that just didn't have that something, whatever it is, that lets them grasp what seems like totally basic math. A lot of them probably ended up dropping out of college. There were other grad assistants that *BRAGGED* about how their Fail/Drop rate was over 85%, for freshman-level classes. People that might have made perfectly good English or History teachers, or journalists or translators or a gazillion other fields that need a good education but not a single ounce of math skill... do we benefit from forcing them to go work at Wal-mart or McDonald's?

You look at Cohen's article and it's clear he has some compassion for people like that, unlike a majority of posters here.

Posted by: deb | February 17, 2006 3:03 PM

----- I'm a little fed up with my attitude being called elitist----

Well sure, 'elitist' hurts and it's very phony - but it seems to be working as a tactic. It must resonate with somebody. The right is nothing if not expert on taking a message that benefits their purposes and staying on it, and they are getting pretty good mileage.

In this blog, 'algebra' became a metaphor for the value of learning. I am just saying, if you want to argue the value of learning, do it from a position that is to your advantage.

It's more than a little geeky to list and illustrate all the ways algebra and math are used or useful, that's a given and it is operating on Cohen's level. You leave yourself wide open to the elitist charge going at it that way. These days, any word over three syllables long is 'elitist', and math is deep into 'elitist' territory.

Years ago I was an high school Industrial Arts teacher. Many of my students took the classes due to genuine interest. But many were there because such a class was the only way they would accumulate elective credits. It wasn't unusual to have students who could not read and comprehend a textbook written at a low seventh grade level, eventhough it had plenty of pictures and diagrams.

I could have made the courses too difficult for many to pass, but what would that do for someone who can't even read? Their math skills were also nonexistent.

Posted by: Kristine | February 17, 2006 3:15 PM

TexasLib, I struggled, too. I stayed after Chemistry class all the time to work the mathematics with Mr. Erpelding at the board. (Mr. Erpelding will forever be in my fond memories for going to my family's church but forbidding any "Goddidits" in his class--"Even if God takes my class and raises His hand and says, 'Organic compounds form because I did it,' He'll get an F from me!") I loved proofs and hated actual problems; I tried and I tried, and I still can't master calculus--but I'm determined. I bought that humiliating Calculus for Dummies book, and then realized what I need was also the Trig for Dummies, too. Not an ego-booster at my age.

I really think that Gabriela should have gone back and admitted that she had never mastered arithmetic first, as that is obviously her issue if she can't even make change at her Subway job without the digital cash register. Considering that she also employs double negatives ("I don't want to be there no more,"), she has a real problem, and it's not algebra class. Richard Cohen is not showing anyone any compassion--he is bestowing a benediction to failure.

Posted by: shaker | February 17, 2006 3:31 PM

he's right that claiming that math "teaches logic" is a pretty bogus argument....
Take a math course if you want to obtain a useful tool for doing science and engineering.

Have you ever taken a course in pure maths? Mathematics used to be viewed as just a "tool" for science. But that has changed since Gauss, Hilbert, et al in the 19th century. Now mathematicians do maths for its own sake. Even the most abstract of maths have been put to practical use, however that is not why mathematicians study them. You can't do mathematics without logic. The most famous logicians Frege, Russell, Godel, Tarski and others were mathematicians. Their very important contributions to logic would be impossible without their deep understanding of mathematics.

If you want to learn logic, take a logic course -- you can find them in any philosophy department.

Last semester I took a course in symbolic logic. Guess which department ran the course. Mathematics. That's right! The philosophy majors also have to take the same course and it was taught by a mathematician.

Posted by: Kagehi | February 17, 2006 3:36 PM

Ack.. Stupid thing ate my equation..

c = c + abs(a > b) - abs(a

Posted by: G Johnson | February 17, 2006 3:42 PM

Kid, beware of any geezer who says, "I didn't need that, so you don't either." And beware of geezers who say, "we've always done it this way." They're both geezers!

Got trouble with algebra? The most frequent cause for trouble with algebra is trouble before algebra. Some people never got basic arithmetic: "the times tables" or more typically, fractions. When you can correctly answer, "what is 9/16 + 3/4?" you are going to be successful in algebra! Yay! Kids, parents, schools, and teachers are often too proud and too pressured to go back.

The second most common roadblock in math comes from not knowing how to read and write. The Cohen geezer is right in that reading and writing are first. He is wrong in thinking that reading and writing are last.

Breasts!

Height!

Abstract ability!

Different folks develop these at different rates. The third most common root of algebra struggle is ability to handle abstractions like variables and rate. If a teacher and kids are patient, most will be rewarded by seeing the lights come on in a year or two. In my experience, when that growth comes most who were behind catch up quickly and go on ahead. Unfortunately, some teachers can't tell what your issues really are. So kids think, "I'm never gonna get math" Wrong! Or they think, "I'd rather look like a slacker than dumb-bone." Wrong!

