Here is a serious problem:
Here’s the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know—never mind want to know—how many boys it will take to mow a lawn if one of them quits halfway and two more show up later—or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note—or reason even a little bit. If, say, the school asked you for another year of English or, God forbid, history, so that you actually had to know something about your world, I would be on its side. But algebra? Please.
That’s Richard Cohen, who is supposedly the ‘liberal’ columnist for the Washington Post, giving advice to a young girl.
It’s outrageous.
Because Richard Cohen is ignorant of elementary mathematics, he can smugly tell a young lady to throw away any chance being a scientist, a technician, a teacher, an accountant; any possibility of contributing to science and technology, of even being able to grasp what she’s doing beyond pushing buttons. It’s Richard Cohen condescendingly telling someone, “You’re as stupid as I am; give up.” And everything he said is completely wrong.
Algebra is not about calculating the answer to basic word problems: it’s about symbolic reasoning, the ability to manipulate values by a set of logical rules. It’s basic stuff—I know many students struggle with it, but it’s a minimal foundation for understanding mathematics and everything in science. Even more plainly, it’s a basic requirement for getting into a good college—here, for instance, are my university’s mathematics entrance requirements.
Three years of mathematics, including one year each of elementary algebra, geometry, and intermediate algebra. Students who plan to enter the natural sciences, health sciences, or quantitative social sciences should have additional preparation beyond intermediate algebra.
This isn’t what you need to be a math major. It’s what you need to just get in, whether you’re going to major in physics or art. Richard Cohen is telling Gabriela to forget about a college education.
I’m sure that he has never once rued not being able to use algebra. If I had never heard a poem or listened to a symphony or read a novel or visited Independence Hall, I could probably dumbly write that I don’t miss literature, music, or history…never heard of ’em. Don’t need ’em. Bugger all you eggheads pushing your useless ‘knowledge’ on me!
That kind of foolish complacency is what we’d expect of the ignorant, but it takes the true arrogance of the stupid to insist that others don’t need that knowledge…especially after you’ve dismissed the utility of algebra because they can just use calculators. What, Mr Cohen, you don’t think the engineers who make calculators need algebra?
Cohen insists, though, that algebra is useless and doesn’t even teach reasoning.
Gabriela, sooner or later someone’s going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers. Writing is the highest form of reasoning. This is a fact. Algebra is not.
That’s easy enough for a man to say, especially when his very next sentence is an example of the quality of the reasoning he believes he mastered with his ability to write.
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.
Maybe it’s because I was bamboozled by all those teachers who taught me algebra, geometry, trigonometry, and calculus, but I don’t think a bogus anecdote (seriously—the college prep crowd at my high school were taking math, languages, English, etc., and doing well at all of them) is “proof” of much of anything.
It’s about what you’d expect of a fellow who brags elsewhere in his essay that his best class in high school was typing. That’s right, figuring out mindless, mechanical reflex action, rote memorization, and the repetition of stock phrases from a book were the height of intellectual activity in Richard Cohen’s academic career. And the highlight of his elementary school education must have been mastering breathing. This is the man whose advice about education should be taken seriously?
After all, education isn’t important to live a happy, contented life.
I have lived a pretty full life and never, ever used—or wanted to use—algebra.
If sheep could talk, they’d say the same thing.
Yeah, a person can live a good, bland life without knowing much: eat, watch a little TV, fornicate now and then, bleat out opinions that the other contented consumers will praise. It’s so easy.
Or we could push a little bit, stretch our minds, challenge ourselves intellectually, learn something new every day. We ought to expect that our public schools would give kids the basic tools to go on and learn more—skills in reading and writing, a general knowledge of their history and culture, an introduction to the sciences, and yes, mathematics as a foundation. Algebra isn’t asking much. It’s knowledge that will get kids beyond a future of stocking shelves at WalMart or pecking out foolish screeds on a typewriter.
We’re supposed to be living in a country built on Enlightenment values, founded by people who knew the importance of a well-rounded education—people like Thomas Jefferson, who had no problem listing the important elements of a good education.
What are the objects of an useful American education? Classical knowledge, modern languages, chiefly French, Spanish and Italian; mathematics, natural philosophy, natural history, civil history and ethics. In natural philosophy, I mean to include chemistry and agriculture; and in natural history to include botany, as well as the other branches of those departments.
Note “mathematics”, which would have included geometry and algebra. In Richard Cohen we have a 21st century man insisting that an 18th century education is too much for our poor students.
While Cohen may think a little more English or history is an adequate substitute for elementary mathematics, Jefferson would suggest otherwise…and if anything, this sentiment has become more true in these modern times.
[I have] a conviction that science is important to the preservation of our republican government, and that it is also essential to its protection against foreign power.
I can’t resist. I have to let Jefferson dope-slap Cohen one more time.
If a nation expects to be ignorant and free, in a state of civilization, it expects what never was and never will be.
(via the SciAm blog)
This is a disturbing coda to the story. Gabriela gave up on school and got a job at the local Subway sandwich shop, but now she has new aspirations:
“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.
Ahem, what? 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.
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.
Can I agree with both of you and still retain my sanity?
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.
What a total ass. Yes, I suppose if you work the fry machine at Wendy’s or are a clueless pundit for a has-been paper for the nation’s capital, you don’t find much call for algebra. No reason to go bragging about it.
This quote from Cohen really caught my attention:
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.
At the risk of sounding sexist, don’t forget nursing! I want the person mixing my medicine to know some math and proportions!
I think RAH summed it up best:
“Anyone who cannot cope with mathematics is not fully human.
At best he is a tolerable subhuman who has learned to wear shoes,
bathe and not make messes in the house.”
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.
Richard, you have never once used algebra? Did you go to high school?
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.
While I agree that Cohen calling Algebra useless for the great mass of students is the height of ignorance, I do have some sympathy for the “Gabriela” of his piece. I have known a few people in my time that really did have a fundamental problem with math and suffered accordingly. Is there something we can do for these people, or do we just abandon them to the limited world of those without a high school diploma?
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.
Don’t you guys know? The purpose of the American educational system is to churn out mindless office drones with no abstract reasoning ability whatsoever.
Wait… all those jobs are getting outsourced…
My G*d this country is screwing itself over.
Yes, there are students who can’t grasp algebra. You try to help them and find other avenues for them to explore…but you don’t just tell them something as stupid as “you don’t need algebra.” You have to be honest and explain that that shuts down whole swathes of career choices. You don’t deny that there are major life options that demand basic math skills.
I was with you 100% until I read Cohen’s column.
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.
Don’t worry. They won’t pass their boards if they can’t do at least some basic dimensional analysis – so they hopefully won’t give you 10 grams of medicine when you really needed 100 milligrams. Heck, they won’t even pass my introductory chemistry class if they can’t do that – let alone the boards.
Nursing students at my (2 year community/technical) college are required to take a college level algebra class. So, Gabriela can cross nursing off her list of future jobs.
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.
I guess Cohen has never prepared food from a recipe and had to adjust the recipe in proportion to the number of servings. There’s a use for elementary algebra in daily life.
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.
I am a software engineer and have had math classes up through elementary integral calculus. In my career I have never used calculus or even very much algebra. However I do use the abstract reasoning skills taught via mathematics every day. I can also write an english sentence and I can read a history book.
Cohen is an idiot. Math is good and the logical reasoning taught by studying mathematics is important for taking apart stupid arguments such as Cohen’s.
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.)
Well, Atrios linked to this site and I was all prepared to loathe Richard Cohen for some lapse in liberalism. But what Cohen posted was fundamentally compassionate, much more so than the screed above. It concerned a girl who had no knack for algebra and had flunked the course six times. As a result, she dropped out of school because of rigid academic criteria. Cohen essentially said what most of us KNOW, that advanced mathematics is hardly a prerequisite for a meaningful life, so it’s insane to make graduation from high school dependent on it.
All of you self-righteous math whizzes may mock this sentiment, and I’m sure you’re every bit as wonderful as the born-again Christians you resemble. Still, a little compassion does go a long way, and ultimately matters a great deal more than your numeracy.
!!!, 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!”
Since I finished up with calculus ten years ago, I’ve had absolutely no occasion or desire to use algebra.
Last year I took a course in graph theory and at the end of semester the lecturer said “I know that in two years time most of you won’t remember a single thoerem from this course. That is not a problem at all. The whole point of studying mathematics is that you learn how to think logically and thinking logically will serve you in anything you do.”
And he is right. Most of the abstract mathematics I learnt have no practical purposes. However I think I gained most out of the pure maths courses I took.
“Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.” –G.H. Hardy in A Mathematician’s Apology (1941).
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.
I think one of the reasons kids have a hard time learning math is, if they’re anything like me, they don’t really have a goal in mind when they’re learning it. In 3D graphics you not only need to know discrete math and and derivative/integral calculus, but also trigonometry, differetial geometry, linear algebra and many other highly specialized mathematical methods. It took me a painful 3 years to catch up and learn what I did, but I learned it because, essentially, I wanted to learn it. In high school I didn’t want to learn it. Big difference.
why does anyone care if you are a self-described “liberal” or not?
Many people’s problems with math is not to ability, but is psychological. I’ve known people to overcome an almost complete inablity to pass elementary math to go on to major in it and graduate at the top of their class.
I wonder how Cohen thinks the little lady calculates fabric geometry and stitch counts while he’s doing whatever manly men do that’s so important all the time?
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.
walt, I have no problem with Cohen’s criticism of the California requirement. Maybe people should be allowed to graduate regardless, I don’t know. Sometimes you have to set standards, or people won’t even try to rise to them.
The problem I think most of us here have with Cohen’s blather is his direct assault on algebra as an apparently useless subject, and the pernicious claim he makes that algebra teachers who claim the subject teaches reasoning are lying. Not only is he dead wrong, but it’s evil to frame it that way.
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.
Gabriela – don’t listen to this moron! Whatever field you end up pursuing, you’ll use the principles of reasoning you learn in algebra class; math skills might even make you a better writer. Some of the best writers I have known and some of the most distinguished teachers I have had in the humanities started out to be scientists or engineers, and I don’t think that’s an accident. The rigor you learn from mathematics is eminently carried to other disciplines. Don’t drop that math course!
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).
I wonder why trueLiberal thinks that none of us have taken humanities courses. I did a double major in chemistry and a minor in literature. Might I add that I got better marks in the humanities courses I took, than the supposed majors in those fields. They gave up when it got too hard, and I was trained to keep working until the answer came through. I think the earlier poster might be right – the fact that I could do BOTH, i.e. that I could get an A in their courses but they couldn’t get an A in mine, really galled a few people. And yet ironically the professors were usually thrilled to have science majors in their classes because they worked hard and were interested.
But back to the original comment. Maybe this girl was a specific case. And yes, we aren’t all meant to be scientists. But people should have basic knowledge, and whether or not Cohen’s statements hold true for some people, it shouldn’t be used as an excuse for kids to just give up. And most people are still able to learn high school level topics if they are properly taught. I blame this girl’s school, not her, if she can’t learn math. Math and science are not ‘hard’ but require cumulative knowledge and attention, which is difficult to provide or enforce in a high school where teachers are faced with 35 students of varying ability.
I think a lot of the criticism is being made towards Cohen’s attitude as much as towards what he is actually saying. He could have said the same thing, worded differently, with more of a disclaimer towards those of us who DO use algebra regularly as adults, and maybe people wouldn’t be getting as teed off. It’s the fact that he is so arrogant and narrow about how he discusses this topic that is a big part of the problem.
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.
I think it’s obvious that he’s deliberately tweaking the math intelligentsia or whatever fictional thing he perceives is out there. He’s looking forward to the 5000 outraged emails he will inevitably get from algebra teachers and college professors over the next week or two.
Jackass.
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.
I read Cohen’s column in the San Jose Merc, “Silicon Valley’s Newspaper”. Were they trying to be ironic? Thanks for your brilliant retort.
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”.
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?
“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.)”
CP Snow dealt with this one decades ago:
——
“A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: ‘Have you read a work of Shakespeare’s?’
I now believe that if I had asked an even simpler question — such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, ‘Can you read?’ — not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their neolithic ancestors would have had.”
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.
trueLiberal: Talk about intolerance.
“Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note�or reason even a little bit.”
trueLiberal, you want to tolerate such nonsense? Then why not tolerate intelligent design, flat-earthers and geocentrism as well? Or how about tolerating racism and bigotry as well? Some things should not be tolerated, especially if it harms others. In this case his nonsense has potential to harm the education of kids.
Students need training in maths, science and also humanities for them to develop critical thinking abilities. I have a feeling you are not very fond of maths.
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?
Oh yes … in Cohen’s raging torrent of bull, I almost missed this nugget. Some of my students come into my class thinking this – that they don’t need to know anything about numbers because their calculators or computers will “do it for them”. These are the same students who will swear up and down that their patient needs to be injected with 1,400,000 ccs of a drug – because they don’t realize that (1) they have to understand how the math works to get their calculators to do it for them and (2) the things they calculate represent something real.
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.
I never really liked Richard Cohen, but now I realize he’s an insufferable arrogant moron.
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.
Having a high-school kid in the house does bring back memories of the attitude “it’s too hard” re algebra. Funny, tho’, it all comes back, and rather easily. Seems we use it all the time, in everything, and don’t even notice it. Cohen is a complete idiot. But we knew that already.
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”.
To paraphrase someone, no one ever took up algebra because they couldn’t get into journalism school.
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.
Imagine my surprise becoming an a professional artist, then discovering I was not only using algebra, but trigonometry and some physics lessons to do my job. =/
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.
The more people that perpetuate the image that “I suck at math and succeeded in life” the worse math will be off for our younger generations. How can people imply that “I know less” is good? It’s sending the completely wrong signal.
Ironically, I’m not that good at mathematics and I’ve always fancied journalism as an occupation.
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).
Holy crap! What a moron!
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!
Speaking as a mathematician, this makes me cringe.
The thing is, there’s this whole philosophy of math education that focuses on “math in the real world” — and 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.
Basically (and this is my short-form party answer to “what’s the point of doing math?”) math makes you smarter.
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.
Shorter Richard Cohen: don’t worry, sweetie, boys don’t like smart girls anyway.
Wotta fucking maroon.
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?
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.
That option can never be characterized as useless even by ignoramuses like Cohen, for no matter how well you write, you cannot make any decent argument without logic.
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.
Writing is the highest form of reasoning. This is a fact. Algebra is not.
Hey, Mister “Highest Form of Reasoning,” you do realize that by flipping the order of the last two sentences you actually have said “Algebra is not a fact,” don’t you?
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.
What are the objects of an useful American education? Classical knowledge, modern languages, chiefly French, Spanish and Italian (…)
Spanish, certainly. French, maybe. But…Italian? The operative word here, I thought, was “useful.” Try Chinese, Arabic, any number of South Asian/Southeastern Asian languages.
Geez. Welcome to 2006, guy.
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
Also about that “highest form of reasoning” point:
a) One who has thought about or if familiar with the idea of reasoning would not suggest there are higher or lower “forms” of it. Reasoning is just a casual term for logic, and it comes into play in chess, writing, math, decisions, science, etc. But if one had to pick a domain that made the most use of it, and demanded the most care, math is probably a pretty safe bet (one can make a career on poorly argued writing; one can never do so with incorrrect math.)
b) Isn’t it funny how a writer who admits he could never do math claims his domain is the highest form of reasoning. He couldn’t cut the level of reasoning in basic alegebra, but somehow he knows that he is working at the highest level. So did he not get algebra because it was at “too low a level” of reasoning for him?
Still, I have some sympathy for Cohen’s position, only in that it is true that for many people high school math is a delight to leave behind and lack of algebra skills often doesn’t thwart a happy life. But I agree with most here that the message sent is way off, unthinking, and he is irresponsible to write it.
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
During my halcyon “Have Chalk Will Travel” days, I had the fascinating experience of walking into a Technical College classroom full of adults, almost all older than I was at the time, and starting the festivities with “Lesson One: Adding Two Positive Numbers Together.”
By way of an introduction from that point, I felt compelled to warn the class, “I know that many of you already know how to do this; however, some of you may not, and this is where this course starts. Even if this is something you already know, I would ask you to try to pay attention anyway, because there will probably come a point where we start covering material you don’t already know; and if you’re not paying attention at the time, you’ll look up suddenly sometime later and realize that you’re lost.”
I was right, too: There were adults in that class who didn’t really much know how to add and subtract.
By the end of that quarter, we were doing Algebra.
Mind you, it was only Baby Algebra; the point of the remedial course was to get the students ready to learn Algebra for real in a subsequent class. Still, I did take them from Zero to Algebra in just a few weeks; and many of the other college courses I taught around that time involved taking students from about that point all the way up to the borders of Calculus.
One of the best things about teaching adult students in Technical Colleges and night schools is that I rarely had to field the classic bored adolescent complaint of “What do we need to know this for?” â these folks were paying their own good money to sit in my class because they had been out in the big, bad world for long enough to bump up against the cold, hard reality of the fact that they needed to learn what I was teaching.
I taught HVAC technicians, secretaries, and assembly line workers at paper mills and computer manufacturing plants; I even taught a class composed entirely of Sergeants at Fort Jackson. Too bad I never got the opportunity to teach any Washington Post Op-Ed columnists.
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.
I wonder what this fuckwit would say about calculus?
Here (Englsnd) you have to have done at least a little differential and integral calculus to get to University in a science course.
Of course, as an engineering M.Sc. I’m naturally illiterate and ignorant according to this twat.
Well, balls to you, mate, some of us can also write poetry (badly) and dance, and write literate essays …..
It is called “being fully and roundly educated”
IGNORANCE IS STRENGTH
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…
“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.”
This is actually the most useful comment I’ve seen in this thread. Yes, Cohen’s column–like most of his columns–is poorly-argued and full of unsubstantiated assertions. I can think of any number of times when I’ve had to use algebra–and it’s possible that if I hadn’t slept through trig in high school I would have been a better lighting designer.
…or not, because I simply don’t visualize. I can follow directions that are given in words, but give me a map and I’m lost because I can’t translate two dimensions into three. For me, math is very similar, in that it’s an abstraction that at a fundamental level doesn’t make sense to me. It’s not because “at some early stage [I] failed to master one or more essential skills.” It’s because that’s just not the way my brain works.
I was surprised when I took the GREs and found that my score on the Analytic section was as high as my Verbal score–both of which were much higher than my Quantitative score. Then I remembered the one part of high school math that I *had* liked–the section in Geometry where we did proofs using words rather than numbers.
Cohen is wrong, but his post raises some interesting questions about the American educational system. Obviously, whatever this girl is learning isn’t working for her. Instead of seeing thinking people ranting about the obvious fallacies in Cohen’s argument, I’d like to see some genuine proposals for teaching students in a way that they’re suited to learn, rather than forcing everyone to learn the same things in the same way so that they can pass the same damned tests.
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.
Plato (Greek philosopher of some repute) hung a sign over the door of his school saying, roughly, “No entrance for the mathematically incompentent”.
This man knows better?
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.
If Mr. Cohen’s arms are 31″ long, and the distance from Mr. Cohen’s shoulders to his hips are 26″, could he reach both buttcheeks to pull his head out?
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?