Algebra is everywhere. It is in compound interest and gasoline prices and your every meal. Real-life problems can be hard to describe and understand. They wouldn't be problems otherwise! Hence, school problems are often introduced as stick-figures "ax+b" or in ho-hum hokey scenarios: "a train left the station".

Mathematics will not teach thinking any more than any other subject can. If you practice, mathematics can build discernment for structure, accuracy, reliable methods, and checking results.

I am a geezer that has spent a lot of years helping people struggling with math. These are the three most common roots of math frustration I have seen. Blaming yourself or society won't help. Hunt around for someone who can help you understand what the root of your struggle is, and fix it. I wish you well.

Posted by: RavenT | February 17, 2006 3:57 PM

"as Raven will doubtless attest"

Huh?

"suck, Mr. Cohen"

Sorry--for some reason, I was off daydreaming about Leonard Cohen.

Anyway. Back to theAmericanist's point.

You guys have all tried Cohen's product: that's what he's selling.

And if his goal was to get me never again to waste money on the WaPo or time and brain cells on his uninformed elitist-arrogance-disguised-as-pseudo-leftist blatherings, Mission Accomplished(TM)! Heckuva job, Richie.

Posted by: MYOB | February 17, 2006 4:07 PM

I wouldn't be surprised if we don't see efforts by the likes of Cohen to question why we need public education at all. In his universe everyone has money and jobs, and can pay for private education without having to leach it like democrats from the hard working taxpayers.
Even if secular schools rise to meet the needs of private education the religious schools will always have higher enrollment numbers and will be able to teach flat earth, creation, geocentrism, holocaust revisionism, slavery glorification, and eventually that Jesus loved tax cuts.

MYOB'
.

Posted by: shaker | February 17, 2006 4:13 PM

Shame on you math bigots!
It's all about Gabriella, not the algebra. Unfortunately, Gabriella got the message that since she didn't pass algebra, she is a failure to be ever shunned by the college educated world. Now, that's a great message to give a kid!

No one here is saying anything against the kid. People are critisizing Cohen, not Gabriella. What we are saying is that he is not helping her or kids like her by his arguments. Instead of saying that maths or some other subject is useless it would be more helpful to try and find out the reasons why kids find maths hard. It may very well be that because people like Cohen say that maths is hard and useless kids take that attitude as well. I nearly failed maths in 8th grade due to bad teaching. Through out high school I thought maths was hard (but usefull). I managed to improve my grades in maths. When I went to uni I had to take maths as part of my studies. One of the professors was very good at teaching and was encouraging, and I found out through him that real mathematics is very different to what I thought it was. From then on I got hooked. I love mathematics now and take time to learn on my own. However I am not a mathematician.

So my own experience tells me that instead of telling the kid that "math is useless", he should have tried to find out why she failed and what can be done to help kids like that. So the bigots here are actually Cohen and those who support his views.

Posted by: Hannah | February 17, 2006 4:36 PM

Okay, why is everyone going on about the school system's failure to help "the poor girl", or how hard she must have tried to pass? According to the LAT article Cohen's working from

"Gabriela didn't give Seidel much of a chance; she skipped 62 of 93 days that semester."

If she can't even show up to class enough to legitimately fail, she has no one to blame but herself.

Posted by: shaker | February 17, 2006 4:44 PM

At John F. Kennedy International Airport today, a Caucasian male (later discovered to be a high school mathematics teacher) was arrested trying to board a flight while in possession of a compass, a protractor and a graphical calculator.
According to law enforcement officials, he is believed to have ties to the Al-Gebra network. He will be charged with carrying weapons of math instruction.

Posted by: Rick @ shrimp and grits | February 17, 2006 4:54 PM

If she can't even show up to class enough to legitimately fail, she has no one to blame but herself.

The reason people are going off on the school system is that it seems to have signed her up for this same class six times in a row when it's obvious that she had other problems that needed to be addressed. (Lack of basic english and arithmetic skills, judging by the article - not the Cohen op-ed. She could even have had a learning disability of some kind, but I'd leave that to a school psychologist to determine.)

But you're right - if her main problem with passing classes at school was not showing up for them in the first place, then it's not right to shed too many tears for her.

Posted by: theAmericanist | February 17, 2006 5:21 PM

Demonstrating once more the difficulty of mathletes to handle precise wording, Nerp complains about me: "he seems to ignore that there was slavery until 1863, women couldn't vote until 1920, and full civil rights were not guaranteed by federal law until 1968."

Um, no. On the contrary, if you didn't confuse what you do with my posts as 'reading', you'd know that I was BRAGGING about these achievements -- as proof that this American citizenship invention actually worked, where the other examples cited as precedents, all failed.

That whole 'reach exceeds grasp' thing.

The Founders began with the Declaration, which said two Revolutionary things: 1) we're all born with rights, so governments don't grant 'em, and 2) the purpose of government is to protect those rights.

Joe Ellis' take on this makes sense: the Constitution, the other Founding document, promptly contradicted the proposition. Without the proposition, we wouldn't have had a Revolution.

Without the contradiction, we wouldn't have had a country.

That is the dynamic, centered on citizenship as the Founders invented it, which MADE us America -- as a process, not some bullshit historical 'gee, what about the Swiss? How 'bout them Athenians?" crap.

The Founders proposed that in this country, we'd ALL be equal -- and they invited, expected, that people would come here to take them up on it. (You cannot name any other nation on earth, much less any of the precedents cited, which was founded on a similar proposition: American citizenship.)

It is certainly true that until the 14th amendment, there was no such thing as an effective NATIONAL citizenship. The Trail of Tears cases (the precedent for Dred Scott) held that while Cherokee, Choctaw and Creek might be by treaty citizens of the United States, that did not mean they were citizens of Alabama or Georgia -- which could, accordingly, dissolve their property rights.

But, as it happens, even that atrocity was based on the Revolutionary fact that the Scots-Irish could show up in Alabama and Georgia and BECOME citizens.

Don't underestimate the significance of the Germans, either, starting even with the Hessians in the Revolution, but particularly those Lincoln recruited into the Union Army, whose passion for American CITIZENSHIP was absolutely vital to abolition.

Kindly show us any similar application of that concept of citizenship, before the Americans invented it.

Nerp wants to argue that Greek and Roman citizenship was incomplete, and so was the actuality of freedom at our Founding -- but this demonstrates that Nerp really does have trouble with this 'reading' thing. Perhaps if I made it an equation: (Greek and Roman +time) = failure

BTW -- just for fun: many people misunderstand the relationship between women's suffrage, the 14th and 15th amendments, and Jim Crow. Before and during the Civil War, abolitionists and suffragettes made common cause, naturally: both blacks and women should be free, and able to vote.

But the war and the aftermath was hard, so the momentum that passed the 13th amendment slowed when it got to the 14th (which damned near DIDN't pass, and two states tried to withdraw their approval), and all but vanished with the 15th -- so Frederick Douglass, among others, simply ditched the women: the 15th, originally conceived to provide voting rights for BOTH freed slaves and women, applied only to men.

Susan B. Anthony was pissed.

So she brought a lawsuit under the 14th amendment, arguing that "all persons born" would naturally mean women, and therefore that -- under the 14th, if not the 15th -- women should be allowed to vote.

The Supremes looked at this, couldn't figure out how to refute it, and simply said: Um, voting is up to the states.

Which is how we got Jim Crow.

Reality is a lot messier (and more interesting) than algebra to me -- but that's personal taste.

I only posted in this thread because it truly amazed me how many folks seemed to utterly miss the point: math is simply a tool to teach you how to think, and it's particularly useful to solve certain kinds of problems, like making change.

But it isn't thinking itself.

Posted by: DOF | February 17, 2006 5:43 PM

Doh! It is possible to misread my comment - for clarity change "avoiding big trouble" by not avoiding (math) problems. Guess I need to work on my writing ;-)

Posted by: Anonymous | February 17, 2006 5:54 PM

I only posted in this thread because it truly amazed me how many folks seemed to utterly miss the point: math is simply a tool to teach you how to think, and it's particularly useful to solve certain kinds of problems, like making change.

But it isn't thinking itself.

No one was making the claim that math itself is thinking. Demonstrating once more the difficulty of *mathphobes* to handle precise wording

I was BRAGGING about these achievements -- as proof that this American citizenship invention actually worked, where the other examples cited as precedents, all failed.
What is there to brag about when you were keeping slaves while most of the rest of world had already abolished slavery?

Posted by: managal | February 17, 2006 6:23 PM

Hannah:

If she can't even show up to class enough to legitimately fail, she has no one to blame but herself.

Isn't the real question how many times she went to class the first time around? (Or, if she skipped often the first time, did most of the skipping happen after failing the first test?) There's no way to know, but I think that most people find it a lot more difficult to persevere after repeated failures, and the more failures there are, the harder it gets.

Posted by: AndyS | February 17, 2006 6:46 PM

Joe Shelby makes one of the few reasonable comments to this sad post by PZ and the comments that follow. Shelby says: ...Cohen is wrong, yes, but the real failure was on the school system itself for not taking care of this person 5 semesters ago.

Cohen may have made his argument poorly but he was exactly right in saying that mastering algebra has nothing to do with leading a good, productive, intelligent life. The notion that everyone must pass algebra to get a high school diploma is as assinine as the notion that the "one size fits all" diploma itself.

Allowing (perhaps encouraging) this woman to take the same class six times is the educational equivalent to that poor kid who was beaten to death in a boot camp for juvenal offenders recently. Where is the condemnation of the system that does that?

(I have a minor in math and scored 100% on the math portion of the GRE. My comment doesn't come from sour grapes. It's just that I don't worship mathematics or see it as critical for everyone living in a modern society.)