Dear Gabrielle,
I’m sorry that you find algebra so hard and i must say i’m impressed that you didn’t give up and tried so hard to pass a subject that you obviously didn’t enjoy. I’m also immensly dissapointed that your teachers and school administrators let you down and didn’t recognise that algebra for you is like Shakespeare for dyslexics (yes, there is a parallel and some estimates put math ‘dyslexia’ at around 10% of the population) and couldn’t figure out a way to accomodate your learning needs.
Gabrielle, let me give you a piece of advice that may actually be useful: it’s not uncommon in later life to find that you don’t have the time or the talent to be gifted or even competent at some tasks (i for one will never be a concert pianist) but while recognising your own limitations is part of becoming an adult, recognising that you have other strengths equally as important should allow you to realise that dismissing a skill out of hand is akin to burning a book because you don’t like what it has to say – the act says far more about you as a person than your inability to master an arbitrary challenge.
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.
Move over, Douglas Feith.
The title of “stupidest human alive” has a new contender, and his name is Cohen.
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
Let’s see here, Mr. Cohen has found one case, out of how many millions of California public school students, where the requirement to get at least a C- in basic algebra kept someone from graduating. Then, rom this huge sampling, we are told that California must scrap algebra as a requirement? Worse still, intelligent people on this thread are falling for this bullshit. What if I found TWO examples where students were forced to take algebra, passed, and then went on to college and studied a technical subject that they never imagined they would before they took algebra? Would that change your mind? After all, my sample number would be double Mr. Cohen’s.
There need to be some basic standards in order to graduate from High School. I am sure that I could find a sob story where someone flunked basic reading ten times and was unable to graduate. Should basic literacy not be a requirement? Most 12-year-olds can pass basic algebra with little to no effort. It is certainly not too much to ask all High School students to pass this class.
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.
Maybe he was being sarcastic.
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!
Joe Gammon,
I think you’ve definitely hit the right chord here. Mindless rants against Cohen aren’t going to fix the problems with Gabriella’s school.
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.
For years I have had a friend who argued almost the exact opposite, that English and literature were dead and useless and that the east coast Liberal Arts college we were BOTH attending wasn’t a “real school” because it didn’t offer a degree in engineering.
He later transferred to an engineering school, but got a degree in General Studies. He’s also a disciple of Rush and Hannity now and believes the worst thing to ever occur in the history of the country is the stained blue dress, but that’s another story.
My point is that this may be the first time I’ve ever heard the opposite argument about education made and I find it equally repulsive to the one made constantly to me in my youth.
With the whole “ignorance is bliss” meme, Cohen sounds like he has a touch of “Dubya envy”.
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.
Gabriela,
This is your grampa. I realize you don’t know me and I think that is part of what I would like to explain, albeit, briefly. Your grandmother was my wife. She was dressed in the finest clothes, two “car assembly jobs” could buy, while being entrained and conditioned as a child and young woman, to a way of thought that led to her demise. It, (the conventional “rearing”) included concepts of her as a china doll and sexual pincushion. It promoted, or was evoked, in tangentially adjacent sub-themed ideas, you might say, in juxtaposed terms that her personal intellect was of no consequence and self expression and curiosity outside a dread filled co-dependency were meaningless, valuing less than zero, (think negative integers). If you ever find yourself dreaming as you look beyond the window, about what life was like for your grandmother before her tragic and untimely death, I feel you’ll need at least some math to understand.
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.
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.
I think you’d have a hard time mastering the propositional calculus without knowledge of algebra. The fundamental notions of symbol manipulation, and the idea of implication are embedded in algebra. It’s one’s first introduction to the idea of proof, and the use of abstract symbols to represent values. That’s at the heart of logic classes, but since they are even more abstract (x being a number is a lot easier than x being a philosphical construct). I think a student with no algebra would have a very difficult time.
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.
“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.”
And also avoid parallel fifths, and the dreaded hidden parallel fifths. And the seventh(septime) has to go to the first(prime), and you must not use diminished or augmented intervals. Classical choral harmony. Sorry if I mix up the english terms, I learned it in Norwegian. Probably one of the more useless things I’ve learned, and the teacher was a nut. Quadratic equations are a lot more useful, why, you can even use them to find eigenvectors and stuff! ;-)
Seriously, yes, the man is an idiot to belittle the importance of math and reinforce negative gender stereotypes, but I always thought it unfair that your individual grades didn’t matter, only your average. I still do. It’s weird and illogical that someone with a an A in gymnastics/physical education and a D in mathemathics is as qualified as someone with the opposite. Perhaps Gabriela can make up for her poor algebra results in other ways?
I share the sentiment that if an othewise ordinary girl fails miserably at algebra again and again, something bad has happened in the educational system. I’m not a teacher, but God, I wish I could do something for kids like these!
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.
I don’t agree with Richard, but algebra does suck.
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.
“You guys really believe algebra is more important than history? (Yeah? Was it algebra — or America, that invented citizenship.)”
Nobody has said that, at all, anywhere in this thread.
And in answer to your historical question, it was neither of the above.
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.
>You guys really believe algebra is more important than history?
Let’s put it this way, will the government charge you with failure to file your taxes or failure to celebrate Presidents’ Day?
Algebra (along with other mathematics) is more important than history, not to the exclusion of history, but America will need more mathematicians, engineers, and scientists than historians. Sorry, that’s just the way it is.
Speaking of learning to comprehend what one reads…that is completely false.
I’m not arguing that math is the only important thing, or that all those other disciplines are a stupid waste of time. That would be following the Cohen pattern of belittling huge chunks of the core academic mission. Read those Jefferson quotes — he is saying that one needs a range of skills to consider oneself well-educated.
Dear America,
Please teach your kids that biology is a load of lies, that the Bible is true, that the earth is flat, and that math and engineering are useless.
We’d rather like to rule the world for the next few centuries.
Lots of Love,
Everyone In China
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.
Like many at the Washington Post, Richard Cohen appears permanently stoned from inside-the-beltway cocktail parties.
Well-fed, useful idiots.
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.
I went back and read the whole column. And, Cohen’s clearly a wanker. Perhaps if he had paid a little more attention in his higher math classes, he may have gained better reasoning skills.
First of all, algebra’s not the enemy. Algebra doesn’t ruin anyone’s life. And Cohen doesn’t provide us with enough of the story to be able to nail down the real culprit.
You can’t really have a meaningful dialogue about school standards unless you have something of an understanding of why failing students are failing. To go off and attack the subject matter is silly and does little more than help foster a pride in ignorance.
There could be any number of reasons why Gabriela failed algebra 6 times. Was she having to work to support herself, leaving no time for studying? Did her school district raise standards without providing schools with sufficient resources to help students achieve those standards? Was Gabriela distracted by emotional problems? We’ll never know.
What we do know is that Cohen can’t even figure out that it’s not typing he does for a living; it’s writing. Then again, maybe that explains everything.
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.
Jonathan Badger : He doesn’t say logic, he says reasoning. Reasoning includes but is more than just logic. Memorizing where deserts are, on the other hand, is not even reasoning.
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.
That’s Richard Cohen, who is supposedly the ‘liberal’ columnist
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.
There are some conservatives who place a high value on scientific knowledge, just as there are liberals who view science and math with indifference at best, outright hostility at worst. Cohen’s low opinion of algebra in no way makes him less of a liberal.
Troutnut says:
Same here, and I went to school 25 years ago.
Perhaps this guy went to Stereotype High.
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.
;)
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…
I think there is a little too much caffeine and spite in the air. First, I agree that it is patently ridiculous for any intelligent person to counsel another to avoid algebra, such a basic building block of several areas of higher knowledge. But for that matter, why is logic itself taught to kids? However, I think part of the point that Richard is making that is being ignored here is this: education has been transformed from a pursuit to enrich and involve an individual in the world around him/her into a purely practical training ground for worker units. And then there is the pressure from the more radical elements of the right that want education to consist of reading the bible.
Whenever we measure the crisis in education we point to the brain drain and measure success or failure by the number of scientists, doctors etc. that our country is producing from natives.
And yet we find ourselves increasingly in a society that has no appreciation of the past or in the use of the english language or in living and communicating in a well reasoned and consistent manner. In fact consistency is attacked as theory and only belief is extolled. Belief will not lead anyone to learn more, because one cannot learn more, one can only adhere more rigidly to the belief (which conveniently is unknowable as a mystery).
Our educational system is being transformed by an approach where only performance on standardized tests is important. We have very clever individuals who cook up the many layered fraud that was Enron; we have lawyers who can with pride point to memos where torture is rationalized. Where does this come from? Will algebra solve that problem?
What is not being taught today is the love of learning, the appreciation of those who have thought alot about thing or who have the talent to express themselves in a way that challenges us (art?).
Yes, it’s disingenuous of Mr. Cohen to complain about algebra when one of today’s pressing problems is the de-legitimization of science.
But it is just as disingenuous to pounce on him for perhaps pointing out that education, in order to be “liberal” must look beyond simply preparing student for a career in science. The standard should be to prepare students to live in a world where they can participate in a democratic republic with some sense of history and knowledge so that such participation will lead to the common health of society.
I think the worst thing that has happened to education, especially elementary education, is the abandonment of music and arts as both substantive and normative areas of learning for children.
Kutsuwamushi, the “useful American education” quote is from Jefferson, not Cohen. I think we can forgive Jefferson being occasionally a little old-fashioned!
I’m going to take a wild guess that the Americanist is getting his/her notion of what was taught in math classes a century ago from watching too much of “Little House on the Prairie.” That’s fiction; here’s the Wikireality of education a century ago: “In 1870 only 2 percent of 17-year-olds graduated from high school. By 1900, however, 31 states required 8- to 14-year-olds to attend school. As a result, by 1910 72 percent of American children attended school and half of the nation’s children attended one-room schools. Lessons consisted of students reading aloud from their texts such as the McGuffey Readers, and emphasis was placed on rote memorization.”
His/her history also seems a little challenged. America, he/she might be surprised to learn, did not “invent” citizenship.
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.
Brad Delong points to part of the problem.
From the Fifteen-Year-Old’s geometry textbook, Geometry for Enjoyment and Challenge, Theorem 68:
If an altitude is drawn to the hypotenuse of a given right triangle, then (a) the two triangles formed are similar to the given right triangle and to each other; (b) the altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse; and (c) either leg of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg (i.e., the projection of that leg on the hypotenuse).
A friend of mine teaches junior high school math. He despairs of the curriculum he’s supposed to follow. So he doesn’t follow it. He says math teachers are rare enough that he doesn’t feel at risk.
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.
Well, from having worked at a yarn shop, I can safely say that many women who were allowed to go all “Math, ick! I won’t need that!” do regret it later. They don’t know how to adjust knitting patterns to suit their bodies or substitute different yarn for the one called for by the designer. The choice of yarn and needle size determine the gauge, or stiches per inch. You determine how wide you want the finished piece to be and multiply by the gauge to find out how many stiches to cast on. Playing with these numbers is the basis for all knitting design.
One thing I noticed was that anyone educated outside the US could understand how the system works in a broad sentence or two. About one-third the Americans never figured it out, even when I sat down and did the math in front of them and showed them knitted samples with different gauges. They just glazed over an tuned out.
I read the Cohen piece and he takes the wrong tack entirely. Instead of realizing that the problem of someone who flunks algebra 7 times is one of teaching, not the student. When my grandfather lost most of his hearing, we quickly learned that repeating something multiple times wouldn’t help him to understand any better, you had to come up with different words meaning the same thing until he latched onto one of them.
That said, if someone made a real effort and took several math classes with different teaching approaches, if they couldn’t pass the exam, I would offer a non-exam pass diploma.
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!
Anon: my source for the math is the test which it was required for all high school graduates in Iowa in the 1890s.
And it is simply a fact — evidently neglected in your education — that the United States of America invented citizenship. It has Greek and Roman roots, and there are nuances with Venice and Switzerland.
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.
Too complex for you, with all your math skills?
Clearly, your education had… holes.
Bartkid also proves my point: WHY the U.S. government cannot prosecute you for failing to observe President’s day is a helluva lot more important than mere algebra.
LOL — and trying to use the complexity of the tax code proves my point, again. The last time I had to use algebra was to comprehend why our immigration system doesn’t work: it DOES work — if all you care about is the math.
If you actually care about people, well — you got something more out of your education than Anonymous or Bartkid who are nevertheless, QUITE proud of their math skills, while demonstrating bone ignorance of what counts.
I’m all for BETTER math classes — but if you guys are the ones designing ’em, I ain’t hopeful.
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.
What I find completely silly is that Cohen says he hasn’t used any Algebra since his Calculus days.
When I was taking Differential Equations in college, we were going over a homework problem involving integration and trig functions, and the professor remarked “Do you ever stop and think that you weren’t born knowing that the integral of sinX dX is cosX?”. He was pointing out how doing the math for years just makes it part of you, and even completely non-intuitive things can become second nature.
Richard Cohen took mathematics through Calculus and doesn’t think it affected the way he thinks, how he evaluates things, how he reasons. He assumes that because he isn’t concious of it, it didn’t happen.
Actually, looking at the reasoning in this column, it may not have.
For the record – Math major, History and PoliSci minors.
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?
Professor Myers, I’m sorry you ever had to write that.
Signed, a polymath (see? You can’t even have multiple skills in this world without using the word “math!”)
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. :-)
I am pretty sure we could find any number of successful people who couldn’t pass a high school algebra test to save their lives. Sure, most of them use math concepts everyday, or use tools that pop out ‘magic’ answers because a programmer did the math.
Whatever happened to ‘Consumer Math’? Back when, if you weren’t college bound (whether you should have been or not), at least the school tried to make sure you could balance your checkbook or fill out tax forms. Remember what the average stands for in IQ – half of us aren’t intellectually gifted. We all share the same country though.
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.
Richard Cohen:
Writing is not a form of reasoning–or anyway, it’s not a very good one. Natural language cannot be relied upon to express unambiguous propositions let alone establish their truth. Well, I guess Cohen’s ignorance of 20th century mathematical logic is understandable in light of the fact that his brain hurts when he hears “Johnny has nine potatoes. How many more potatoes does he need to make a dozen?”
The ugly truth about language is that, while the human brain is well adapted for it, it is probably more useful for social bonding than for reasoning. There are simply too many places in which language can mislead. That’s why mathematicians, who have to get every step of a proof right for it to have any merit at all, will introduce rigorous notation.
I don’t know what is the “highest” form of reasoning. The brain has a versatile toolbox and I’m not inclined to make up an arbitrary ranking. But it’s shocking that Cohen would place language higher than, say, spatial reasoning. If the only way the brain could reach conclusions were to string words together, then we’d really be stuck when it comes to understanding the world around us. Without numbers and spatial visualization, the human brain would be at a loss to confront reality. Here’s what “reasoning” with words looks like: “It’s really big; it’s kind of curvy; it’s far away; uh oh, it’s getting closer.” In fact, you might have a similar stream of consciousness in such a situation, but unless your brain is dealing with quantities and spatial concepts a bit more efficiently than you can put into words, all your words aren’t going to help you react to it.
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?
Well, I’ll agree with Cohen to the extent that if your interest is in making money, then math or science is a waste of time, just take the minimum. Of course, writing and history fall into the same categories. In the U.S., the financial rewards do not flow to those abilities.
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+3×6=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.
Give anybody here 45 minutes a day with Gabriela, for one term, let alone six, and she’ll know math inside out. Problem is our public education stinks.
One specific point – and speaking as a literacy teacher and not a mathematician:
Could be – I’ve had a few moments where I almost seemed to grasp, very dimly, a bit of that ‘beautiful and elegant’ stuff folks talk about. But – for elementary and middle school, and into high school, especially for struggling students – you have to take into account ability and interest. After all, you want to teach the whole class, not just the kids who really like math in the abstract and/or show obvious ability. [Also, a more concrete approach is developmentally appropriate, as I understand in, in the lower grades – manipulatives are fun! and very helpful for many students; this is sort of an extension of that.] Additionally, you can draw in aspects of children’s real lives, from buying candy to helping grandparents garden to etc., etc., etc., (of course, like everything else, this approach can be routinized, scripted, dumbed-down, intellectually pithed, and turned to utter crap).
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.
“
sorry about endless italics! I hate html. it’s hard! who needs it?! they should get rid of it!
(I was trying to emphasize just “at this point” – since practically speaking, it might be true, but had things gone differently earlier in their schooling . . etc)
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.
Also, I think the failings of the school system, the problems that are damning Gabriela, are worsened by the Republican education strategy. Putting up an absolute wall of standardized testing at the end of your school year is not a way to get better pedagogy.
Oh, and I called Cohen a supposed ‘liberal’ not because his advocacy of stupidity calls his liberal credentials into question, but because he has been soft on the current administration…something completely independent of the fatuousness of his essay.
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.
I don’t want to be flamed by the math uber alis crowd, but as a professional in the humanities, I, and almost all that I know, make a great living without knocking about the the world of algebra.
When an educator, I was amazed at the number of non-college bound students who were fluid at basic math, but were being shot down by exit level math exams. To me it was a misallocation of scarce resources. Not very logical.
“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.? : )
The real problems with math education start quite early in elementary school. The fundamental problem is teachers who are entirely unprepared to teach math (even the basics of arithmetic are not so simple and obvious to teach properly as they may seem, and later on fractions, mastering the manipulation of which is essential preparation for algebra, become a major disaster area in far too many classrooms) greatly exacerbated by “reform” curricula which might be exploited successfully by a gifted teacher who would also know when to depart from them, but are far too diffuse and unsystematic to be anything but a disaster in the hands of a teacher who is shaky to begin with. People who think they don’t “get” math were probably lost by the educational system way back at the elementary stage, with the deficit subsequently being compounded every year.
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.
LOL — Nerp provides evidence: “writing maketh an exact…”
If you want to get all PHILOSOPHICAL about it, it depends on what “inventing” means. The Greek concept of citizen was more like an overlord — there were citizens, who were equals among themselves, and then there were the underlings and slaves.
The American concept of citizenship was revolutionary: All of us.
But we’re a practical people, and so was our revolution was not theoretical. (It was the only conservative one in recorded history, btw: the Founders originally sought rights they would have had as Englishmen but were denied as colonists, precisely because the Crown had not granted them. So the Founders decided on the Revolutionary idea that governments don’t grant rights, we’re born with them).
But, not to be too blunt here, I wouldn’t give a rat’s ass for the theory involved. The guy who “invents” something is the one who builds it so it WORKS.
(This distracts from the subject, but I recall the late Barbara Jordan pointing out HOW American invented citizenship — by the kind of perfection grounded in our Founding on a universal principle, which the practical effects of our history drove toward a broader and more truthful American identity: the promise did not apply universally at first — she noted she was black, and female — but because the principle WAS universal, folks came here to take us up on it: and made it more true. The ancient Greeks? fugedaboudit. You might as well claim da Vinci invented the helicopter.)
LOL — but the evidence Nerp provides is that these shades of meaning, this sifting for sense that denotes the love of learning, is PRECISELY what is missing from “algebra”.
Understanding that (X = Y, Y = Z, therefore X= Z), is a tool for thinking, but it’s not the capacity for thinking itself.