Posted by: Joe Shelby | February 17, 2006 7:13 PM

AndyS: Actually, I do support the idea that high school degrees should be raising their requirements, or offering different graduation levels that colleges and/or recruiters can use to quickly recognize what kind of a candidate they're looking at. Virginia has had scaled graduate diplomas for years, one that recognizes high academic ability (3 years of math algebra 1 and above, 3 years science, 3 years social studies/history), one for a general "i got through it, didn't I?" level (2 years math, 2 years science w/out maths, 2 years social studies).

So it defines a minimum for the college-bound, and a minimum for the "straight to work" types.

I respect the desire that minimum requirements for graduating should be raised, but as I wrote, the approach taken ("raise the minimum, let them bums fail") was assinine. You change the standards by changing how you approach teaching them while they're young, then when you have the studies to show that the changes made in elementary school are actually working, you raise the standards at the high school level *for that elementary school class* when they get there.

It can be done. Private schools have been improving their standards that way for decades.

Posted by: marcia | February 17, 2006 7:31 PM

Richard Cohen's email page
(I sent him a link to this P.Z page

http://projects.washingtonpost.com/staff/email/richard+cohen/

the WashPost letters to the editor:
letters@washpost.com

Posted by: marky | February 17, 2006 8:08 PM

Darkrose,
I don't think I disagree with any of your points, which I have now read thanks to Linnaeus's recommendation.

Posted by: wolfa | February 17, 2006 8:32 PM

She can't do basic algebra, and she's going to be a medical assistant? That is terrifying—remind me not to ever get sick anywhere near LA.

That's unfair, PZ. Perhaps now she that she has a goal (something better than a minimum wage job), she'll be willing to push herself enough to learn the necessary math to do it, because she knows not learning it is harder and sucks more than learning. Yes, the story makes it seem like otherwise -- but you know, it's an article, not a perfect description of reality. But high school fuckup does not necessarily mean permanent forever fuckup.

Posted by: Rick @ shrimp and grits | February 17, 2006 8:46 PM

PZ, a medical assistant's not going to be doing any drug calculations - so don't worry about the lack of algebra knowledge. A medical assistant might take your urine sample from one place to another, or maybe take your blood pressure or temperature and write it down. Or do some of the office work at your physician's office, etc.

(The community college I work for offers a medical assisting certificate, and my wife happens to teach their required human anatomy/physiology course.)

I will say this, though. Just because she signs up to get a certificate doesn't mean she'll get one. Unless she's a more serious person than she was in high school, she'll probably bomb out of the basic anatomy/physiology course. Personally, if I were taking that course I'd cosnider it harder than Algebra I, and a lot more work.

Posted by: Christian | February 17, 2006 9:01 PM

Okay, there have been a lot of posts on this one, so what the heck, here is my two cents.

For everyone who is saying to back off of Cohen because maybe Gabriella simply wasn't good at math: I call bullshit.

There is no substantiation that she truly had a learning disability. Her last semester she skipped almost two thirds of her classes for that subject. That is a definite recipe for failure in itself, and without knowing if her previous attempts at the class contained the same attendance rate, we cannot just say that "Oh dear, she has a learning disability". She could have simply blown off attending her previous classes in that subject to the same degree that she blew off her last attempt.

I am sorry, but in my high school, you had to have algebra, geometry, and pre-calc. If you had a knack for math, you ended up taking calc. Of course, my algebra teacher was one of the Christian Brothers, who also happened to be an ex-golden gloves boxer. You paid attention in class, did your homework, or else. I am sorry, many may consider me privileged for having gone to a parochial school, but damnit, many teenagers really almost need to get the schoolwork beaten into them.

Ok, that was probably a bit over the top, but public schools (not colleges) do not seem to enforce the rule that you must respect your teacher. Of course, public schools cannot always afford the same quality of teacher as the private schools. But, if the teachers were allowed to maintain some sort of discipline in their classrooms, it might get a little better. In the original LA Times story, one of the teachers talked about a student who came to class, never took off his back pack, and simply drummed on his desk until class was over. In my school, if a student attempted that, the teacher would remove the backpack for him. In a public school, a teacher who did that would be subject to firing and prosecution for assualt. It seems that respecting a students rights has gone too far. Obviously, beating a student to a pulp is not right either, but it seems that public school teachers have no real authority to discipline their classes.

This removal of a teachers authority doesn't simply come from the school district. It comes from the parents who send their kids to school, and the IDiots who elect the school boards. "You don't have the right to spank my kid" is the message that the parents send to the elected officials who run the schools. To keep their office, they comply. The problem is, as a parent, if you abdicate your responsibility to discipline your child, and then refuse to let a teacher discipline your child, what right do you have to complain when all little Johnny does for a living is flip burgers or ask "Would you like fries with that?".

In my high school, we had a PARENT orientation. The gist of it was this:

1. We have a tradition of acedemic excellence for more than a hundred years.

2. We believe that students are here to learn. We also understand that they are teenagers who need a structured learning environment that focuses on acedemics and in teaching students to be contributing members of society, both in their professions and in their private lives.

3. We believe in corporeal punishment. If your child does not respect his teacher, his classmates, and himself we will not hesitate to discipline him. If you do not like this, please remove your child from school, we do have a waiting list.

In my four years at the Brothers, I never saw a child get "spanked" who did not openly communicate to the teacher "This class is boring, so I don't have to pay attention and you can't do anything about it".

Enough on that particular soapbox.

Now, for the next soapbox.

Mr Cohen states that Gabriella will never have reason to use algebra in her "real life" since computers do it all for you these days. We see what Gabriella's "real life" has so far turned out to be: chopping onions at the local Subway. Yes, she is planning to go back and become a medical assistant, but guess what, the logic process that algebra helps to teach will become quite necessary in her endeavor to become a medical assistant. And that isn't the only career path that will require her to understand the underlying concepts of algebra.

This may be a wake up call to our currenct "service business" society, but in any business setting that requires at least a modicum of analysis, you must be able to solve for X. Period. You might have to solve for X and....wait for it.....Y as well. If you cannot convert raw data into some sort of trend and build a simple mathematical model to complete that trend, you are pretty much doomed to answering phones in a call center, or going back to Subway.

Not everyone can be a great writer, and get lucky enough to get a salary paid for spouting of bullshit in a newspaper. For the rest of us, basic math skills are a necessity.

Okay, enough for now, I am so incensed at Cohen's attitude, I am losing my formerly coherent train of thought. There is so much crap in his opinion, that the number of reasons that he is wrong is daunting to sort through.

Posted by: Christian | February 17, 2006 10:15 PM

Leonidas,

To quote you:

"All of these comments are so typical of the mindless number worshipping that the left engages in reflexively. Numbers mean nothing if they can't be interpretted. Knowledge means nothing without faith to guide it. Cohen is right. Why do we need to be able to crunch numbers? There are plenty of Asian people who are more than capable. But they lack our passion, our wisdom, our soul. Isn't that what we should be teaching our children?"

I am afraid that is an asinine, and bordering on racist comment.

My wife is Chinese, so setting some asians loose to "crunch numbers" ignores the reality of our economic situation.

We are no longer the innovator who brings new products manufactured at home into the world. Thus, our balance of trade shifts away from the US. Why is that, because we don't have people who are bright enough to even be on a manfuacturing line of that level. Additionally, many of the advances in products were created by foreign nationals, we simply licensed the product from them. Who is to say when another government will decide to ignore the international laws regarding IP and manufacture the ideas that we own the license to, but one of their nationals created? China is an excellent case in point, since the technology is invented elsewhere, but they have people with the brains who get paid cheaply enough to produce the product we buy.

And how dare you say that asians lack passion, wisdom, and soul. Having climbed a Chinese sacred mountain (or two), and seeing the steps carved into the side of the mountain, and carvings dating back before Europes Dark Ages, and the passion that went into that construction, your counterfeit passion is amusing.

As far as wisdom in the public arena, for centuries before the Europeans got around to it, China's public servants were tested for their abilities, as opposed to Europes version of "you were born into the right family, so you must be able to rule" stupidity.

Granted, China's emperors came into their power by birth, but as soon as they went away from an administration composed of independantly tested individuals, they lost their rule.

As far as soul, you cannot say that they do not have a soul either. From your post, I assume that you are a Christian, so therefore, in your limited worldview, they must have a soul. In terms of art,they have plenty of homegrown artistry, from either stone carving, painting, all the way through pop music (although I must admit, I don't like pop music in general, not enough "soul". Give me Husker Du anyday over Britney Spears). If artistry is an example of soul, you are ingnoring a few billion souls worth.

So, what are we teaching our children in public school? How to foist off your personal responsibility by saying "Society abandoned me?"

Go away small man.

Posted by: marky | February 18, 2006 12:10 AM

I think the probability that Leonidas was posting tongue-in-cheek is approximately .873

By the way, I didn't see any discussion of a two-track, European-style system, although I haven't read all the posts.

Posted by: Alon Levy | February 18, 2006 3:23 AM

I've got to call BS on that one. Does anyone here remember people in high school who were good at math but couldn't write?

I sort of was one. My grades in the humanities in middle school were fairly low, though it was more because of lack of effort than because of lack of aptitude. In math I got A's without trying; in English, I didn't.

By the way, Walt, the ancient discipline of algegra isn't advanced mathematics. That's a myth pushed by people phobic of math. It's a step above the rudamentary skill known as "arithmetic".

On the contrary, algebra is a very advanced discipline, one that is usually not taught until the 2nd or 3rd year of college. Solving linear and quadratic equations is not algebra, but arithmetic. Algebra starts at things like proving that there are no solutions in integers to a^2 - 7b^2 = 3. Latter-day algebra's main efforts involve a huge theorem I can't even begin to describe, let alone state precisely (look up "Langlands program").