Every commonsense observation you guys make that “algebra” is everywhere, like making change, is proof of precisely the COMMUNICATION failure that learning how to read, write, think and speak is designed to fix.
(grin) I love watching highly educated folks brag about their ignorant prejudices. By all means, continue.
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.
LOL — and as long as I’m picking on folks who can’t handle precise concepts —
Anon wrote: “I’m going to take a wild guess that the Americanist is getting his/her notion of what was taught in math classes a century ago from watching too much of “Little House on the Prairie.”
I wrote: “my source for the math is the test which it was required for all high school graduates in Iowa in the 1890s…”
Dan S. blundered: ” 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….”
On the contrary, Dan: you made mine.
The words denote not what it meant to graduate from high school, nor what proportion of kids did graduate, but WHAT AND HOW MATH WAS TAUGHT.
Basic literacy: don’t leave home without it.
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.
That’s OK- I’m laughing too. And I’m not laughing with The Trollicanist.
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.
What baloney from Cohen. I myself was a math major; I then went to law school and practiced law for several years. Even though law is a verbally intensive profession, I can testify without any doubt that lawyers who know math – including algebra – are at a distinct advantage to those who don’t. Calculating economic damages and lost profits, making present and future value computations, and understanding what the heck your expert witness is saying are all made easier by knowing math.
I’m now a professional writer. Guess what? I still use math. And while Cohen may think I cain’t rite real good, I’ll assure him that’s certainly not the case.
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.
“Most of math can now be done by a computer or a calculator.”
Indeed. No need to learn how to spell or proper grammar, since these can now be handled by the spell/grammar check on your word processing program. And soon no need to learn how to read since everything will be in audio files (recorded there by the nerds and dweebs who actually do know how to read, but hey, whatever…) Following that, pre-chewed food – just put it in your mouth and swallow.
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…
“I don’t want to be flamed by the math uber alis crowd, but as a professional in the humanities, I, and almost all that I know, make a great living without knocking about the the world of algebra. When an educator, I was amazed at the number of non-college bound students who were fluid at basic math, but were being shot down by exit level math exams. To me it was a misallocation of scarce resources. Not very logical.”
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.
“all that I know” should be “everyone I know”–you are talking about people, not knowledge, after all.
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.
Normally, I wouldn’t edit another post so much, but since your point was how much we “math uber alis” [sic] types don’t get it, I thought I’d help you try to communicate your point.
Back on-topic–the poster above who remarked on Cohen’s missing the bigger story had an excellent point. He has a forum where he could make an impact. He could draw attention to how our school system is failing students like her, but instead, he chose to indulge his own math phobia.
Too bad that seminal typing class he took didn’t teach him how to recognize the makings of an important story, and how not to throw it away with both hands.
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.
the (former) student in question does have an easy out, if college isn’t her thing: take a GED from some other city that doesn’t have the algebra requirement and at least she can say she “graduated” high school.
i fully *want* students to know algebra and geometry, but how, as a society, should we handle those that simply can’t grasp it no matter what? do we force them to the menial jobs of fast food and/or hotel housekeeping in spite of any talents they may have in other things but not math?
Of course *some* of this can be pinned to the teachers for not finding alternative ways of getting the knowledge through; math teachers have a knack for teaching as if the student knows it already, which is certainly the case for those students like me who were on the fast-track to high school calculus.
the school system should have addressed this problem, found alternative teachers and/or tutors, particularly someone who specializes in getting mathematics into students who feel they can’t grasp it (first rule is to get the student to stop thinking they can’t do it; THEN you can actually show them how easy it is when looking at it from a different perspective).
Cohen is wrong, yes, but the real failure was on the school system itself for not taking care of this person 5 semesters ago.
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.
A few random anecdotes:
1) Quite aside from whatever subconcious intellectual substrate math provides me with, I did use algebra just the other week. It was a little home carpentry project that included a couple of funny angles, and in order to figure out how long to cut the wood so it all went together right, I had to solve a system of two trig equations (OK, a rule-of-thumb carpenter could probably have got it together by guess-and-by-golly, but my way was fun ;-).
2) Some years ago I attempted to tutor a young friend of the family in HS math. It was an up-hill battle, and in the end I he managed to just scrape through. He went on to get a degree in History, but then got stuck for a while not quite knowing what to do with his life. Now he’s in the (Canadian) military, learning the aircraft maintenance trade (he loves flying and has a pilot’s license). Among other things, he’s taking electronics — and finally “getting” the math required. He recently thanked me for my efforts lo those many years ago. I always loved math myself, but I have an idea that there are students who just can’t handle it as an abstract subject. They need to have a concrete problem, in which they are interested for its own sake, and when they can see how the x’s and y’s and angles and differentials and whatnot actually describe things in the real world, things that they care about, suddenly it all clicks.
3) While I’ve run across my share of semi-literate techies, I utterly reject the stereotype. I assert that Cohen’s school anecdote is atypical — or is just a stupid bit of creative rhetoric.
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.
All of you self-righteous math whizzes may mock this sentiment, and I’m sure you’re every bit as wonderful as the born-again Christians you resemble.
Oh, please go fuck yourself.
This is, hands down, the most moronic thing I have read on the internets. Even more so than a Ben Shapiro column.
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.
I’m sympathetic with Richard Cohen. I’m a scientist. I sometimes use algebra, I frequently use geometry and trig, I never use calculus. And I use numerical analysis more than most of my colleagues and think it important.
I teach in a medical school. To get into med school students take rigorous courses in chemistry and organic chemistry. These are fequently the weed-out courses. Yet chemistry and organic chemistry are only used at a very low level in medical education.
I’m particularly critical of the current High School science curriculum. Biology, chemistry, physics, and, for the ambitious, AP biology AP chemistry and AP physics. This is a curriculum defined over 50 years ago and set in stone. Ask yourself what a good citizen should know about science. Many of the topics are earth science and barely taught — in my school district earth science is not formally taught after 6th grade. Ask yourself what are the hot fields in science. Certainly one is Neuroscience and the biological basis for behavior. Not taught. 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.
I think math and science educators should take a long hard look at what they are doing well and doing poorly. Currently they sit smugly holding the keys to advancement, assuming anything that is their field, anything that is rigorous, has value, should be required and is good. I think they that attitude needs serious examination.
Siamang, that was the most hilarious retort to Cohen that I’ve read yet. Brilliant!
“Dan S. blundered: ” 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….”
On the contrary, Dan: you made mine.
The words denote not what it meant to graduate from high school, nor what proportion of kids did graduate, but WHAT AND HOW MATH WAS TAUGHT.”
Looking back, you’re right – it seems your point was that “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?”
(and indeed, this was the approach much earlier as well).
I don’t entirely see how this a)supports Cohen or b)has much to do with learning how to think. It sounds like basic computations using familiar situations, possibly practical. I’m not sure whay sort of math chops your average late-19th century Iowan might need The modern equivalent probably would be ‘consumer math’. Being blundering, I think I’ve stumbled past the obvious inferences you wish your readers to make
“For what this kid is doing, learning to THINK is a helluva lot more important than the abstractions of algebra . . .the school system’s failure is a helluva reflection on its capacity to get it. ”
. Are you saying that algebra is useless to her life, as much as bushel-and-wagon problems were back then – that both sets of kids should have taken crit. thinking classes? Are you saying that she should have learned to think in relation to making-change math class? That she doesn’t need math – at least not algebra – but something else entirely? Help me out here!
Certainly the structure of educational options and subsequent employment opportunities -in the past, and now – is relevent here. That’s what the issue is about. What do kids need for the near future, how do we attempt to give to them, what degree of differentiation do we employ, etc.
ahrg, typing too fast . . .
John Sully: in software you are doing *nothing but algebra*. you don’t take calculus to use calculus (although it helps as background understanding for big-O notation and algorithm analysis and optimization). you take calculus so that by the time you get to *using* algebra and analitic geometry, it is so practiced and ingrained its natural and just happens.
just because you’re using more functions than raw math, on strings more often than numbers, doesn’t mean your not manipulating variables just as much as you would be in an algebra two class.
in fact, i would propose that real string manipulation (substrings, replacements, indexing, searching, regexps) is actually *harder* than most of content of an algebra one class and you couldn’t do it without knowing those rules first.
and, of course, any visual graphics rendering requires knowing and using analytic geometry, even without going 3-D. a simple little map library i wrote, requiring java-2D, made me go back and re-learn (well, re-derive) 2 weeks worth of linear algebra to know what was going on to make sure the scrolling system worked, but because i knew it the code worked first time with no bug-fixing required.
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! :)~
A lot of people are arguing a math vs. humanities theme. I don’t think that’s fundamentally what Cohen was doing. He probably thinks he was being the friend that comes over to your place when you’ve just been dumped and tells you how you’re better off rid of him/her anyway. While this provides emotional release, and helps you feel better about yourself in a time of depression, there’s not a whole lot of forward motion involved.
It’s the backward motion that I, and I think a lot of people here, worry about. Cohen didn’t just say you’ll be okay without algebra to Gabriela, he wrote it to all the readers of the Washington Post. In doing so he is no longer trying to make Gabriela feel better; he’s trying to make a bigger point. In doing so he felt the need to trash not only algebra, but also its teachers and the students who did well in it. Why? For the little, temporary relief offered by our psychological defense mechanisms?
No one here disputes that people all over the world lead complete, meaningful lives without algebra, or without history, or without literature, etc. But what about the kids who start to generalize Cohen’s attack and want to try a life without algebra, and without history, and without literature, etc. I think this is what most people here are worrying about. It isn’t that those who aren’t good at math won’t learn it and thus might be a lesser person. That argument works to some extent for any and all subjects. It is that people won’t try as hard in each and every subject in which they experience any amount of failure, and lose out on something that would have helped to make their lives more interesting to themselves.
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.
Sweet Lord! This is the most ignorant, ridiculous, outrageous advice ever given to a young, struggling student.
My husband flunked alegebra twice in school, partly because he was undiagnosed ADD. He went to college as an adult and passed algebra with flying colors. Just because something is difficult, or you struggle to learn it, doesn’t mean it’s worthless.
Basic algebra — used to balance a check book, calculate recipe amount, resize photos, figure out postage. Yeah, this girl won’t need to know how to do any of that.
Cohen ought to be ashamed of himself.
I’m confused. The Greeks didn’t have real citizenship because they had slaves and excluded women. The framers, on the other hand…
Did anybody else notice that Cohen tried to prove his point about math whizzes being poor writers by sharing an anecdote about a math whiz who was bad at geography? Right in the same paragraph where he pontificates about how writing is the highest form of reasoning?
Oh, the irony.
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.
I’m loving this discussion. For instance “What’s the broad purpose of an education? It’s to learn to read, to write, to think and to speak – in that order.”
This is Cohenism at its zenith: first you read, then you write, then you think. “Ready, shoot, aim” as it were! No wonder the poster agrees so strongly with Cohen.
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.
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.
His failure to learn algebra may be behind the fact that much of what he says doesn’t add up.
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 :)
spencer said:
Good eye.
And the conclusion that the math whiz community in general is bad at writing is one that to my mind that can only be “reasoned” using a statistical model (not a cheesy anecdote about an individual) – such a model necessarily entailing mathematics.
More irony.
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?
Yikes. A lot of hard feelings here.
I think everyone agrees that the situation described in the LA Times story is lamentable, and represents a failure of the educational system. 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. You can see the traces of that in Cohen’s writing, and what he sees as an opportunity for revenge against his math teachers and the kids who were good at it.
Another contributing factor is the myth, pervasive in the U.S. (but, not, interestingly, pervasive in India) that capacity for basic math is innate. See e.g. a comment above about “people to whom math comes easily.” What this means is that when little Sally comes home from third grade with a C in math she is typically told that’s OK, some people just can’t do math. This is seen as compassionate. Reading is also hard, but when students have trouble learning to read they’re not told that’s OK; they’re pushed until they learn. Cohen annoys a lot of us because he’s using a position of authority to encourage people to give up.
The other real difficulty in communication is that those of us who did get, at some point, the sheer beauty and power of mathematical reasoning feel that we have been let in on some of the secrets of the universe. The world really does have a certain structure; there are links between ideal thinking and tangible reality, there is something called logical proof; reasoning has axioms and rules. But it’s impossible to communicate the sheer joy of this to people who never got it. And when the argument comes down to narrow “use,” like algebra is the equivalent of typing, you just want to throw up your hands.
Another area where geometrical and algebraic reasoning come in handy is in the ability to deal with any substantial amount of numerical data. This has something to do with one’s capacity to be an informed citizen.
“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.
“Another contributing factor is the myth, pervasive in the U.S. (but, not, interestingly, pervasive in India) that capacity for basic math is innate.”
I think this extends beyond just math to intellectual achievement overall – innate ability is seen as more important than hard work. Anyone have real references?
“The world really does have a certain structure; there are links between ideal thinking and tangible reality, there is something called logical proof; reasoning has axioms and rules.”
Forget the whole “two cultures” snow-job – I think you hit on the real cultural divide here!
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.
I’ve lost any sympathy I had now, both with the girl and with the school system. From the original LATimes article(reg required)
but earlier in the article, the systems own flaws revealed themselves
and
In short, the system set itself up for utter failure. Rather than create a gradual improvement system where preparation for high school algebra was improved in the earlier grades, so that when the mandetory requirement was enacted, they had students ready for it; the system simply shoved this arbitrary requirement on a totally unprepared student body and simply let the failures fail. In short, I am disgusted with the school system far more than the students.
In fact, the guy responsible for this disaster used Cohen’s own “i have one example, therefore i’m right everywhere” reasoning:
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.
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. – Steve LaBonne
I agree with you — innumeracy like Cohen’s is a huge problem.
But you don’t need to use algebra directly to spot the lies in Bush’s speech (although being able to solve linear equations would help you pinpoint exactly what’s wrong in those fiscal policies). You do need to have an appreciation for math that learning algebra develops.
It’s about “building character” … whatever happened to “building character”?
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.
Quote from LA Times article: 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.
I encountered a lot of these people in university-level classes. Sometimes it was in a big lecture hall, in a situation that had to have been, frankly, boring. Sometimes it was in a class of 20 to 25 students in what was supposed to be a stimulating, hands-on, discovery-learning situation.
I’ve met college students who couldn’t pass an exam without constructing flash cards for themselves, and who came to my office hours crying because they couldn’t figure out how to make flash cards for the material we covered in lecture. (Or, even worse, because they used the flash cards for two whole hours the night before and still did badly on the exam.) When I gently recommended to them that they start weaning themselves off flash cards, more than a few looked at me as if I’d just slapped their faces.
What are we doing to these kids? Are we forcing them to memorize their way through elementary school without tolerating the fleeting life of one original thought? Poisoning them in utero with environmental endocrine disruptors that adversely affect their brain development? Teaching them that it’s more important to work two menial jobs to support a car than to string three concepts together into a coherent thought?
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.
Algebra is essential for the social sciences and business disciplines as well. In fact, I can think of very few programs in college that do not use algebra in one way or another. Perhaps Cohen’s field of “hack journalism” is one that doesn’t require it- but then Cohen and the other hacks shouldn’t be able to write about economic policy if they don’t even know algebra and have the kind of attitude toward it that Cohen has.
waltw:
Possibly, but there’s also the valid point being made repeatedly here that quantitative reasoning is a teachable skill that turns out to be very useful, and that we ought to be encouraging people of normal intelligence to develop this innate capacity instead of making excuses for them.
Good link. It is a shame that there are some people that think like Cohen, but somewhat encouraging with the almost single-sided negative response he provoked. Didn’t President Bush talk about a lack of scientists and engineers in his sotu address?
What Gabriela needs is not someone to tell her to give up, and that giving up is ok, she needs someone to teach her algebra!
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.
Natural philosophy? Including chemistry? And without knowing any mathematics? What a load of crap. And the history of the world is incomprehensible without knowing the history of science and technology, which needs knowledge of science and technology, including mathematics.
I too am appalled by a school system that allowed to get someone to this point..
The above said, I think there’s a fair case to be made that the mathematics stream for those interested in mathematics, engineering and natural science might be different from other students… but I don’t know how to do this.
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.
What, is no one going to correct Geeno’s assertion that “the integral of sinX dX is cosX?”
I think it’s quite possible that some people do have an innate “gift” for math and can pick it up very easily, and some people have the converse, a sort of block that makes it more difficult for them than the average person of similar overall intelligence. But of course the vast majority of people do not fall into either of these categories and it would be helpful if math was seen as just another subject, that can and should be mastered with a reasonable amount of work, not something you can only do if you were born with the “gift”.
That false assumption tends to go along with the twin belief that people who are good at math are bad at everything else (except maybe physics or programming), are ignorant of literature and the arts and have no social skills or empathy. Why the need to push such an unpleasant stereotype? Bitter and insecure much?
It’s funny to hear people say that no one needs mathematical skills any more, because “computers do all that now”. As though the computers design and build themselves, and write their own software (though wouldn’t that be a scary thought…).
On the subject of practical uses of algebra, what about the use of linear algebra in analysis of NMR scans?
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.
timothy and Dan S.
Thanks for your comments. I, too, think high school algebra is good stuff and not esoteric. But I’m uncomfortable making it a requirement for High School graduation. On the one hand, I can believe that many smart people might have a real algebra block. On the other hand, I could believe, that, given the right instruction, any solid student could become a better student having gone thru algebra. But I’m not at all convinced that tutoring a weak student to get a 65 on an algebra competancy test is productive. In my experience, most students who get just-passing scores on multiple-choice tests have learned almost nothing. This is really a sticky situation.
If I were education czar, what I would look for from a High School graduate would be postiive evidence of educated thought, perhaps in 3 out of 4 domains (to make room for students with particular problem areas — for example, I couldn’t learn a foreign language). I would be less concerned with spots of misinformation than with evidence of true competence in areas of strength. Survey coureses are extremely valuable, but these should be balanced with seminar-type courses. Math and science seem stuck in survey mode. Moroever, survey courses should not be challenging or frightening. They should be aimed at getting the central ideas of an area. If you want to separate the good or great from the average, have the students focus. This would, hopefully, move school work out of the realm of competition and into the realm of achievement.
Enough fantasy. In the realworld, we have mediocre schools. They fail many of our students, from the bottom to the top of the academic ladder.
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:
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:
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.
Lots of issues are being confused here.
1) Mathematical illiteracy–like scientific, historical, or technological illiteracy–is widespread and as amazingly harmful as the inability to read.
2) 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. In fact, because Algebra is training in the arts of being even more abstract than writing, it is, by FAR, the MOST abused of the mathematical skills. 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. When economists like Veblen, Keynes, and Galbraith wrote in plain English, they were respected. The current crop of econometricians is so reviled, they must hold their meetings behind ranks of armed men.
3) If I could have my say, I would wish that every adult will have learned enough math to:
a) Understand orders of magnitude. Anyone who thinks that drilling in ANWAR will replace imported oil has obviously not learned this basic skill.
b) Understand how polling data is generated. I know statistics can be dreary but without knowing this subject, it is almost impossible to read a newspaper. And since most television newsreaders are also statistically illiterate, they get as excited over statistically meaningless events as significant ones.
c) Understand the reality of compound growth. Anyone who seriously believes that compound growth is possible in a finite biosphere is deranged–or a member in good standing in the economics profession.