I feel that the same argument could be made about any class in high school. I don't use history in my everyday life, why not get rid of it? English? Nothing in my profession requires analysis of symbolism in literature, so why bother there? And on and on.

You can extend the argument to every class, but not at the same time. It's common in many educational systems to let you choose which subjects to take in high school with few restrictions. In Britain you take 3-4 subjects in grades 11 and 12, any indeed many take only science and math subjects, or only arts and humanities ones. Though granted, 9th grade math in Britain is roughly equivalent to 12th grade math in the US, and anyway there's talk of changing this system on the grounds that it's too narrow.

May be for girls (and boys) like Gabriella they should have a course in logic (to substitute for Algebra), where they learn and apply the basic rules of deduction. Of course this has to be done using words rather than symbolic logic.

Actually, it sounds like a really good idea. On top of it, it's likely that teaching elementary logic will help students understand arithmetic and geometry better, much like how learning a constructed gateway language like Esperanto or Interlingua helps students learn natural European languages better.

Try Chinese, Arabic, any number of South Asian/Southeastern Asian languages.

It's not "any number of South Asian/Southeasten Asian languages." It's "Hindi and possibly Malay." Right now the most important languages to know in general are English, Spanish, Mandarin, Japanese, and Arabic. Unfortunately, in the US there's a chronic shortage of people who speak Mandarin, which causes an even more chronic shortage of people who speak Mandarin and are willing to work for a public school teacher's salary.

Plato (Greek philosopher of some repute) hung a sign over the door of his school saying, roughly, "No entrance for the mathematically incompentent".

Plato also said in so many words, "Real-world evidence is for idiots."

Your boyfriend takes you to an intimate little restaurant that doesn't take American Express. You will have to pay your tab in cash. There's a 6% sales tax and you both agree that, unless the service really sucks, less than 15% for a tip is tacky. You have $250 between you. What can you spend on the meal.

Ironically, here, in the perhaps most mathematically apt country in the world, you won't have to make this calculation (by the way, my rough answer is $206; a calculator gave $206.61), because prices always include GST, and restaurant prices include service charge.

The problem is that people hear "algebra" and see quadratic equations.

I don't - I hear "algebra" and see Galois theory and commutative algebra.

Why is it that every topic that wants to justify itself falls back on the old canard "it teaches logic"? Latin teachers also like to claim that Latin "teaches logic."

It's not the same kind of logic. The thing about Latin is, in a lot of modern high schools, they don't teach the native language's grammar, because it's too deductive and leaves some people behind, although evidently everyone can speak a language correctly without learning deduction. Modern language courses concentrate on vocabulary and grammatical peculiarities rather than on syntax. Hence for a lot of people, learning Latin helps them understand their own language's grammar. Incidentally, one case study shows that what teaches students their language's grammar most is guiding them through a class project of inventing their own languages.

Mathematical logic is completely different. Though interestingly, I think that the arrow of foundation goes the other way around: learning logic helps you learn math, rather than the other way around (unless you're specifically talking about real mathematical logic, including formal systems and Gödel's theorem, in which case knowing some mathematics will make you more familiar with the proofs).

Generally speaking, algebra doesn't teach skepticism. Mathematics has an abstract quality, a sense that if the facts contradict the theory, it is the facts, not the theory, which is wrong. (Yeah, yeah, yeah -- I know that this turns science on its head, but remember what you're defending by attacking Cohen's column: a kid who flunked a class six times, which means she took it six times, and the school system couldn't find a way to graduate her: that's not an abstraction.)

Knowing arithmetic gives you the tools to be skeptical of fuzzy math promoted by politicians. It's of tremendous help to know that if you make $50,000 per year and pay 32% of your income in taxes, then you won't be better off if your taxes are cut to 29% but you need to spend an extra $1,000 on your children's education and $1,500 on transportation. Understanding the idea of an accumulating national debt requires knowledge of arithmetic and geometric progressions. Calculating your probability of dying in a terrorist attack, or of needing an abortion, or of being murdered, requires a fairly good grasp of not only statistics but also ordinary mathematics.

Conservatives do not have a monopoly on scientific & mathematical ignorance; it just seems that way because they're the ones currently in power, and their King George is the dumbest anti-intellectual idiot to ever sit in the Oval Office.

You really need to read something about Warren Harding.

So why learn those three? Learning languages from different families would teach you much more about language, and give you a more well-rounded language education. For example, you could learn Spanish, Japanese, and Arabic.

It's true, but the less similar the languages are, the harder it is to learn them. An educated non-German North European typically speaks his native language in addition to English, French, and German. A North Indian typically speaks his native language, any nearby powerful languages (e.g. Bengali if he lives in Orissa), and Hindi. All of these are very similar - the European languages because of their Latinate vocabulary, and because Germanic languages share many idiosyncrasies, and the north Indian languages because of shared vocabulary, like the Romance languages.

But at the time of the Founding, every other human was a subject, excepting the handful who were sovereigns.