Do I really need to point out that compounding is, yes, an ALGEBRAIC concept??
I meant fluid, as in: Marked by facility, especially of expression: easy, effortless, flowing
Resorting to dictionary definitions is so leaf-node, Keith, and we all see how well leaf-node thinking has worked out for a certain chronic blogwhore here. I doubt the rest of us would want to settle for his degree of literalness.
Abstracting a little gets us past the dictionary definition, and into how the words sound together, and how they convey meaning to the listener. Although “fluid” does have the meaning you cited, it doesn’t really work as a predicate adjective.
“He is fluid at math” is klunky at best, and a malapropism at worst. Now, had you said something like:
“The fluid expositions and elegant application of abstract thinking exhibited by the non-college-bound students belie the necessity of algebra as a graduation requirement.”
then the ratio of language errors to words in your post wouldn’t have been high enough to trip my irony alarm.
Seig Heil, baby! :)~
As long as we’re on the topic of how a humanities education is so much more valuable than a math one, let me help you out again here. I believe what you’re trying to communicate is “Sieg Heil, baby!”
I’m actually ok with your sparing me any further Nazi references, though.
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.
Re:
“In my experience, most students who get just-passing scores on multiple-choice tests have learned almost nothing.”
Yes. We shouldn’t fool ourselves that a lot of the passing students have learned much mathematical reasoning either — often they’ll have simply developed mnemonics to get them through the test. Indeed in my experience a lot of students who have passed intro calculus have just memorized a bunch of formulas long enough to pass the test and can’t tell you what it means. Once you turn a subject into a filter, it becomes a mere ordeal for a lot of people.
I may have been the only kid in the U.S. who got instruction in the “new math” when it came out in the mid-1960s and really liked it. Clearly that experiment failed, but its developers tried to start with basic mathematical reasoning and move upward from there, which is not a bad idea.
I’m not sure how you study statistics without algebra. Algebra is simply the use of symbols to stand in for unknown quantities. You don’t even have to be solving for unknowns to be “doing algebra.” I’m sure of wondering how, for instance, you’d explain an application of the normal distribution without having some symbols to stand in for the mean and standard deviation.
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.
Criticizing Cohen is shooting the messenger. Many of you could have taken the same set of basic facts regarding Gabriella and written a more reasoned commentary – so Cohen isn’t the salient point – for me. Nor is it for 90% of his audience.
The point is, Gabriella and many thousands like her exist. When some get up too high on their ‘algebra’ soapbox they are typifying the ‘liberal elite’ image the conservatives have so pervasively and successfully tagged them with.
Consider that most participants on this blog come from a culture of achievement measured against what the prevailing image of academic success means. It just didn’t and doesn’t happen that way for many people.
What motivates Gabriella to learn algebra? Who (probably didn’t) ask her if her homework was done, or dicuss school events with her, everday from pre-school to college freshman?
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!
Interestingly, Cohen is himself sevely dislexic, spelling at an elementary school level, and dictates his columns. See http://www.nldline.com/sally_smith.htm!
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.)
Boy, I should warn all these new people: don’t cross Raven, or she’ll have you flensed and flayed and crawling away wondering how you suddenly lost so much blood.
I’m a little fed up with my attitude being called elitist. I am saying that education is important, and if we did it right, we wouldn’t have people like Gabriela failing very basic fundamentals. Cohen is saying education is unimportant, that people like Gabriela are going to suffer and fail, so leave them alone. You’ve got it wrong: believing in the ability of people to learn and improve themselves is egalitarian, and it’s the defeatists who want to surrender others to the fate of ignorance who are at the core elitist.
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.
As many have pointed out, algebra is everywhere and learning it is useful. Many people have a very difficult time with it, but the solution is not to eliminate math courses.
However, the proffered examples of everyday algebra that we do all the time without realizing it just go to show that the amount of knowledge needed for basic functioning is pretty low. You don’t need to know calculus to count change, or how to find the hypotneuse to make a quiche. Passing an algebra class obviously requires more.
The problem, as a few have noted, has more to do with standardized testing, teaching methods, and our general philosophy of the purpose of education. “Teaching to the test” has removed any possibility of a teacher actually teaching. My mother teaches english to eighth graders (at a failing school); only it would be more accurate to say that she reads lessons to students. Her kids can barely distinguish nouns froms verbs, and, obviously, fail their FCATS. So they repeat a grade and get “taught” the exact same things in the exact same way. Then they fail again. I have no doubt that if they actually let my mother apply all the education she worked for that she could get these kids (mostly) up to speed, but that’s probably not going to happen.
As a counterpoint, I attended what was, at the time, the best high school in my town. Teachers were generally able to teach in any way they saw fit, and yet, in math classes, I encountered the same style of teaching that my mother is forced to use. Maybe it’s because math is so strongly logical that the teachers thought it should be plainly obvious, or maybe math just doesn’t lend itself to a lot of different approaches, but it tended to be taught in a rather authoritarian and unforgiving manner. In fact, it was a lot like foreign language classes—both felt that “total immersion” would somehow lead to me picking them up by osmosis. (For disclosure, I took everything up to and including calculus, and four years of French. Although I was pretty bad at everything except geometry, and the onlly sentence I can cobble together in French is Mon chien est � la plage.) As such, it would have worked just as well if my calculus class had been taught in French.
For all the “math teaches logic” talk, most of the higher levels of it seemed quite anti-logical. Most math teachers started off the new year telling us that, although the way we had learned to do things the previous year worked for that level, they were actually wrong. Consequently, nothing ever seemd to build on what had come before, and a lot of it seemed to contradict it. There never seemed to be any “why”, just “how”. Any question I asked regarding why a certain theorem came to a particular conclusion would just be met with the restatement of the theorem, as if that was answer enough. It truly felt like we were speaking different languages. I had really never thought of the question of “innate abilities” before, but I realize know that we had all, our teachers included, internalized that idea. Math got taught to the few who really “got it” and the rest of us struggled along as best we could.
I’m sure there are a lot of kids who just don’t care or try, and I don’t beleive that all the fault of a failing student can be laid on the teacher, but it’s definately time to rethink or educational system.
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?
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.
“Consequently, nothing ever seemed to build on what had come before” is preeminently what’s wrong with the currently fashionable new-new-math curricula I’ve looked at. Some things, sadly, never seem to change.
“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.
Oh, and it’s absolutely correct that American education is damaged by the idea of innate ability determining success. Yes, there is innate ability, but an early flair for a subject is not a necessary precursor of success in that area. Hard work is what matters, for those with talent as much as those without.
no idea what you’re talking about, PZ; I’m a total pussycat :).
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.
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”).
Richard “Wanker” Cohen, from his article:
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.
Yeah, keep telling yourself that, Richard, but the people I knew that could manage science could also read and write. Pretend that you, Richard, yes, you, have some “talent” at least that these whizzes didn’t have. But I’d have to say that you might have better luck to claim some gift for comedy instead. Or satire. Because as far as persuasive writing goes (much less informative writing), you suck, Mr. Cohen.
Cheers,
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.
Carol:
I was with you 100% until I read Cohen’s column.
Let me amen(d) that: I was with you a thousand percent until I read Cohen’s column. ;-)
Cheers,
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.
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?
That’s Cohen’s line of work, yanno.
I know a guy who did not have a great academic record (although he had a great handlebar moustache) who wound up getting an associates’s degree from a business college, just so he could point to it as “college”. (This being the early 70s, well: ’nuff said about what he really did with his time.)
He took a marketing class, and the professor tried to teach Techniques, and Communication — for all I know, the professor might have worked in algebra. As a class assignment, everybody had to attempt to sell a product to the class. The class had some kids (like the guy I know) who were just marking time, the hairier folks. Others were looking ahead to making money from what they’d learned in marketing 101.
So some students made up pitches for widgets based on price, others brought in real products and made up their own ad campaigns, I think the guy I know told me one guy was an Amway salesman.
When it was his turn, he stood up — utterly and obviously unprepared, he didn’t like the teacher — and pulled a tube of moustache wax out of his pocket. He said, “This is the product I’m going to show you for my marketing project. It works like this” — and he applied it to his moustache, which he did all the time anyway, making these long pointy things sticking out on either side. Half the class was laughing, it was so obvious he hadn’t prepared — and the teacher was scowling, barely controlling himself until the presentation was finished. My guy took his time, grooming himself in front of the class, just to annoy the teacher.
One of the other hairy guys was watching closely, never having seen the wax applied before, so my guy tossed him the tube, and he started to apply it to his own moustache with the little comb, while my guy was making his heavily waxed tips stick up on each side. (He really did look odd in those days.)
So he sits down, and the professor stands up and announces that my guy had just failed the project, and was about to fail the course: the project didn’t do this, as assigned, or that…
and my guy said: wait. I’ve sat here through every other presentation and sales pitch — and I’m the only one that got ANYBODY to actually try the product.
You guys have all tried Cohen’s product: that’s what he’s selling.
—– 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.
[Cohen]: Most of math can now be done by a computer or a calculator.
Oh yes … in Cohen’s raging torrent of bull, I almost missed this nugget. Some of my students come into my class thinking this – that they don’t need to know anything about numbers because their calculators or computers will “do it for them”.
When I TAed sadistics, we were just coming into the age where scientific calculators were ubiquitous amongst students. And in the sadistics class, we allowed calculators even in the exam room. But that wasn’t going to help you one bit, even if you had a fancy model that did auto-S.D. on the “M+” keys…. My rules for grading were: First, pick out the correct type of analysis to be performed, and write down the formula. Plug in the data in the right spot. If, in the end, you didn’t make any arithmetic mistakes (which, barring a finger fumble, you shouldn’t do using a calculator, you get the final 25% or so of the point value. But the meat of the question, in my mind was to understand the problem, and know how to solve it. FWIW, once you know that, then you should be able to “see” almost immediately if you’ve made a gross error in the calculations too, so if perchance you were using a calculator and fat-fingered it, you’re likely to know you made a mistake somewhere. This is something that people ought to learn: If your tax return has your witholdings at $15000, and you’re calculating a $12000 refund, you need to go check to see what went wrong.
Cheers,
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.
I don’t recall bragging about my numerical or literary skills. Though I will say, said skills pay the bills.
anotheranon – i was going for sarcasm, the point was to determine precisely the difference between the ancient greek citizen, and the Revolution-Era American one.
theAmricanist’s definition of citizenship is interesting. For one who doesn’t “give a rat’s ass for the theory involved. The guy who “invents” something is the one who builds it so it WORKS,” 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.
So did the framers “invent” citizenship, or did LBJ? I’m sure if it is the latter, you better be ready to defend yourself against some Europeans who will argue they built citizenship into something that worked pre 1968.
How exactly were Roman citizens and Greek citizens not equal to one another? Sure, not everybody was a citizen, but neither were they at the begining of the Republic. We had to fight a civil war (amongst other things) to get to “all men created equal.”
What is this tribe silliness? At the peak of Athens, there were about 300,000 people in the city. In 1790, at the founding of our republic, Connecticut had 238,000 people; Delaware 59,000; Georgia 83,000; Maryland, 320,000; Massachusetts 379,000; New Hampshire, 142,000; New Jersey, 184,000; New York, 340,000; North Carolina, 394,000; Pennsylvania 484,000; Rhode Island 69,000; South Carolina, 249,000; Virginia 692,000.
I don’t hear any talk of the tribe of Georgians, or Delawarians, or Connecticuti (sp?), Jersians, South Carolinians, or Rhode Islanders, even though those states were smalller than just the city of Athens.
Next, check out Wikipedia on Cleisthenes, whose rule began the Golden Age of Greece
“After this victory Cleisthenes began to reform the government of Athens. He eliminated the four traditional tribes, which were based on family relations and had led to the tyranny in the first place, and organized citizens into ten tribes according to their area of residence (their deme). Most modern historians suppose there were 139 demes (this is still a matter of debate), organized into thirty groups called trittyes (“thirds”), with ten trittyes divided among three regions in each deme (a city region, asty; a coastal region, paralia; and an inland region, mesogeia). He also established legislative bodies run by individuals chosen by lot, rather than kinship or heredity. He reorganized the Boule, created with 400 members under Solon, so that it had 500 members, 50 from each tribe. The court system was re-organized so there were 5000 jurors selected each day, 500 from each tribe. It was the role of the Boule to propose laws to the assembly of voters, who convened in Athens around forty times a year for this purpose. The bills proposed could be rejected, passed or returned for amendments by the assembly.”
so the tribes in Greece were based on location for equal representation in the government – just like our states and their representation in the Senate. Seems awful citizen-like to me.
Also – you cite examples of China and Saudi Arabia – exactly how are they similar to ancient Greece and Rome? Saudis are probably not citizens, because the nation is a kingdom, not a republic, so they are subjects. China is a little different, because it at least claims to be a republic. I agree I wouldn’t want to be a “citizen” there either, but you haven’t convinced me being a citizen of Greece would be much worse than a citizen at the founding, nor have you convinced me I would rather be a “non-citizen” at the founding of the American republic than a “non-citizen” in the Ancient Athenian Republic.
You are right about one thing, though – I am not confused.
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.
All of you self-righteous math whizzes may mock this sentiment
As people pointed out here and on other blogs linked by the Post, if you need to adjust measurements for baking or even figure out how long it will take to drive a 300 mile trip, ***you are using advanced math***.
As for the software engineer.. While admit I use algebra maybe 1% of the time, the times I do need it myself save time, program bloat and processing cycles, not that anyone gives a shit about those last too anymore, which is why every time the HD doubles, so does the size of the software that now runs slower, has only 2-3 new features and takes more system resources to do mostly the same thing it did in the prior version. I am not impressed. The more math you have, the more interesting tricks you can manage to make the software better. It was fairly common practice, for people who had a clue, for example, to replace something like:
if a > b then c = c + 1
if a < b then c = c - 1 with c = c + abs(a > b) – abs(a < b) Its harder to read, but compiled the first one goes like: get a, get b, compare a to b, if a > b then branch, get c, increment c, store c, return
get a, get b, compare a to b, if a < b then branch, get c, decrement c, store c, return This was 24-32 or more processor cycles, depending how the compiler handled the branching. In basic on an apple, this is worse, since its not even compiled, but interpretted, so each step required 4-5 processor cycles *each*. The other one was: get c, get a, get b, compare a to b, if a < b then branch to 1 else if a > b then branch to 2
1: increment c, store c, return
2: decrement c, store c, return
Basically 13 clock cycles “total”. The interpreter would increase that too, but the result would still be a doubling of the speed, or better. Now we have people complaining that the lastest copy of Word runs worse one a 1ghz system than 1.0 did under Windows 3.11 on a 100mhz processor. Hmm… Could it be sloppy design, no one thinking of optimizations and everyone relying on the compiler to magically turn inefficient code into something that will run at blazing speed? Nah!! Of course, the minor irony here is that I recently read an article from someone researching the methods used by scientists to code their own software… Most used vi and console based compilers. Most also had no clue what a IDE was, that things existed to track code collect and track code changes between compiles, etc. There method is almost universally the same as mine was for a long time, throw stuff together and hope it runs. lol But when you have 5-6 people contributing stuff that can break other stuff, this means that most of them spend years just trying to get things to run at all, and failing. I hate trying to code things without an IDE now… :p
Seriously though, I wish I had the patience to do what Carlo DiPietro did and slog through a Calculus book or two. I was actually so good at math I “refused” for almost a year to repeat the same rote assignments in the basic math classes along with the other drone, got sort of held back a bit while the school tried to find every excuse for why I wasn’t doing the work, other than the real one, and ended up jumping about half a grade in a single year while in a class that specilized in actually figuring out what the problems are. I still ended up a year behind the top runners, so never got the chance to take Calculus. Some of my ideas for programming, just for myself, have been derailed precisely “because” I don’t have enough math. But as boring as classes are with teachers running them, trying to study on your own from a book is mind numbing. lol
Ack.. Stupid thing ate my equation..
c = c + abs(a > b) – abs(a < b)
And did it again, even “after” I replaces the less than with the correct html tag… Sigh.. I think you can all guess what it was. :p
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.
Linnaeus wrote:
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.
That was my experience as well. I learned to read when I was two. I wrote my first poem–admittedly, not a very good one–when I was six. All of my early teacher evaluations included the comment, “Talks too much”. 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. Even in college, the courses like “Physics for Poets” were sneered at, reinforcing the idea that real intelligence is mathematical–yeah, we’ll teach you “fuzzies” this in a way you can understand, but it’s not “real math”, so it doesn’t count. Bartkid’s comment that “Algebra (along with other mathematics) is more important than history, not to the exclusion of history, but America will need more mathematicians, engineers, and scientists than historians” is pretty much what I heard in school.
That attitude is just as short-sighted as Cohen’s. The fact that the Bushies can’t do the basic math to figure out that cutting revenue while increasing expenditures is going to cause the debt to increase is a huge problem. So is the fact that they don’t seem to understand that just maybe, one of the big reasons people in the Middle East are skeptical of our promises to spread democracy is because in 1953, the U.S. forced the democratically elected prime minister of Iran out of office and returned the hereditary monarch–the Shah–to power. The complete ignorance of history is directly related to why so many people are wandering around post 9/11 saying, “But I don’t understand why they hate us so much!”
“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.
You look at Cohen’s article and it’s clear he has some compassion for people like that, unlike a majority of posters here.
Ever read King Lear, TexasLib? There’s some interesting stuff in there about the difference between true compassion and pretty lies.
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’
.
Marky,
Let me clarify:
Here’s your original passage:
I see some contradictory sentiments here. On one hand, you argue not only for the primacy of quantitative reasoning, but go on to suggest that “reasoning in the humanities” is actively negative, something with which I disagree, but that’s for another day. You then hedge with the modifier “alone” in your last sentence. That, coupled with your own liking of humanistic subjects suggests that you do see some value in them.
I don’t disagree with the value of quantitative reasoning; I would say that the questions it helps us answer are of a particular kind and that it’s one of many kinds of reasoning that we employ in making all kinds of decisions every day, at every level.
I disagreed with Cohen’s approach, and that much we agree upon. Let’s just be careful not to perpetuate an intellectual divide that doesn’t get us anywhere.
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.
One last post, and then back to work.
Cohen wrote:
Here’s the thing, Gabriela: You will never need to know algebra.
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?
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.
You had me at “breasts.”
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.
Linnaeus,
Thanks for the updated response. I was half tongue-in-cheek anyway, but I disagree on the question of the two culture divide: it definitely exists, and is largely perpetuated by math-hating ignoramuses such as Cohen who believe that one can apprehend the world fully without mathematics. Most academics I know in the sciences are rather cultured, or at least appreciate the value of history, music, literature. If I meet someone who is a writer, my first response is not “Oh, English. I hated that in school. I’m glad someone likes it”. Substitute “math” for “English” and that is what I have heard thousands of times. Let’s not kid ourselves—the hatred of mathematics by many in the humanities exists, and is a combination of jealousy and laziness.
As far as public policy questions goes: Absolutely I agree that a background in humanities and history is helpful, but possibly not essential. On the other hand, I don’t want anyone without an appreciation for quantitative reasoning anywhere near my tax dollars.
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.
Marky:
If I meet someone who is a writer, my first response is not “Oh, English. I hated that in school. I’m glad someone likes it”. Substitute “math” for “English” and that is what I have heard thousands of times.
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?”
Let’s not kid ourselves—the hatred of mathematics by many in the humanities exists, and is a combination of jealousy and laziness.
This is exactly the attitude that reinforces many people’s dislike of math–becing told that if you don’t like it, it’s obviously because you’re jealous of people who do, or you’re lazy.
I know people who don’t like to read for pleasure. I have a hard time understanding that, because reading is so integral to who I am, but I don’t assume that anyone who doesn’t like reading for pleasure is jealous of me because I do, or is too lazy to sit down with a 700-page Tad Williams novel for fun.
As far as public policy questions goes: Absolutely I agree that a background in humanities and history is helpful, but possibly not essential. On the other hand, I don’t want anyone without an appreciation for quantitative reasoning anywhere near my tax dollars.
And I don’t want someone who thinks that the Middle East is where Jesus and oil come from, who doesn’t understand how British Palestine became the state of Israel, trying to promote a “peace plan”. I’m terrified by the fact that the people in charge of the federal budget can’t comprehend why deficit spending is bad–but I’m also terrified of the neocons who apparently missed the part in their history classes where all empires have a finite lifespan.
Yes, we need people with good math skills. We also need people who can communicate effectively, and who are at least familiar with basic science and the history of the world around them. Privileging one discipline over another is a fool’s game from any direction.
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 < (America's Founding + time) = success. 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.
As a ‘math dyslexic’, I actually love math despite how hard I have to struggle to get things straight. The concentration needed even to do relatively simple things wears me out, but I do them anyway. Many times this has resulted in avoiding big problems or finding good solutions.
Here’s the thing; computers can’t “do” math. I use one, yes, and an old slide rule (because it is so hard for me to read numbers without them jumbling up), but computers do not know when to add, subtract, multiply, or divide, or to apply those functions in what order. That’s my job.
Tell kids the truth: “It looks like you are not going to pass algebra. That is going to hurt you and make your life more difficult in ways that might not be completely obvious right now. It doesn’t mean you are a bad person but it can limit you. That’s the truth; just be aware of it and try not to let the world pull a fast one on you.”
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 ;-)
Marky:
Common ground. Good. :)
I don’t want anyone without an appreciation for quantitative reasoning anywhere near my tax dollars.
No argument from me on that one.
I disagree on the question of the two culture divide: it definitely exists, and is largely perpetuated by math-hating ignoramuses such as Cohen who believe that one can apprehend the world fully without mathematics.
It is a reality; I wasn’t disputing that, but saying, rather, that we ought to work against this divide. There’s no reason to think that it helps anyone, whether it’s perpetuated by a Cohen or a Rutherford (“There is physics, and there is stamp collecting.”). We ought to encourage knowlege of all sorts, even with the understanding that some forms of knowledge are more applicable in certain contexts than others.
Darkrose above is expressing very effectively what I’m ultimately trying to get at. I think we’ve all heard negative comments about what we do, its relative value, and what it says about our intelligence. At risk of sounding really banal, we all can’t do the same thing, and society is enriched by people with different interests and talents.
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?
“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.”
?
This may well depend on how you define “thinking”. You are saying there is sort of one unitary process which you can learn and practice in various ways?
“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.”
And up above, if you noticed, I agree with you – up to a point. But past a certain point, you have to start talking about x, baby. At some point you have to use technical terminology and abstract problems. If you’re teaching kids about cloud classification, it might be useful to start off talking about heap, layer, and curl clouds, but if you never go from there to cumulus, stratus and cirrus (and etc.) you’re doing them a disservice.
_________
Hannah:
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.
Right — I think beginning with concrete examples is a fine way to start, but the real value is when students begin to use abstractions. Realizing that that strategy for figuring out how to divvy up the pizza bill is also applicable to calculating your gas mileage is important.
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.)
Kagehi:
Most “scientists” who write programs write extremely simple math-processing things designed to chunk out numbers, and if they format the numbers right, they can feed it into a spreadsheet and let Microsoft Excel graph it for them.
That’s programming, not software development, and doesn’t require the same tools that real software development (you know, mission critical, robust (garbage in, reasonable error message out), acts like a real windows application or a nicely behaving web site with modern features like Ajax and DHTML while still being cross-browser). the comparison is useless.
As for algebra, you didn’t read what I wrote. I wasn’t talking about “if a > b then c = c + 1”.
Yeah, that’s kinda what you get in the early parts of algebra one, but the core of software development and even basic programming is writing functions and actually giving functions meaning by *calling* them. The entire concept of a function call is from Algebra 2 and pre-calculus. Writing functions that take mathematical relationships and reverses them to find the right one, before you’ve actually stuck a number in there, is algebra two. I do it *constantly* in my work.
Taking a series of functions that do string manipulation and figuring out which ones you need to call, in what order, to properly parse out a URL into form variables so that some server-side code can respond to a web request and give back the right answer: that’s *algebra*. Just as one can be abstract with numbers, one can be abstract with variables representing strings and it is still algebra. Its the very essense of what an algebra II class covers.
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.
One thing that I’m surprised I haven’t really seen expressed here is that, while mathematics isn’t a science, it’s the language of science. You can’t really do anything in science without some more-advanced-than-algebra math. Sure, your research may involve quarks or zebrafish, but presenting your data is going to involve advanced math of some sort.
Maybe your average high-school graduate won’t use formal algebra all that often, but I doubt they use the history of the American Revolution or Shakespeare all that often, either. That doesn’t mean these things aren’t important.
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:
[email protected]
Linnaeus,
thanks for a pleasant interchange, for a change:)
Darkrose,
I don’t think I disagree with any of your points, which I have now read thanks to Linnaeus’s recommendation.
If one gives away high school diplomas, then they do become worthless pieces of paper. The value of the diploma lies in the fact that it is supposed to guarantee that the holder has certain minimum competence. Giving a person a pass because they’ve done the time devalues everyone else’s diploma.
Anyway, if the student who flunked algebra is a good writer, then she’s intelligent enough for a good teacher to help her get through the course.
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.
Joe,
You wrote,
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 â but I’m too cynical to believe that will happen very quickly.
I wonder how many people these days have read the gifted educator John Holt (1923-1985)? See here. An excerpt:
Holt eventually decided that schools could not be reformed and spent his remaining years thinking about, supporting, and writing about places where and people from whom children could learn without conventional schooling. Instead of Education: Ways to Help People Do Things Better (Dutton, 1976, Sentient, 2003) called for an underground railroad to help children escape from compulsory schooling, which Holt felt hindered more than helped children’s learning.
It’s a shame that his work, to my knowledge, is not used today to improve schools. One of the things he noted is that the basic form and structure of our schools (the fundamental way we understand how to do education) have not changed in a century or more. Schools are generally big centralized things, not particularly comfortable or pleasant to spend time in, and “learning” takes place in a classroom full of desks in nice rows (or, if you have a radical teacher, a nice circle) with the students aimed at a “teacher” who imparts the learning to the students. The first thing taught to every student is to “sit still and pay attention”; this is the basic lesson for first grade. I guess today students who don’t learn that lesson well get labeled ADHD and get some prescription drug; they used to just be labeled troublesome or stupid and put in the C track.
Where is the science of education? Who is challenging basic assumptions about how we provide educational resources to the next generation?
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.
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?
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.
AndyS: Who is challenging basic assumptions about how we provide educational resources to the next generation?
Actually, some of the problems and the fears of trying to change the system now come from the failures of trying to change it before, and the fact that the current generation of adults who are in the position to change things are the ones most affected by the failures of the past.
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.
Fortunately, teaching elementary ed, she doesn’t need it that much except when having to look at some statistics stuff (and she gets my EE brother or myself (CS) to help her through the vocabulary). So she was very weary of trying new teaching methods as the attempt to try “new” on her failed her completely.
Actually, she is using a relatively new technique for teaching maths to her elementary students, one that better supports the building of skills rather than the rote “practice upon practice” of 3×2 digit multiplication that I was stuck with for 4 years because the school systems had no belief that anybody in elementary could actually grasp more complex concepts from pre-algebra…and again, it is because when “new math” tried to introduce sets and logic to elementary school kids, it failed.
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.
I’ve never had a medical assistant who wasn’t an absolute moron. So, this explains it.
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.
Knowledge means nothing without faith to guide it.
You mean you first take faith in your bible and then decide to let it “guide” your knowledge? That aproach was tried for centuries and was abondoned because it always led to wrong conclusions.
there are plenty of Asian people who are more than capable. But they lack our passion, our wisdom, our soul.
Oh, we Asians don’t have passion and wisdom!!?? Are they qualities only whites have? The bigots in America seem to be starting to come out like roaches now that they think their king has made the world safe for bigots once again.
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.
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”).
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.
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.
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 also said in so many words, “Real-world evidence is for idiots.”
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.
I don’t – I hear “algebra” and see Galois theory and commutative algebra.
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).
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.
You really need to read something about Warren Harding.
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.
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).
Frederick Douglass would have flipped in his grave if only you had any political clout.
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.
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.
Cohen is obviously wrong. Deserting from an army is alright regardless of whether Cohen did it or not.
Look up “dyscalculia.”
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.
Let me guess: the only thing you know about anthropology is the name of the discipline?
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.
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.
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.
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.
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?”).
“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”)?
How many of them have the level of education in the sciences that the math-detractors have in the humanities?
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.”
As opposed to writing?
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.
You either write very convincing satire, or are incredibly moronic.
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.
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.
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.
Golly, ignorance compounded: Anon asks ” What is there to brag about when you were keeping slaves while most of the rest of world had already abolished slavery?”
Ending it ourselves, at great cost.
America is a unique story: historically, geographically, etc. That western Europe had abolished slavery by the 19th century isn’t particularly impressive (Brazil still had ’em after us), since it had never had chattel slavery embedded in its economy that way, f’r instance, South Carolina was founded on it, following the English in Barbados, then later the Danish in the islands. (It’s interesting to note that the first British Empire — us — was largely built on slavery, while the second — the Africa campaigns — was driven by the do-good desire to destroy it.)
Something like 400,000 Union soldiers, many of them immigrants and nearly all of the rest the sons of immigrants, died to abolish American slavery. (This is proven not simply by the historical fact of our war aim to save the Union, but by the overwhelming support the Union army gave to Lincoln’s re-election after the Emancipation Proclamation.) I dunno that I’d be as eager to dis their motivations as some of the posters here — the 48ers didn’t move to Milwaukee to emulate Robespierre or Napoleon.
Citizenship: the American invention.
It’s such leftist, Eurocentric crap to hallucinate that the French, ye Gods! are more important than us to the advance of human freedom.
For one thing, it is flat-out wrong (got that? Zinn is full of shit) that ordinary Americans were somehow duped by the Founders: the new Boss, same as the old Boss? Puh-leeze.
For another, well, we can tell one of the holes in Levy’s education: the Constitution’s ‘tude toward slavery was to KILL it. Without the compromises in the Constitution, we woudn’t have had a country — but don’t kid yourselves, the Convention intentionally gave slavery a generation to die off.
First, the 3/5s clause countered the slaveowners claim that slaves should be counted as population, thus effectively doubling the political power of the slave states like South Carolina. It wasn’t NOT counting slaves (which would have been more honest), but 3/5s was still 40% better than the slaveowners wanted. Second, the slave states knew that IF the Constitution did not prohibit banning the slave trade (the first real immigration law, btw), the free states would have promptly outvoted ’em and banned it in the 1790s, as in fact they did as soon as they got past the one-generation Constitutional ban.
They punted. And they figured they’d have good field position — Washington, who truly was a great man, had a real homely insight, more solid than Jefferson’s hypocrisy: at one point he needed to have the walk at Mount Vernon paved, with only a few weeks to do it. The job should have taken less than a week. Since he was responsible to feed a few dozen workmen anyway (he’d inherited them, after all), naturally he had the guys he was feeding do the job — and it took FOREVER, nothing went right, he was running out of time. So he hired guys from outside to do it, offering them a bonus if they got it done on time: which they did.
So he learned the great economic weakness of slavery: you get what you pay for, based as it is on America’s revolutionary insight: “all men are created equal”.
But the cotton gin changed the economics: a kind of plantation factory system fueled by slave labor became profitable, which nobody anticipated in 1789. With very few exceptions, the Founding generation was embarrassed by slavery. Two generations later, the slaveholders had talked themselves into being proud of it, as the natural order; while abolitionists were willing to risk the survival of the nation to destroy it.
That dynamic would not have been POSSIBLE, without the American invention of citizenship — and there ain’t another nation on earth that did, or ever could have precipitated, much less survived, that self-inflicted upheaval without tyranny. (The closest comparable event was the Tsar freeing the serfs — by imperial edict.)
It’s funny, actually, how folks who pride themselves on abstract reasoning, on the superiority of instruction in algebra as mental training, know so little about American history — and, from that ignorance, have been trained to scoff at its importance.
But, hey: scoffing at algebra is what makes you mad.
Well, you provide a pretty good psychological study, entitled, “The Adverse Effects of Patriotism on the Brain’s Capability of Dealing with Dissonant Information.”
I’m sure that George Washington, at one time the richest man in the colonies, and Patrick Henry, who wasn’t but was fairly close, really wanted to help the common person. I’m sure they had the people’s best interests when they denied them the right to vote, and when they actively sabotaged Rhode Island’s attempt to legislate universal male suffrage. After all, they said so themselves, so it must be true.
Were Paine and Jefferson so important that they count as more than the rest of the Founders combined? And even he didn’t have the sense to free his slaves.
Boy, have attitudes changed since the 19th century… after all, a generation now is 30 years rather than 76. I had no idea people had kids that late back then.
Being so knowledgeable about American history, you obviously know what percentage of the American population over the age of 18 had the right to vote in 1789.
If you think you’re important enough to make me mad, you’re an idiot. At most, you can make me fling your ignorance in your face. I’m about as mad at you as I am at an ant I squash. You have neither the intellectual capacity nor the level of argumentation and writing required to make me treat your posts as anything but a fun exercise at invective.
Citizenship: the American invention.
However many times you repeat that it’s not going to convince anybody.
It’s funny, actually, how folks who pride themselves on abstract reasoning, on the superiority of instruction in algebra as mental training, know so little about American history — and, from that ignorance, have been trained to scoff at its importance.
Not all of us are Americans and for us there are more important and interesting things than worrying about American history. I didn’t see anyone here scoff at teaching and learning history or any other humanties subject. It is you who insists on scoffing at the importance of mathematics learning. And for you American history is “America is the greatest nation. It can do no wrong. America’s founding fathers were almost devine.”
I have a feeling that you are so angry at mathematicians because you failed miserably in maths. You are not very good at history either.
So, what are we teaching our children in public school? How to foist off your personal responsibility by saying “Society abandoned me?”
Children should be taught values and the importance of leadership and initiative. Look at our government right now: we have a president who is certainly not a number-cruncher, but who is certainly a strong leader. Clinton was the opposite. And look at how much better this government has been. Clinton left us with a recession and porous borders that allowed a massive terrorist attack. Now our economy is strong and our nation is safe.
I am sorry if my comments about Asians sounded racist. That is not what I meant — what I meant is that China and India have systems that produce number crunchers while we have a system that produces leaders and innovators. For example, in the Chinese and Indian educational systems, not much emphasis is placed on sports while in the United States sports are one of the most important parts of high school. Sports, especially team sports, help produce strong leaders. You can always import more number crunchers, but more leaders are hard to find.
And when the bill comes due for deficit spending?
What we have now is an illusion of prosperity. And, I might add, an illusion of safety, though it is quite a transparent one.
It amazes me how Bush could say no one saw the New Orleans flood coming when it was predicted by scientists and journalists in excruciating detail, then turn right around and say Clinton was supposed to predict 9/11, which was a deliberately hidden conspiracy.
I want my number cruncher back.
Leonidas, your comment sounds like complete satire again. Bush is a strong leader? The US supports leaders and innovators? You sound as if you’re trying to parody Ann Coulter.
Oh, and decrepitoldfool, I want a number cruncher, period; Clinton was a magician, not in the sense that he could do the impossible, but in the sense that he played tricks on the people. Can you guys please pull Jed Bartlet out of the TV screen and into the real Oval Office?
(grin) You guys are sorta the opposite of intellectual exhibitionists — you flaunt your ignorance in public.
“Were Paine and Jefferson so important”, Levy wonders, that they were, he implies, somehow the ONLY among the Founders, who were embarrassed by slavery?
That literacy thing is a real obstacle for you, huh?
What I said was that with few exceptions, ALL the Founders were embarrassed by slavery. The paragraph which Jefferson drafted for the Declaration which condemned the slave trade as an atrocity forced on the colonies is a pretty fair example — it was only removed because without it, we’d have lost South Carolina and perhaps Virginia, even more maybe, from the original 13.
But NOBODY in the Founding generation’s leadership (except the SC delegation, and then only to delete the paragraph) defended slavery as a positive good. EVERYBODY else publicly stated that slavery was, in Jefferson’s phrase, like ‘holding a wolf by the ears’: supreme folly, nothing to brag about.
The curious thing, of course, is that presumably you don’t misread equations this way. Or do you often divide when you need to multiply, with all that precise thinking algebra teaches?
Likewise, you exhibit rank prejudice: how wealthy Patrick Henry and Washington were, so of course (very Eurocentric and class conscious of you) they couldn’t possibly have had the interests of their “fellow Americans” (nice phrase, that) in mind.
One of the peculiar things about Washington’s character, not easily reduced to equations even for those of us who can keep multiply and divide straight, is that when he was young, what he really wanted was to be a British officer. He also tried damned hard to become unbelieveably wealthy in what was essentially a land scam, before the Revolution, potentially cheating his own soldiers, and finally of course his own initial war record was close to a war crime followed by a desperate failure at Fort Necessity.
So by the time he became an enormously powerful figure, which even then happened only after epic defeats and ordeals, he was quite simply beyond the predictable course of political ambition. European contemporaries simply couldn’t believe that he gave up power to “We, the People” — and of course the American Revolution, BECAUSE we invented real citizenship, had nothing like the bloodbath that followed every other Revolution I can think of: Burr’s duel with Hamilton compares rather well with the Terror. (Try equations with “less than” and “great than”, if it helps.)
Washington’s actions speak to his character as a person in a way that helped form our character as a nation, much the way the humanity of his insight into the cruel folly of slavery helped to form us, in subtle ways that were nevertheless as deep as anything Jefferson did. (Mount Vernon has a slave cemetery, and Washington cared for the humans who were his responsibility until he died, then freed them all. Monticello has no slave cemetery, and Jefferson never freed his slaves: witness Sally Hemings, he wasn’t holding the wolf just by the ears.)
There is an impressive tradition in American politics, much neglected lately, of restraint and self-sacrifice in the cause of freedom, e.g., LBJ giving up the South to Republicans by signing the Voting Rights Act. Because no other nation invented the modern concept of citizenship, you cannot find any prior instances of this political culture (though Washington consciously emulated Cinncinnatus): He resigned command of the Army before winning election to the Presidency, and he set the two-term precedent.