Thus, the American invention of citizenship. Before us, nothing much, and all failed. After us -- most of the planet, thank God.

And after the Founding, everyone was de facto a subject except for a tiny ruling class. More people had the right to vote in ancient Athens than in the USA in its early years. The modern idea of citizenship is due to the French Revolution, not to the American Coup (if it's fomented by wealthy aristocrats who change nothing but the name of the regime, it's not a revolution).

The American concept of citizenship was revolutionary: All of us.

Frederick Douglass would have flipped in his grave if only you had any political clout.

Under these four common definitions of citizen, there were multitudes of citizens extant elsewhere at the time of the founding of the USA.

The USA invented all that is good in the world. Every other place is either a tyranny or a copycat of the US. Anyone who says otherwise is unpatriotic. Get on with the program, and stop trying to confuse patriots with facts.

Other hot fields are barely taught. Many standard fields in science, particularly behavioral science, are not covered. Some examples: anthropology, robotics, psychology, linguistics, and AI. Technology is also sporadically taught. A well educated citizen should have good exposure to these fields on graduation from high school.

There's a reason for that: schools prefer to teach established, textbook science instead of newer, generally more controversial science. But you're right about social and behavioral sciences, which high schools everywhere are wrong to ignore. Plus, in general, I think it's going to be a win-win situation to teach real controversies, such as the Darwin Wars and Sapir-Whorf. Sticking to textbook science while ignoring frontier science promotes a skewed perspective about what science is and how it is done, and hazardously shelters students from uncertainty. Teach frontier science and social sciences and students will on the one hand learn more up-to-date knowledge and on the other get to practice writing and critical thinking more.

Richard Cohen was also the fellow who argued that because he deserted from the National Guard, it was ok for George Bush to have done so.

Cohen is obviously wrong. Deserting from an army is alright regardless of whether Cohen did it or not.

No one with the intelligence to pass a history class or an English grammar class is incapable of learning algebra.

Look up "dyscalculia."

Natural philosophy? Including chemistry? And without knowing any mathematics? What a load of crap.

In Jefferson's defense, at the time physics was the only science that had been mathematized, but then people called it mechanics and considered it a part of mathematics.

The ancient Greeks, the Vikings in Iceland, these were all essentially TRIBES.

Let me guess: the only thing you know about anthropology is the name of the discipline?

The modern concept of citizenship is an American invention: "all men are created equal...", so that rights are not granted by governments, which are established "to protect those rights, deriving their just powers from the consent of the governed".

That's in theory. In practice the American Coup did not increase anyone's level of freedom, except the local aristocracy's. As Howard Zinn explains, the Founders used rhetoric of liberty and equality to get the people to support their coup, but did nothing to increase the level of liberty or equality. On the contrary, the US Constitution codified slavery in all but the word, and prohibited any restriction on the slave trade before 1808, whereas in Canada slavery was outlawed in 1801, and in Britain in 1807.

It is NO surprise that the post-war prosperity came to end with the rise of economic advisors who actually consider it wise to model human behavior with Algebra.

The post-war prosperity came to end because of three coincident practices: the oil shock, the saturation of WW2 technologies, and continual inflation. Of these, only the last can possibly be attributed to economists, and even so, it's likely Johnson would've pursued a guns and butter policy even if Phillips hadn't been there to tell him inflation always reduced unemployment.

Unable to resist clueing y'all in, against your will (a fault, I know, as Raven will doubtless attest): how many of you have ever written (or, I suppose, syllogized) anything that folks promptly started to argue about?

Everyone here who has a blog people read, or who comments regularly on blogs people read. And at least in my case, the ensuing debates are typically constructive as opposed to Alon-is-an-idiot fests.

Last semester I took a course in symbolic logic. Guess which department ran the course. Mathematics. That's right! The philosophy majors also have to take the same course and it was taught by a mathematician.

Well, different universities have different practices. Here there is a course for philosophers, which I presume includes fallacies, syllogisms, different types of reasoning, and other informal topics; and a course for mathematicians, which includes formal systems, axioms, recursion, and Gödel's theorem.

Words have always been intuitive to me in a way that numbers weren't. The first message I got through elementary school and into high school was that because I did so well in verbally-oriented subjects, the only reason I couldn't do the same in math was because I wasn't working hard enough. The second message I got was that math skills were more important and more valuable than verbal skills.

Well, different people have different experiences. In 5th and 6th grade I had a homebase teacher who taught literature, history, Hebrew, and Bible studies, and continually denigrated the science-oriented kids. "What's the point of knowing math if you can't analyze songs?" she would ask (to which a friend of mine replied, "What's the point of analyzing songs if you can't do 1+1?").

but he forgot to finish the thought. Allow me:

"Here's the thing, Gabriela. You will never need to know algebra, because if you did, you might realize how much those payday loan places, those rent-to-own places, and the whole system of just-short-of-usury poor-and-low-credit establishments that exist to prey on people who make $7/hour at Subway actually end up costing you. And then it would be clear that pseudo-leftists like me are really counseling you to stay ignorant, so that predators can take advantage of your desperation and financial illiteracy. I'd much rather look like I have compassion for you, by using my national forum to trash my imagined childhood tormentors, than do something real like giving you meaningful advice that might help you break the cycle, instead."