Another sign that folks aren’t good with the whole words and concepts thing because their thinking has been crippled by math, is stuff like this: Levy figures he’s thinking with this “a generation now is 30 years rather than 76…”
The generation which wrote and ratified the Constitution in 1789, was passing out of public life by 1808, e.g., that was the end of Jefferson’s Presidency. Madison, Monroe — these guys were exceptions: the Rule was the complete turnover in the House and Senate. That’s what ‘a generation’ means, the turnover from one set of parents to their children — I wasn’t talking about a cohort, the more precise term for following the guys born around 1740, adults in the Revolution, who were getting on by 1808. The political transition was complete with Jackson, but excepting only the Presidency, it was well underway in Congress, which is what enacted the slave ban — actually in 1819, now that I think on it. I misled you guys that it happened in 1808, and the truth of it (which I had forgotten) proves my point — and, not incidentally, illustrates you don’t know what you’re talking about it.
I suppose math does that to you.
One last point, just cuz it’s so much fun to pick on folks who try to write but can’t read: Anon writes “And for you American history is “America is the greatest nation. It can do no wrong. America’s founding fathers were almost devine.”
Without trying too hard, this is what I actually wrote — I called the Trail of Tears an atrocity, and noted: “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….”
I noted of the late Barbara Jordan that she testified on this point “the promise did not apply universally at first — she noted she was black, and female…”
‘Course, Anon can’t handle precise concepts, so he sorta rounds ’em off down to his level. (Did algebra teach you that?) Like Levy, he figures patriotism is a kind of mental illness, that recognizing the unprecedented engine for good in the world which the United States is, was, and continues to be, is like saying America “can do no wrong..”
To get THERE from what I’ve actually said, well: clearly, for many of you, your capacity to read, write, and think has been damaged by training in algebra.
What REALLY pisses you off was in my first post:
“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.”
Ah, I was wrong: Congress did ban the slave trade in 1808. (The 1819 law is what is usually credited as the first immigration law, a requirement for a list of passengers, which is what confused me: I may be the only one who connects the ban on the slave trade — a an immigration law, refusing to admit folks who were barred from citizenship — with the development of that American invention.)
A dead horse, tenderized.
Still talking about the slave trade? Talk about being stuck in the past. That was 200 year ago. I suppose that somehow you’re going to say it was all George Bush’s fault ;)
What REALLY pisses you off was in my first post:
“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.”
What makes you think I remember what you write?
Leonidas, your comment sounds like complete satire again. Bush is a strong leader? The US supports leaders and innovators? You sound as if you’re trying to parody Ann Coulter.
Unless Leonidas is a dedicated satirist, his blog indicates that he’s entirely serious. He’s not engaging in Coulter Parodied, but Coulter Regurgitated.
Levy asks: “What makes you think I remember what you write?”
That you just quoted it.
Sad that such a mathematically educated person has so little to say that he’s reduced to sneering at what he doesn’t understand.
That you just quoted it.
I remember what I quote. I forget within two minutes of posting, because you’re just too much of a lightweight. There are intelligent religous, patriotic conservatives, who make good points I remember months after debating. You just don’t make the cut. Don’t feel bad: being a debate lightweight and a poor writer is like getting rejected from Harvard.
Unless Leonidas is a dedicated satirist, his blog indicates that he’s entirely serious. He’s not engaging in Coulter Parodied, but Coulter Regurgitated.
Coulter intensified, more likely. One feature of extremists of all kinds is that it’s always possible to find a greater extremist. All the jokes about leftist groups that fight amongst themselves more than against the right stem from this practice; but the extreme right suffers from similar problems (witness the ID vs. YEC schism).
LOL — way to sneer, Alon Levy. Next time, you might try thinking — or even, heaven forfend, being right.
I refuse to believe that Leonidas is not a troll. Nobody can be that stupid. I can’t say that about Americanist though—he’s a garden variety hack who enjoys typing random thoughts onto random blogs.
While I hate to ruin a good hissyfit, and theAmericanist is clearly a smug jingoistic idiot, in this case it’s the UI of the new blog that misled him, not what Alon wrote. So he does have some plausible deniability for that one bit.
He and Alon are talking past each other, because Alon quoted two of his paragraphs, while the blog made it look like Alon quoted one and then wrote one. Then it was off to the races with the misunderstanding.
This new space of yours is nice in some ways, but also very irritating on a couple of different usability levels, PZ.
BTW, nice one about Bushido, Alon :)
Posted by: John Sully:
John, unless you write programs without the use of variables, you use algebra (and algebraic thinking) all the time. As for the calculus, it was used by your university faculty to separate those who could become competent software engineers from those who couldn’t as early as possible (rather than having them fail their Junior-level CS courses). And, you never know, you might need to write a program involving calculus some day. It happens.
Well, he could be Scott Adams in disguise. On this blog, it’s certainly possible. :)
Icelanders were not a tribe, but a settled farming people living in homesteads in the old European manner. They had parliaments and so did many other European people in the middle ages — it was the European way and had had been probably since before the Romans. The novelty was not parliaments, but 17th century absolutism. The Dutch, Genoese, Venetians, and Swiss Republics were carrying on a tradition, as much as innovating.
A twelfth century German official writing to the German Emperor about his nominal “subjects” in North Italy noted that the [formerly German] Lombards [who invaded and settled in Italy at the time of the fall of Rome(fifth century)] had lain aside the bitterness of their barbarous ferocity in consequence, perhaps, of their marriages with the Italians; so that they had children who inherited something of Roman mildness and intellect from their maternal parentage, or from the influence of soil and climate, and retain the elegance of the Latin language and a certain courtesy of manners. They also imitate the activity of the ancient Romans in the management of the cities and in the preservation of the state. Finally, they are so attached to their liberty that, to avoid the insolence of rulers, they prefer to be ruled by consuls [rather] than by princes.
He and Alon are talking past each other, because Alon quoted two of his paragraphs, while the blog made it look like Alon quoted one and then wrote one.
We weren’t talking past each other before?
No, you were talking AT me, or ABOUT me, while I was talking TO you, and to other posters about what you and others had posted. (That literacy thing, again.)
Look, folks: this thread is most thoroughly played, but the point stands: Cohen dissed algebra because the LA school system failed a kid. Our host, and a long series of you, got huffy because, well my goodness, algebra is SOOO important.
No, it’s not. It’s much more important to be able to read, write, think and speak. A sense of compassion, the capacity to overplay toward the concrete rather than the abstract — these are much more important.
In passing, as a f’r instance of what IS important, I noted that America invented citizenship. (I forget if I did it before or after somebody said, hey, the government will come after you if you flunk your taxes, but not if you fail to honor President’s Day. I noted that was PROOF of how important citizenship is.)
It is simply amazing the sheer bigotry a number of you guys exhibited from that point on, in a different but entirely consistent direction than before.
One person posted a definition of citizenship that BEGAN with the obligation that imposes on the individual. (Re-read the Declaration, dude: that literacy thing. Citizenship, that American invention, is not based on what we owe the government.)
And so on. Time and again, the way you guys reacted to what I’ve actually said showed that you simply cannot READ for the actual meaning of the words. I was teasing the first two times, but I’m beginning to wonder if there really isn’t something to the Notion that a mathematical inclination doesn’t train people to fail to get that words can be used more precisely than you guys can evidently handle.
Levy is a pretty fair example.
I’d far rather a kid get out of high school with the skills to recognize that a dictionary definition like ‘a citizen is somebody who owes loyalty’ for the bullshit it is, than a kid who has been taught to repeat rote formulae, whether it’s in math or anthropology.
Evidently, you guys can’t hang with that level of thinking — and, LOL, Levy, just on a point of personal privilege: your invective skills are lame.
But don’t feel badly: lots of folks are educated beyond their intelligence, and we have affirmative action programs for ’em. I’m guessing you’ve benefited from a few.
so define “Think”, ’cause Cohen’s example of “reasoning”, as was pointed out by PZ, was bluntly flawed in 1) using only 1 example as indicative of the norm, and 2) the example wasn’t even relevant as he was talking about writing and presented an example from someone with a lack of geographical knowledge.
one of the things that gets practiced in algebra and geometry is that of knowing when a set of rules for reasoning are taking you in the wrong direction to something that isn’t what you’re aiming for. in other words, it helps with being able to *think* clearly.
…and if you’re “teasing”, put a smiley on it or something. the trouble with posts to Pharyngula are that when some people post garbage, particularly ID proponents, they actually mean it and its really hard to tell the difference sometimes.
“There’s glory for you!”
“I don’t know what you mean by ‘glory,’ ” Alice said.
Humpty Dumpty smiled contemptuously. “Of course you don’ttill I tell you. I meant ‘there’s a nice knock-down argument for you!’ ”
“But ‘glory’ doesn’t mean ‘a nice knock-down argument,’ ” Alice objected.
“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to meanneither more nor less.”
“The question is, ” said Alice, “whether you can make words mean so many different things.”
“The question is,” said Humpty Dumpty. “which is to be masterthat’s all.” –Lewis Carroll
SERIOUS PROBLEM: NOT !!!!!!!!!!!!!
Cohen was not being sexist in any way in this item- !!! had the best response above- this girl is never gonna be a technical person and she now does not have a diploma either. Algebra is a bullshit requirement for all people, just as college is not right for everyone.
What a bunch of frontrunning conforming snob comments this collection represents..
“one of the things that gets practiced in algebra and geometry is that of knowing when a set of rules for reasoning are taking you in the wrong direction to something that isn’t what you’re aiming for…”
That is surely not the most effective way to say it.
Somebody suggested way upthread that if she couldn’t pass algebra, wouldn’t it have helped if she’d been able to take introductory logic, instead? Probably — except the same folks who came up with the algebra requirement, and designed the class, and failed her a half dozen times so she couldn’t graduate, would be the ones running the logic program, too.
I think what you meant in that sorta dense sentence is that a good math class teaches you rules for thinking, which work on their own. If the solution you get using the rules doesn’t work, the problem isn’t with the rules but with the way you applied them. Maybe you didn’t measure something correctly, or you misunderstood the problem — like I noted of somebody above when he couldn’t read the plain words that I wrote, maybe you were dividing when you needed to multiply.
For most folks, I think, that is done more effectively with language than with numbers and symbols, not that I underestimate how difficult and subtle it can be — but mostly for emotional, not logical reasons. This entire thread has been conducted with words, after all.
But look at the errors, and where they’ve come from. (Which is why I used the word “bigotry”.) Some of you guys are just plain obstinate (or anti-American, take your pick) on the historically-obvious American invention of citizenship — but it’s curious to observe how it proves the insight, however provocatively expressed, that’s Cohen’s point.
Somebody quoted CP Snow way up, about how a room full of educated folks might have real trouble if asked what’s the Second Law of Thermodynamics. But if you’d asked ’em what happens when you drop an ice cube into a cup of hot tea, and if that demonstrates something universal, it’s not like most people wouldn’t know what you were talking about.
But if somebody confused that with, I dunno, inertia, or said Einstein had disproved the Second Law, or argued the whole thing depended on Heisenberg, or some damn thing, you guys would rightly be upset with such plain ignorance.
Yet you accept it blithely in words and civics — even as you argue with words about civics.
That’s the meaning of the Alice in Wonderland quote (written, of course, by a guy who made up logic puzzles). Words do have meaning, generally ever more precise ones, when they are used precisely. They sharpen with use. That is, using the word “purple” as if it meants “reification”, is nonsense. (Dodgson loved to write logically correct nonsense.) But using the word “citizen” so it precisely does NOT primarily denote “one who owes loyalty”, is the kind of basic language skill (not to mention knowledge of civics and history) that a good many of you utterly lack.
What do you suppose it says about a mind when it first cites a dictionary to make such an inaccurate and unAmerican claim and second, doesn’t even notice when it’s refuted?
(grin) If I was being mean, I’d suggest it means training in algebra.
It impresses me that folks who are so eager to dis a kid for failing algebra cuz it teaches thinking skills, have so much trouble using the SAME thinking skills when presented with words. It’s as if you all spoke up to say “of course X can mean Not-X, any fool knows that! Only a jingo would say otherwise…”
That’s why I think this thread proves Cohen’s point, as well as a couple others raised in the discussion (at least, among those of us who HAD a discussion, which sorta leaves Levy and a couple others out of it):
1) The way we teach math to teenagers sucks;
2) Lots of folks who DO manage to pass math, know jack about things that are much more important, e.g., the guy who thinks the complexity of the tax code is less significant than political freedom,
3) Lots of folks who brag about their math skills cannot actually read plain English, and exhibit simply astonishing ignorance about civics when they cite dictionaries, or examples which support what they’re objecting to, to prove that they can, too, read.
I could go on, but it makes sense to stop a proof when the propositions are proven. Yet I’d add — I don’t think ANY of those points were raised by folks who kvetched about Cohen’s column: what’s that tell you?
OK, so you don’t like the algebra requirement; we get that. Is there any path back to the point where a high school diploma means anything at all?
BTW all the talk about the jobs you can’t get without knowing algebra misses another important point – math is an important tool for knowing when someone is lying to you. Lies often don’t add up.
Algebra is as much a language as English — that is, both are systems of communication (which presuppose a basic consensus about what words/symbols mean).
Science is also a system, as is music, as many other posters above have remarked.
In a recent issue of the NYReview of books, Charles Rosen writes: “Of all the arts, msic has the greatest kinship with science, even abstract science: Greek and Roman philosophers specualted about the relation of music to mathematics, and in the latter part of the eighteenth century the philosopher and economist Adam Smith remarked that listening to a fine symphony was like contemplating a great scientific system … .” Rosen continues: “A musical system appears to have a logic of its own that can be inflected but not completely controlled by social pressures; it can act as an inspiration to composers, who often feel as if they were discovering, rather than inventing. That is what the greatest of music critics, E. T. A. Hoffman, conveyed when he wrote that Beethoven was not the wild, untamed genius as so many of his contemporaries thought, but the soberest of all composers, because everything he wrote came from the nature of music itself.” (NYR of Books, February 23, 2006, p. 43)
I made another mistake: “the guy who thinks the complexity of the tax code is less significant than political freedom…” is backward, of course.
The last two posts get close to Cohen’s point: it would be a good thing if we could figure out what exactly a more or less universal floor for education should achieve.
Personally, I think it’d be good to aim at a set of basic skills, and turn kids loose armed with a bullshit detector. I’ve never liked the bumpersticker “question authority”, cuz it’s the wrong goal — you want to be able to RECOGNIZE authority, which is harder than it sounds but more productive than “oh, yeah? Sez you!”
One of my favorite ways to teach kids, which works alarmingly well, is to hold up something heavy and something light of roughly the same size (a 12lb medicine ball and a basketball work pretty good), and ask which will hit the floor first. It’s wonderfully counterintuitive (if a little scary that kids can make it to their teens and still fall for it). But I don’t want ’em to draw the lesson to believe rules, I want ’em to draw the lesson that you can test what you think.
Another is one of the oldest tricks in the book, where you ask a class if anybody can spell something complicated, like “pharyngula”. If anybody says “yeah”, challenge them: “Spell it.”
If they don’t start with “i”, they’re wrong. (Lame, but it works: answer the question you’re asked, not the one you’re thinking of.) And of course there are lots of examples in pretty much any day’s news of that sorta misdirection.
I’ve asked kids to say which emotions — happy, sad, angry, etc. — seem to fit which chords: they don’t all agree on majors or 7ths, but for some reason, a minor chord always sounds sad: why is that?
But the fact is, school systems teach to the test, so actual instruction in the skills of thinking, in the scope of things that equip a person for an enhanced life, is undervalued.
There is always a Levy or Anonymous, some guy like the dictionary writer whose primary definition of citizen is somebody who owes loyalty and the legions of those like the posters here who never thought about it, so nobody should be surprised when our schools reflect that.
Which was Cohen’s point writ large, I think.
I made another mistake: “the guy who thinks the complexity of the tax code is less significant than political freedom…” is backward, of course.
The last two posts get close to Cohen’s point: it would be a good thing if we could figure out what exactly a more or less universal floor for education should achieve.
Personally, I think it’d be good to aim at a set of basic skills, and turn kids loose armed with a bullshit detector. I’ve never liked the bumpersticker “question authority”, cuz it’s the wrong goal — you want to be able to RECOGNIZE authority, which is harder than it sounds but more productive than “oh, yeah? Sez you!”
One of my favorite ways to teach kids, which works alarmingly well, is to hold up something heavy and something light of roughly the same size (a 12lb medicine ball and a basketball work pretty good), and ask which will hit the floor first. It’s wonderfully counterintuitive (if a little scary that kids can make it to their teens and still fall for it). But I don’t want ’em to draw the lesson to believe rules, I want ’em to draw the lesson that you can test what you think.
Another is one of the oldest tricks in the book, where you ask a class if anybody can spell something complicated, like “pharyngula”. If anybody says “yeah”, challenge them: “Spell it.”
If they don’t start with “i”, they’re wrong. (Lame, but it works: answer the question you’re asked, not the one you’re thinking of.) And of course there are lots of examples in pretty much any day’s news of that sorta misdirection.
I’ve asked kids to say which emotions — happy, sad, angry, etc. — seem to fit which chords: they don’t all agree on majors or 7ths, but for some reason, a minor chord always sounds sad: why is that?
But the fact is, school systems teach to the test, so actual instruction in the skills of thinking, in the scope of things that equip a person for an enhanced life, is undervalued.
There is always a Levy or Anonymous, some guy like the dictionary writer whose primary definition of citizen is somebody who owes loyalty and the legions of those like the posters here who never thought about it, so nobody should be surprised when our schools reflect that.
Which was Cohen’s point writ large, I think.
I made another mistake: “the guy who thinks the complexity of the tax code is less significant than political freedom…” is backward, of course.
The last two posts get close to Cohen’s point: it would be a good thing if we could figure out what exactly a more or less universal floor for education should achieve.
Personally, I think it’d be good to aim at a set of basic skills, and turn kids loose armed with a bullshit detector. I’ve never liked the bumpersticker “question authority”, cuz it’s the wrong goal — you want to be able to RECOGNIZE authority, which is harder than it sounds but more productive than “oh, yeah? Sez you!”
One of my favorite ways to teach kids, which works alarmingly well, is to hold up something heavy and something light of roughly the same size (a 12lb medicine ball and a basketball work pretty good), and ask which will hit the floor first. It’s wonderfully counterintuitive (if a little scary that kids can make it to their teens and still fall for it). But I don’t want ’em to draw the lesson to believe rules, I want ’em to draw the lesson that you can test what you think.
Another is one of the oldest tricks in the book, where you ask a class if anybody can spell something complicated, like “pharyngula”. If anybody says “yeah”, challenge them: “Spell it.”
If they don’t start with “i”, they’re wrong. (Lame, but it works: answer the question you’re asked, not the one you’re thinking of.) And of course there are lots of examples in pretty much any day’s news of that sorta misdirection.
I’ve asked kids to say which emotions — happy, sad, angry, etc. — seem to fit which chords: they don’t all agree on majors or 7ths, but for some reason, a minor chord always sounds sad: why is that?
But the fact is, school systems teach to the test, so actual instruction in the skills of thinking, in the scope of things that equip a person for an enhanced life, is undervalued.
There is always a Levy or Anonymous, some guy like the dictionary writer whose primary definition of citizen is somebody who owes loyalty and the legions of those like the posters here who never thought about it, so nobody should be surprised when our schools reflect that.
Which was Cohen’s point writ large, I think.
I am a professional scientist who took roughly as many undergraduate hours in history as in science courses (European and American history; I know next to nothing about the history of Asia, unfortunately). When I read for pleasure (rather than work) I generally read history. Want a number? On the GRE verbal exam I was in the 99th %ile. My mother has had careers as a newspaper reporter and as a historian. My father was trained as an electrical engineer, but also knows a great deal about history, and at one point “dropped out” to design and build a harpsichord, from scratch (not from a kit). That instrument is now owned and used for practice and performance at Stanford. All of this is to establish that I’ve spent time living in both of the Two Cultures, that I know more than a bit about the humanities as well as about science and math. So when someone like “Americanist” types*:
———–
“Our host, and a long series of you, got huffy because, well my goodness, algebra is SOOO important.
“No, it’s not. It’s much more important to be able to read, write, think and speak. A sense of compassion, the capacity to overplay toward the concrete rather than the abstract — these are much more important.”
———–
This, like nearly all the “Americanist” has written here, is not an argument but an assertion. It is also a falsely dichotomous steaming load of horseshit. As is “Americanist”‘s contention that:
———–
“Lots of folks who brag about their math skills cannot actually read plain English, and exhibit simply astonishing ignorance about civics when they cite dictionaries, or examples which support what they’re objecting to, to prove that they can, too, read.”
———–
This and similar assertions (ahem) pepper Cohen’s column and the dumber posts to this thread, but are wholly unsupported by (ahem) quantitative evidence. Or, indeed, by any evidence at all. I would suggest the opposite: that mathematical skills are positively correlated with language and reasoning skills. (Because “Americanist” is the one making the original, preposterous claim, let “Americanist’s” dig up supporting data if s/he wants to try prove me wrong.)
One of the reasons that I love working in science is that I am surrounded by smart and interesting people who read a lot, who love history and music and dance and photography and sculpture, who are MUCH more likely than the population at large to be multilingual and up-to-date on current events. In short, these people are ENGAGED. And they also, pretty much every one of ’em, know some, or a lot of, algebra.
Our western cultural heritage includes science and technology, and our way of life depends utterly on the fruits of these disciplines. Hence our culture, our cultural heritage, and our course through history cannot be understood in a serious way without a rudimentary understanding of mathematics and science, and algebra is one of the necessary rudiments.
This does not in any way depreciate the skills of writing and reading. As should be obvious from what I’ve written above, I take those skills rather seriously. Indeed, my very professional survival depends on the ability to write and speak about technical subjects with clarity and precision. But the effort (by Cohen, and “Americanist,” and their allies in the Battle for Ignorance) to deprecate quantitative skills is nothing less than an effort to intellectually disarm other people, to render them helpless when confronted with problems that require analytical tools.
I’d add that I was taught that if a lot of people are misreading what you’ve written, the problem is with the skills of the writer and not the audience. Before “Americanist” attacks this audience again for misunderstanding what s/he’s writtein, s/he might think about that a bit.
* I.e., Truman Capote’s criticism of Tom Wolfe.
‘pologies for the double: the site froze, and I hit twice. (hanging head in shame)
I am a professional scientist who took roughly as many undergraduate hours in history as in science courses (European and American history; I know next to nothing about the history of Asia, unfortunately). When I read for pleasure (rather than work) I generally read history. Want a number? On the GRE verbal exam I was in the 99th %ile. My mother has had careers as a newspaper reporter and as a historian. My father was trained as an electrical engineer, but also knows a great deal about history, and at one point “dropped out” to design and build a harpsichord, from scratch (not from a kit). That instrument is now owned and used for practice and performance at Stanford. All of this is to establish that I’ve spent time living in both of the Two Cultures, that I know more than a bit about the humanities as well as about science and math. So when someone like “Americanist” types*:
———–
“Our host, and a long series of you, got huffy because, well my goodness, algebra is SOOO important.
“No, it’s not. It’s much more important to be able to read, write, think and speak. A sense of compassion, the capacity to overplay toward the concrete rather than the abstract — these are much more important.”
———–
This, like nearly all the “Americanist” has written here, is not an argument but an assertion. It is also a falsely dichotomous steaming load of horseshit. As is “Americanist”‘s contention that:
———–
“Lots of folks who brag about their math skills cannot actually read plain English, and exhibit simply astonishing ignorance about civics when they cite dictionaries, or examples which support what they’re objecting to, to prove that they can, too, read.”
———–
This and similar assertions (ahem) pepper Cohen’s column and the dumber posts to this thread, but are wholly unsupported by (ahem) quantitative evidence. Or, indeed, by any evidence at all. I would suggest the opposite: that mathematical skills are positively correlated with language and reasoning skills. (Because “Americanist” is the one making the original, preposterous claim, let “Americanist’s” dig up supporting data if s/he wants to try prove me wrong.)
One of the reasons that I love working in science is that I am surrounded by smart and interesting people who read a lot, who love history and music and dance and photography and sculpture, who are MUCH more likely than the population at large to be multilingual and up-to-date on current events. In short, these people are ENGAGED. And they also, pretty much every one of ’em, know some, or a lot of, algebra.
Our western cultural heritage includes science and technology, and our way of life depends utterly on the fruits of these disciplines. Hence our culture, our cultural heritage, and our course through history cannot be understood in a serious way without a rudimentary understanding of mathematics and science, and algebra is one of the necessary rudiments.
This does not in any way depreciate the skills of writing and reading. As should be obvious from what I’ve written above, I take those skills rather seriously. Indeed, my very professional survival depends on the ability to write and speak about technical subjects with clarity and precision. But the effort (by Cohen, and “Americanist,” and their allies in the Battle for Ignorance) to deprecate quantitative skills is nothing less than an effort to intellectually disarm other people, to render them helpless when confronted with problems that require analytical tools.
I’d add that I was taught that if a lot of people are misreading what you’ve written, the problem is with the skills of the writer and not the audience. Before “Americanist” attacks this audience again for misunderstanding what s/he’s writtein, s/he might think about that a bit.
* I.e., Truman Capote’s criticism of Tom Wolfe.
Still talking about the slave trade? Talk about being stuck in the past. That was 200 year ago. I suppose that somehow you’re going to say it was all George Bush’s fault ;)
Speaking of innumeracy: Leonidas thinks that 2006-1864 = 200.
Um… well, technically speaking “the slave trade” is generally used to mean the trans-atlantic commerce in humans, which was largely throttled almost exactly 200 years ago, in 1808 when America ended it. (This was a primary issue in the Amistad case, in the 1840s.) I don’t know any general history that uses “the slave trade” to denote anything but trans-atlantic traffic; the commerce in humans WITHIN the United States is more often simply called “slavery”.
Even within the U.S., slavery was not actually abolished by the Emancipation Proclamation (which took effect in 1863, not 1864) but by the 13th amendment, which was not ratified until after the Civil War. Take your pick — you’re either using the wrong term (and are simply wrong), or you don’t know basic, um, quantifiable facts, as you presume to lecture me by exemplifying what you demand that I quantify.
“Lots of folks who brag about their math skills cannot actually read plain English, and exhibit simply astonishing ignorance about civics…”
QED.
BTW, Merz, when you brag about your verbal skills, e.g., “On the GRE verbal exam I was in the 99th %ile…” it helps to use “i.e.” and “e.g.” correctly.
You wrote “someone like” me, and then gave AN EXAMPLE, namely Truman Capote bitching about Tom Wolfe. This is properly denoted with “e.g.”
Had you meant “that is to say”, you could properly use “i.e.,” because that it is what it means, viz., “Lots of folks who brag about their math skills cannot actually read plain English, i.e., Merz boasts he made the 99th percentile in verbal skills yet misuses the language…”
I.e. (that is, “that is,”) was what I meant to write, and it’s what I did write. For that is what Capote said about Wolfe: “That’s not writing. It’s typing.” There were several stylistic errors in my post but I’m not the one who blundered into this forum and immediately began insulting other people’s verbal skills.
By the way, to get the number of years SINCE 1863, the calculation is:
2006 – 1864.
Not 2006-1863. Innumerate fool.
One more thing: I would put the date for the end of the slave trade at the time when the Emanipation Proclaimation was enacted (January 1863, IIRC) since it ended the legal sale, i.e., trading, of said human beings, not when transnational commerce ended. If you are correct that my usage is uncommon among working historians, I’d reply that the common use is, at best, a distasteful example of linguistic imprecision.
Ugh. That’s what I get for posting with a fever, and while agitated. 2006-186THREE. is the number of years since the EP since it was enacted in JANUARY.
What a dumbass am I.
The answers to this post have gotten huge. Personally, I haven’t kept up with them all, simply because I do not have the time.
But, I will say this, in response to those who believe that my idea’s around schooling may be wrong.
1. Parents must instil in their children a respect for their teachers. This is not a blind respect, for as we have seen in PA and OH, it cannot allow itself to be blind.
2. Knowledge is not optional. Even if you have to be dragged kicking and screaming to it, you must learn to absorb, and truly criticize what you are being told is the current state of science. Sorry to say, even in my limited intelligence, ID does not count.
3. Respect for knowledge starts at home. Parents, wake the fuck up. To be crude, just because you can’t add 2+2, it doesn’t mean that your children should be so disadvantaged. As the various fundamentalists are so fond of pointing out, truth cannot be avoided. You can try all you like to come up with creative ways around it, but it will ALWAYS come back. If you truly believe that your God is in charge, why must you contradict HIS laws that you barely understand? The professors that you fight, badly, have a much closer relationship than you will ever have, simply because they pay much closer attention to creation than you ever will.
Enough for this evening, I am going to bed!
I have just seen Roberto Rossellini’s beautiful masterpiece on the life of Descartes, who helped invent modern algebra. I hope this movie will be made available to US audiences with better English subtitles than the version I saw — but whatever the version, it is worth seeing. It is about the struggle to break free of superstition through the use of mathematics and unprejudiced observation.
Rossellini thought that modern men and women were becoming infantalized by the media. And he dedicated himself in his final years to trying to make people aware of the great achievements of humanity through the use of pictures (actually this is a very traditionally Catholic idea) in his case, film. Rossellini had come under the influence of the Czech educational reformer Comenius (1592-1670), who was radically in advance of his time in advocating universal life-long education (including for women and the poor), and was also founder of the Moravian Church (I believe). “In an age when people believed that human beings were born naturally evil and that goodness and knowledge had to be beaten into them, Comenius believed that they were born with a natural craving for knowledge and goodness, and that schools beat it out of them.” Comenus, Grundtvig (founder of the Danish Folk School Movement), and Socrates are arguably the three most important names in the history of education. It is an irony of history that Comenuis was asked to come and teach at Harvard — which now has the reactionary Lawrence Summers as its president.
Just to keep poking Merz on the picked scab of his intellectual ego, “if you are correct that my usage is uncommon among working historians, I’d reply that the common use is, at best, a distasteful example of linguistic imprecision…” is a petulant example of what I’d noted above.
So, much as you dislike it, and you truly did blunder into being correct: you’re arguing on MY side, there, dude.
LOL — if you weren’t arguing with your ego rather than your intellect (but, hey, gotta go with your strong suit), you might have noticed.
I’d have suggested a better example, of course. In fact, I DID.
It was pretty silly cuz so many folks here have difficulty with precision, plus there is a decided streak of anti-Americanism, but the distinction between the proper meaning of “citizen” and the misconception most folks posting here seem to have, proves the point better than ol’ Merz here.
“Citizen” was defined by somebody upthread as one who owes loyalty: when I pointed out this was a crock, it’s sorta revealing as an intellectual honesty reality check, that absolutely NOBODY tried to defend the bogus definition.
Typical of online discourse, y’all just sorta moved on to dispute ever more tertiary stuff, as if the main point wasn’t proven. A mathematical habit, I suppose.
The meaning of citizenship established (as an American invention) in the Declaration and Constitution, strengthened throughout our history, is not an insignificant advance in human events — yet a lot of you guys were eager to misrepresent that meaning in its own right, and to promote the inconsequential as an alternative. (That whole < and > thing.) I dunno as Switzerland, Iceland, or the Lombards, God love ’em, have been much of a model the way the Declaration and U.S. Constitution have been. I don’t recall Ho Chi Minh trying to reverse engineer Thermidor, much less Iceland when he wrote the Vietnamese Declaration of Independence.
Merz, to his embarrassment, is a pretty good example of … something. (I’m being kind.) There is a value to jargon. Folks who have established a mutual understanding of a body of knowledge, like the history of slavery, use terms that can be challenged in their precision, e.g., “the slave trade” so that they don’t have to waste time constantly recalibrating terms. This is intellectually acceptable until it becomes an obstacle to the truth. Dr. Johnson’s line about cant: “You may TALK as people do, but learn to THINK clearly.”
Like I said, I posted here (on purpose, it’s hardly a blunder: you guys’ prejudices are enormously entertaining) because I was amazed that so many folks bragging about how smart they are — hey, the 99th percentile, gee! — missed Cohen’s obvious point: algebra is a TOOL, not the goal.
Merz is a minor classic: the distinction between 200 years and 140 (which is at best his major point), ranks with the distinction between “the slave trade”, as folks generally mean it to refer to the Middle Passage, or his evidently uneducated or misunderstood use of the term for the commerce in humans within the United States. I noted most folks use the term for the Middle Passage — and he (of the 99th percentile!) promptly blustered that “if”, it’s just an example of a common error.
And yet — on the far more significant example of a common error, reflexively imaging that the primary meaning of ‘citizen’ is ‘somebody who owes loyalty…’ (far more the meaning of “subject”), Merz has nothing to say.
Confusing what is unimportant with what is essential, arguing the value of abstract precision while misusing concrete examples: yet more intellectual potential ruined by algebra.
If you lived in Cuba, you’d cite the Cuban Constitution and Fidel’s proclamations as evidence that your country is the freest in the world. Color me unimpressed: I don’t care about what the leaders say they do (e.g. give freedom to all), but about what they do (e.g. throw political dissidents in jail or strip them of their property).
1. Parents must instil in their children a respect for their teachers. This is not a blind respect, for as we have seen in PA and OH, it cannot allow itself to be blind.
Most teachers are so clueless any respect for them is necessarily blind.
2. Knowledge is not optional. Even if you have to be dragged kicking and screaming to it, you must learn to absorb, and truly criticize what you are being told is the current state of science. Sorry to say, even in my limited intelligence, ID does not count.
3. Respect for knowledge starts at home. Parents, wake the fuck up. To be crude, just because you can’t add 2+2, it doesn’t mean that your children should be so disadvantaged. As the various fundamentalists are so fond of pointing out, truth cannot be avoided. You can try all you like to come up with creative ways around it, but it will ALWAYS come back. If you truly believe that your God is in charge, why must you contradict HIS laws that you barely understand? The professors that you fight, badly, have a much closer relationship than you will ever have, simply because they pay much closer attention to creation than you ever will.
Can I sign my name beneath that?
“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.'”
I guess this is called irony. Since I am a mathlete (something I was unaware of), I don’t know if it is irony, but it sure smells like it. TheAmericanist should heed his own advise – my whole statement was:
“theAmricanist’s definition of citizenship is interesting. For one who doesn’t “give a rat’s ass for the theory involved. The guy who “invents” something is the one who builds it so it WORKS,” 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.”
If the point was not clear enough, I will be more explicit (although I have a sinking suspicion you understood the point quite well, and are trying to hide from the consequences). You originally claimed the United States and the framers created the concept of citizen. I stated that the Greeks had citizenship. You stated that you did not consider the Greek and Roman concept of citizenship as true citizenship, because they failed to be inclusive. Apparently, the framers, while not actually implementing the all-inclusiveness, stated that all men are created equal, and thereby created citizenship. However, you also stated the above disdain for “theoretical invention” vs. “building it so it works invention” This seems, to my lowly math mind (again, I was unaware I was a math mind, my bosses will be astonished) to be a bit of an inconsistency (what mathletes may call a “contradiction” – look out, maybe I am a mathlete).
Now, if you want to argue that the framers invented citizenship, even though they did not implement it (theoretical invention), so be it. However, this of course means, if someone, somewhere, before 1776, expounded a theory that all men should be equal (preferably all women, also), then you would undoubtedly concede America could not be said to have invented the citizen, under your own analysis.
This also must logically mean you actually do respect theoretical invention and the above statement about a rodent’s posterior was an aberration.
On the other hand, if you do not approve of theoretical invention, and instead pay it the same concern as the aforementioned rodent’s posterior, then I am inviting you to confront this apparent contradiction. Since, although I am ostensibly just a mathlete, I believe you have conceded the framers did not implement equal rights for everybody at the founding of the republic, you will have to pick a time (let’s call it t’) at which the invention was finally implemented (Patent law would call it “reduced to practice” – i like that) Now, if some other republic happened to reduce citizenship to practice first, then you would undoubtedly concede America could not be said to have invented the citizen, under your own analysis.
Also, while I appreciate your historical discussion, it still fails to help your cause. Your whole point earlier was that Athenian citizenship was incomplete, however you don’t even get to a point (1968) where it can arguably said America reached the summit. Until 1863 (or the passage of the 13th), I fail to see a distinction between the Greek failure to reduce citizenship to practice and the American.
You do seem to have abandoned the “tribe” argument (wise decision) but you do not address the fact that the Swiss had no slaves, brought up by another poster. You can dismiss as historical bullshit the Greeks, Romans, Swiss and the inconsistency of the framers, but that doesn’t prove your point – it just displays intellectual dishonesty.
Also, why do us American Citizens take a “pledge” to the republic if we do not owe any loyalty to it? Why is treason the only crime defined in the Constitution?
What is your definition of citizen?
Nerp, you’re gonna have to work on your reading comprehension, not to mention civics.
I first wrote, in passing: “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.)”
After Nerp failed to grasp this, I made a further distinction: ” The American concept of citizenship was revolutionary: All of us.
But we’re a practical people, and so was our revolution was not theoretical…”
To which Nerp now argues… about theory.
(patiently) The Framers most certainly did “implement” their vision, it’s the country I live in. It’s done rather well, too.
This is American history 101 stuff, Nerp: the American Revolution began with a proposition, that governments don’t grant rights (i.e., citizenship is not primarily about what we owe anybody), but rather are established to protect the rights we’re born with. The national government was established to secure those rights based in part on the contradiction of the Revolutionary proposition, as I noted upthread: without the Declaration, we wouldn’t have had a revolution; with the compromises that contradicted it, we wouldn’t have had a nation.
Granted, it can be hard for folks who managed to MISS this basic stuff to follow it through the mud thrown on the trail, like the guy who insisted contrary to all evidence that the Founders were proud of slavery, when I noted that, with the sole exception of the South Carolina delegation and then only in the debate to eliminate the anti-slavery paragraph Jefferson wrote for the Declaration, they were all EMBARRASSED by it.
But, hey: you guys are all trained in algebra, so you can’t be expected to follow this, um, difficult stuff too well.