What do you think? Did I capture the spirit of his advice, or am I just being uncompassionate?

"Besides, Gabriella, everyone knows that suffering and ignorance purify you. Leave knowledge and security to incorrigibles like me."

Have you read the article about Bushido, the philosophy guiding the Bush administration ("wealth corrupts, so we're conscientiously taking all of it to protect your purity")?

I've had plenty of people say, "You want a degree in history? I hated that in school--it's so boring--and what are you going to do with that anyway?"

How many of them have the level of education in the sciences that the math-detractors have in the humanities?

Um, no. On the contrary, if you didn't confuse what you do with my posts as 'reading', you'd know that I was BRAGGING about these achievements -- as proof that this American citizenship invention actually worked, where the other examples cited as precedents, all failed.

The only thing that's succeeded about the US is that it's young; so far it's survived for less than Iceland's first attempt at democracy. If there's still a USA in there hundred years, then come back to me with "our experiment is successful."

I only posted in this thread because it truly amazed me how many folks seemed to utterly miss the point: math is simply a tool to teach you how to think, and it's particularly useful to solve certain kinds of problems, like making change.

But it isn't thinking itself.

As opposed to writing?

Clearly if you just raise requirements without offering different graduation levels the number of dropouts just goes up. Of course, one might assume teaching quality might go up as well and ameliorate the dropout rate — but I'm too cynical to believe that will happen very quickly.

High rates of graduation aren't everything. The USA's rate of graduation from academic programs is very high, but Americans are nonetheless on average more ignorant than Europeans, even those who go to vocational schools.

Numbers mean nothing if they can't be interpretted. Knowledge means nothing without faith to guide it. Cohen is right. Why do we need to be able to crunch numbers? There are plenty of Asian people who are more than capable. But they lack our passion, our wisdom, our soul.

You either write very convincing satire, or are incredibly moronic.

Ok, that was probably a bit over the top, but public schools (not colleges) do not seem to enforce the rule that you must respect your teacher.

The last things anyone should learn is obedience and hierarchy. I'd much rather have a generation of youngsters who believe they're entitled to respect and treatment as human beings than have a generation of semi-humans who won't think for themselves and constantly try to break the rules when nobody's looking.

The problem is, as a parent, if you abdicate your responsibility to discipline your child, and then refuse to let a teacher discipline your child, what right do you have to complain when all little Johnny does for a living is flip burgers or ask "Would you like fries with that?".

Actually, right now, corporal punishment is associated with rural areas and the ghettos, which are likelier than the suburbs and the cities to churn out burger-flippers; the parents who resort to it, or to incessant shouting, are typically those who have no clue how to raise children.

Specifically, I'm thinking of the whole "new math" effort. My mom was receiving the high school side of that, where they tried a new method that mixed up algebra 2, trig, and pre-calc into a 2 year mess. Today, she can't even honestly say what she actually took back then.

Actually, new math was quite successful; its problems resulted from excesses, such as teaching set theory in elementary school, rather than from the concept of teaching math rigorously. If you think separating algebra, trig, and pre-calc classes is a prerequisite of good math education, you haven't checked the British and IB systems, where mathematics is a single subject.

By the way, I didn't see any discussion of a two-track, European-style system, although I haven't read all the posts.

I think it's a bad idea, for two reasons. The first is that labeling children a failure lowers their performance. The second is that there's very little to be said for vocational education. Most vocations require a few months' training after high school, rather than four years of vocational school. And the more high-level vocational schools (e.g. the mid-level track in the Netherlands, which typically prepares people for such jobs as teaching) enforce specialization way too early than is advisable: after all, Britain's greatest problem comes from its enforcing specialization at 16.

Rather, what I think should be done is to try to actively bring college down to high school. What I propose the US do is commission a study in which a few school districts - say, 10, spread around the country with respect to geography as well as urbanization and class - gradually increase students' workload to match the European standard in about 10 years, culminating in a requirement that students pass a certain number of AP tests to graduate. There needn't be any compulsory exams, although schools should encourage students to take more than the minimum number. For example, the requirement could be an English test and 6 electives, of which at least 2 need to be in science or mathematics, and at least 2 need to be in the humanities, with some further incentive to take math and a foreign language. Alternatively, if that scheme proves too unwieldy, the test districts can lift the IB program entirely.

At the same time, these districts - or possibly new ones if the first experiment is successful - should institute a new experiment, in which high schoolers, or maybe juniors and seniors, are treated as college students. Among other things, this means a college-style code of conduct, a stricter position on cheating, less emphasis on behavior, and a stance in which the school deals directly with students rather than with parents, except on legal matters requiring parental consent.