The test of an invention, I reminded you guys, is whether it works. I had noted: “it is simply a fact — evidently neglected in your education — that the United States of America invented citizenship. It has Greek and Roman roots, and there are nuances with Venice and Switzerland…” but obviously knowing a root from the main trunk (that’s biological metaphor, for those of you who dunno from algebra or English), much less nuance, is asking too much.
As an example to prove my point, I noted that you might as well claim that DaVinci “invented” the helicopter. There are some way kewl drawings in his notes, but they didn’t fly.
American citizenship not only DOES fly — we taught the world HOW. (Literally, as it happens: the Wright brothers in France, in 1908. It’s not a bad analogy — there were lots of folks TRYING to fly, including the French before Kitty Hawk, and there were some who thought, chauvinistically, that the French were better at it than the Americans in those early days — until they saw Wilbur fly: case closed.)
Since you ask, the modern concept of citizenship (the AMERICAN invention) goes like this: a member of a polity, with natural rights guaranteed by a government over which the polity is sovereign.
If you really want to know more, google up my “Lemon Pledge”, which is a history (actually, the ONLY history, so far as I know) of the Oath of Renunciation and Allegiance, that naturalizing citizens are required to take. (In keeping with that whole greater than, less than thing you math guys have trouble with, the naturalization Oath has considerably more significance in this than “I pledge allegiance to the Flag…”)
“Nerp, you’re gonna have to work on your reading comprehension, not to mention civics.”
I would advise the same to you.
“I first wrote, in passing: “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.)”
After Nerp failed to grasp this,”
I must admit, I’m not sure what that is supposed to mean – I never claimed algebra invented citizenship, so I don’t see what i failed to grasp, nor do I really see the reason for insult. However, it seems to be your preferred way of communicating, so I’ll just let it go. While the algebra discussion on this board is interesting, I honed in on the American invention of citizenship claim, because I found it suspect.
“I made a further distinction: ” The American concept of citizenship was revolutionary: All of us.
But we’re a practical people, and so was our revolution was not theoretical…”
To which Nerp now argues… about theory.
(patiently) The Framers most certainly did “implement” their vision, it’s the country I live in. It’s done rather well, too.”
The revolutionary war was not theoretical. However, the promise contained in the declaration of independence, and internal inconsistencies in the Constitution lead one to believe the framers did not implement their vision, at least in regards to full civil rights for all people. To claim otherwise is either intellectually dishonest, ignorant, or both.
“This is American history 101 stuff, Nerp: the American Revolution began with a proposition, that governments don’t grant rights (i.e., citizenship is not primarily about what we owe anybody), but rather are established to protect the rights we’re born with. The national government was established to secure those rights based in part on the contradiction of the Revolutionary proposition, as I noted upthread: without the Declaration, we wouldn’t have had a revolution; with the compromises that contradicted it, we wouldn’t have had a nation.
Granted, it can be hard for folks who managed to MISS this basic stuff to follow it through the mud thrown on the trail, like the guy who insisted contrary to all evidence that the Founders were proud of slavery, when I noted that, with the sole exception of the South Carolina delegation and then only in the debate to eliminate the anti-slavery paragraph Jefferson wrote for the Declaration, they were all EMBARRASSED by it.
But, hey: you guys are all trained in algebra, so you can’t be expected to follow this, um, difficult stuff too well.”
The insults are just silly, and the substance unresponsive to the question. Also, you miss a couple of important facts – Lexington and Concord were over a year before the signing of the declaration, and Washington had already forced the British out of Boston. The war was on – the declaration did provide a basis for unity and a principled statement, but to claim the war would not have happened save the document is disingenuous.
You are absolutely correct that, morally, most of the framers objected, and had push really come to shove, a substantial majority could have voted to ban it altogether. This still fails to prove the framers “implemented” your vision of citizenship. Quite to the contrary, many framers and founders continued their ownership of slaves.
“The test of an invention, I reminded you guys, is whether it works. I had noted: “it is simply a fact — evidently neglected in your education — that the United States of America invented citizenship. It has Greek and Roman roots, and there are nuances with Venice and Switzerland…” but obviously knowing a root from the main trunk (that’s biological metaphor, for those of you who dunno from algebra or English), much less nuance, is asking too much.
As an example to prove my point, I noted that you might as well claim that DaVinci “invented” the helicopter. There are some way kewl drawings in his notes, but they didn’t fly.
American citizenship not only DOES fly — we taught the world HOW. (Literally, as it happens: the Wright brothers in France, in 1908. It’s not a bad analogy — there were lots of folks TRYING to fly, including the French before Kitty Hawk, and there were some who thought, chauvinistically, that the French were better at it than the Americans in those early days — until they saw Wilbur fly: case closed.)”
This is where your inconsistency shows:
Allow me to try a comparison:
You posit that DaVinci’s theoretical drawings and description of a helicopter does not constitute invention, rather the Wright Brother’s flying of the first airplane (which is very different than a helicopter, but whatever) which made it work, or as I like to say “reduced it to practice,” does constitute invention.
The framers described a citizenry were there was inalienable human rights and equality for all, and though many personally did not believe in slavery, this concept was not reduced to practice until the Civil Rights Act of 1968.
If DaVinci does not get credit, why do the founders? Why doesn’t LBJ and the 90th U.S Congress get credit? Or Wyoming in 1890, which had women’s suffrage when admitted to the union? Or the British and Canadians, who banned slavery in the first decade of the 19th century?
“Since you ask, the modern concept of citizenship (the AMERICAN invention) goes like this: a member of a polity, with natural rights guaranteed by a government over which the polity is sovereign.
If you really want to know more, google up my “Lemon Pledge”, which is a history (actually, the ONLY history, so far as I know) of the Oath of Renunciation and Allegiance, that naturalizing citizens are required to take. (In keeping with that whole greater than, less than thing you math guys have trouble with, the naturalization Oath has considerably more significance in this than “I pledge allegiance to the Flag…”)”
No problem:
“I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by law; that I will perform noncombatant service in the Armed Forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion; so help me God. In acknowledgement whereof I have hereunto affixed my signature.”
Looks like a decent bit of loyalty, obligation, and allegiance in there, and the exclusion of any loyalty to others. Didn’t see anything about the government guaranteeing rights, rather an awful lot of “i’ll do this for my county, i’ll do that.” Also I’d like to point out that the declaration stated all men are endowed with natural rights, not just citizens.
Oh, i forgot – the continental army was also formed, by the Congress, on June 14, 1775, the accepted birthday of the U.S. Army.
yes americans ! do like that guy say, forget mathematical, go on, trash science and education and let European countries replace you in the industrial and technological advances.
thank you.
but,
well, I suppose the too much many smart and educated americans people (girls and boys) will prevent that. so, we will have to be better. :)
It’s bad enough that Meyers is an elitist snob: that “my university” crap really needs to go. I also really like the fact that Meyers is obviously unbiased, just like Cohen. It’s truly wonderful that Meyers owns a weblog, is a college professor, and can easily relate to the situation Cohen described. Obviously.
But what’s even worse is that Meyers refutes none of Cohen’s specific complaint: that algebra has no tangible value outside of academics. Sure, algebra teaches us to think abstractly, but if the girl works at Subway, what incentive does she have to hit the books, especially with an old, rich, white male breathing down her neck?
“Algebra is not about calculating the answer to basic word problems: it’s about symbolic reasoning, the ability to manipulate values by a set of logical rules.”
Wow, could we possibly get more ambiguous? It’s upsetting enough that Meyers thinks he’s somehow better than a journalist whom he disagrees with. It’s even more upsetting that he proves that notion undeniably false.
Nerp, if you’re gonna have me give you lessons in remedial reading, I’m gonna start charging.
1) “to claim the war would not have happened…” without the Declaration. I did no such thing — and ye Gods and little fishes, it’s just stooopid to imagine that I would. I didn’t say “the war”. I said “the Revolution”. Without the Declaration, it was simply a rebellion.
You DO have trouble with literacy, and you don’t seem to know much American history or civics, either.
2) ” You posit that DaVinci’s theoretical drawings and description of a helicopter does not constitute invention, rather the Wright Brother’s flying of the first airplane (which is very different than a helicopter, but whatever) which made it work, or as I like to say “reduced it to practice,” does constitute invention.”
Not exactly. For one thing, I didn’t “posit” anything about da Vinci relating to the Wright Brothers. I noted that if somebody wanted to claim that the Greeks, Romans, Swiss, Icelanders, Venetians or Lombards “invented” citizenship, they might as well claim that da Vinci invented the helicopter. He drew one. It didn’t fly.
LOL — but it’s the “reduced it to practice” notion that is just priceless. I couldn’t have shown you up better, thanks for saving me the trouble. LANGLEY was the guy trying to reduce flight theory to practice: his planes didn’t fly, either.
3) You evidently didn’t read my history of the Oath (that literacy thing), so you got nothing from it. The key in it is the debate between Jefferson and Hamilton’s competing notions of citizenship as something imposed on a person by the government, and the proper definition, the one in our Constitutional law, which (since you asked) I noted denotes membership in a polity, with natural rights guaranteed by a government over which the polity is sovereign.
Since I’ve done that article, a history, and a couple instances of Congressional testimony on the point, I dunno as it’s worth much to keep trying to clarify it for you, but I’ll take one more crack at your thick skull: An individual may be born an American citizen (since the 14th amendment), acquire it from one or both citizen parents, or naturalize. Only a naturalized citizen is required to swear the Oath of Renunciation and Allegiance. The current debate over the Oath is essentially a surrogate for a debate about dual citizenship, about which I’ve written and debated extensively — all lost on you, naturally, since you don’t get the first point: the United States government has NO authority (We, the People never granted it) to remove citizenship from anyone without their consent, once it has been lawfully acquired.
Got that, Nerp? If you are a U.S. citizen, YOU are sovereign, not the government. You don’t have to observe President’s Day, you don’t have to know algebra, you don’t “owe” loyalty, whatever the hell that means.
It’s bad enough that Meyers is an elitist snob: that “my university” crap really needs to go. I also really like the fact that Meyers is obviously unbiased, just like Cohen. It’s truly wonderful that Meyers owns a weblog, is a college professor, and can easily relate to the situation Cohen described. Obviously.
But what’s even worse is that Meyers refutes none of Cohen’s specific complaint: that algebra has no tangible value outside of academics. Sure, algebra teaches us to think abstractly, but if the girl works at Subway, what incentive does she have to hit the books, especially with an old, rich, white male breathing down her neck?
“Algebra is not about calculating the answer to basic word problems: it’s about symbolic reasoning, the ability to manipulate values by a set of logical rules.”
Wow, could we possibly get more ambiguous? It’s upsetting enough that Meyers thinks he’s somehow better than a journalist whom he disagrees with. It’s even more upsetting that he proves that notion undeniably false.
Crap.
PZ, looks like you’ve been infested with a bad case of TheAmericanist.
I’ve seen this happen before, at Orcinus and a couple other places. The TheAmericanist comments multiply and displace other commenters – even attacking them outright – until every single comment thread becomes about TheAmericanist and nothing else.
Spray now, for Cthulhu’s sake! Please!
How about just grading on showing up 5 days a week for five minutes – since there would be no classes.
Too much, OK,let’s just cut reading and writing. Afterall there are computer programs out there that will correct your spelling and grammar. History, chemistry, and biology are out. You can always do a google search. So we’re left with PE, well, let’s cut that, Americans are already getting fat why bother on learning about excercising and keeping a healthy body. Art, music, movies, literature… eh, cliff notes, oh that’s right, you can’t read.
Seriously, I would love to own a business and have all my employees be scared of math… I would tell them I’m paying them $9.13 and hour, and after a 12 hour work day only pay them $108. Don’t worry about the decimals or any time that is overtime (assume 4 hours at 1.5 times base pay). I don’t mind doing the math and realize I’ve gotten an extra $19.82 per employee from them because they don’t know basic algebra.
And my last sarcastic arguement… we’ve been learning Algebra since 3rd grade 3 + [] = 5. [] denotes a shaded box, turn that shaded box into an “x” and you get 3 + x = 5. Good freaking gravy! That’s Algebra.
Not only do we need more math in school we need more word problems. Yes those things most people feared because they couldn’t figure out what was needed and what was just fluff.
Unfortunately, my illiterate self has no money because of my lack of knowledge of American History and civics, so I can’t pay you for your valuable lessons.
I did not read your article, but for someone so literate and knowledgeable, I would have thought you would know it isn’t about my literacy, but rather the fact that I’m not going to waste my time reading your article when you can’t answer the same question I have presented to you throughout this thread.
And you aren’t entirely accurate about loss of citizenship, though it depends on how you define “consent.” Check out 8 USC 1481(a). I do owe loyalty not to take up arms against the US government, among other things. (After all, that is an assault on your fellow citizens).
So, back to the only question that matters.
“If DaVinci does not get credit, why do the founders? Why doesn’t LBJ and the 90th U.S Congress get credit? Or Wyoming in 1890, which had women’s suffrage when admitted to the union? Or the British and Canadians, who banned slavery in the first decade of the 19th century”
You said:
�”Not exactly. For one thing, I didn’t “posit” anything about da Vinci relating to the Wright Brothers. I noted that if somebody wanted to claim that the Greeks, Romans, Swiss, Icelanders, Venetians or Lombards “invented” citizenship, they might as well claim that da Vinci invented the helicopter. He drew one. It didn’t fly.
LOL — but it’s the “reduced it to practice” notion that is just priceless. I couldn’t have shown you up better, thanks for saving me the trouble. LANGLEY was the guy trying to reduce flight theory to practice: his planes didn’t fly, either.”
Of course, through the magic of the scrollbar, we can also see you said:
“As an example to prove my point, I noted that you might as well claim that DaVinci “invented” the helicopter. There are some way kewl drawings in his notes, but they didn’t fly.
American citizenship not only DOES fly — we taught the world HOW. (Literally, as it happens: the Wright brothers in France, in 1908. It’s not a bad analogy — there were lots of folks TRYING to fly, including the French before Kitty Hawk, and there were some who thought, chauvinistically, that the French were better at it than the Americans in those early days — until they saw Wilbur fly: case closed.)”
So, you certainly compared flying (American Citizenship and the Wright Brothers) to not flying (DaVinci and Ancient Greeks). To argue to the contrary is laughable.
Now, this has gotten quite dry. So, you can answer the question, and we can continue the debate, or jump into another invective-filled screed, rambling about everything to avoid discussing the only topic I brought up. If you choose the latter, I would like you to know I shall not respond again, but it surely is not in fear of your “literacy” and vast knowledge of American History you claim to have.
Here’s how I logically see the possibilities of your answer:
1) invention takes place at the theory level, so the framers did invent citizenship when they came up with the idea, though failed to implement it.
2) invention takes place at the time of implementation (or reduction to practice), in which case American citizenship was created in 1968 (or a different time, if you have a good argument for something else, I’m all ears, but certainly not before women had the right to vote (1920, if memory serves))
3) a novel interpretation that explains why you see a difference between DaVinci’s theory that he failed to implement, and the framer’s theory they failed to implement. (this is what I would be really interested to see).
Also, in your response, please address how the framers implemented the concept of the American citizen, when they themselves lamented slavery’s continued existence, and their failure to eradicate it:
“I can only say that there is not a man living who wishes more sincerely than I do to see a plan adopted for the abolition of it [slavery].”
-George Washington, letter to Robert Morris, April 12, 1786
“[M]y opinion against it [slavery] has always been known… [N]ever in my life did I own a slave.”
-John Adams, The Works of John Adams, Second President of the United States (Boston: Little, Brown, and Company, 1854), vol IX pp. 92-93. In a letter to George Churchman and Jacob Lindley on January 24, 1801.
“[W]hy keep alive the question of slavery? It is admitted by all to be a great evil.”
-Charles Carroll, Kate Mason Rowland, Life and Correspondence of Charles Carroll of Carrollton (New York and London: G.P. Putnam’s Sons, 1898), Vol. II, pg. 231.
“As Congress is now to legislate for our extensive territory lately acquired, I pray to Heaven that they …[c]urse not the inhabitants of those regions, and of the United States in general, with a permission to introduce bondage [slavery].”
-John Dickinson, Charles J. Stille, The Life and Times of John Dickinson (Philadelphia: J.B. Lippincott Company, 1898) p. 324.
“That men should pray and fight for their own freedom and yet keep others in slavery is certainly acting a very inconsistent as well as unjust and perhaps impious part.”
-John Jay, Correspondence and Public Papers of John Jay, Henry P. Johnston, editor (New York and London: G.P. Putnam’s Sons, 1891), Vol. III, pp. 168-169. In a letter to Dr. Richard Price on Sep. 27, 1785.
“Christianity, by introducing into Europe the truest principles of humanity, universal benevolence, and brotherly love, had happily abolished civil slavery. Let us who profess the same religion practice its precepts… by agreeing to this duty.”
-Richard Henry Lee, Memoir of the Life of Richard Henry Lee and His Correspondence With the Most Distinguised Men in America and Europe (Philadelphia: H.C. Carey and I. Lea, 1825), Vol. I, pp. 17-19. The first speech of Richard Henry Lee in the House of Burgesses.
“[I]t ought to be considered that national crimes can only be and frequently are punished in this world by national punishments; and that the continuance of the slave trade, and thus giving it a national sanction and encouragement, ought to be considered as justly exposing us to the displeasure and vengeance of Him who is equally Lord of all and who views with equal eye the poor African slave and his American master.”
-Luther Martin, James Madison, The Records of the Federal Convention, Max Farrand, editor (New Haven: Yale University Press, 1911), Vol. III, pg. 211.
“Domestic slavery is repugnant to the principles of Christianity… It is rebellion against the authority of a common Father. It is a practical denial of the extent and efficacy of the death of a common Savior. It is an usurpation of the prerogative of the great Sovereign of the universe who has solemnly claimed an exclusive property in the souls of men.”
-Benjamin Rush, Minutes of the Proceedings of a Convention of Delegates From the Abolition Societies Established in Different Parts of the United States, Assembled at Philadelphia, on the First Day of January, One Thousand Seven Hundred and Ninety-Four… (Philadelphia: Zachariah Poulson, 1794), p. 24. “To the Citizens of the United States.”
“Slavery, or an absolute and unlimited power in the master over life and fortune of the slave, is unauthorized by the common law… The reasons which we sometimes see assigned for the origin and the continuance of slavery appear, when examined to the bottom, to be built upon a false foundation. In the enjoyment of their persons and of their property, the common law protects all.”
-James Wilson, he Works of James Wilson, Robert Green McCloskey, editor (Cambridge, MA: Harvard University Press, 1967), Vol. II, pg. 605.
“It is certainly unlawful to make inroads upon others…and take away their liberty by no better right than superior force.”
-John Witherspoon, The Works of John Witherspoon (Edinburgh: J. Ogle, 1815), p. 81, “Lectures on Moral Philosophy.”
Bigotry is the disease of ignorance, or morbid minds; enthusiasm of the free and buoyant. Education and free discussion are the antidotes of both.”
-Thomas Jefferson, Thomas Jefferson Papers, Library of Congress, Manuscript Division, 1816
“I believe a time will come when an opportunity will be offered to abolish this lamentable evil.”
-Patrick Henry, letter to Robert Pleasants, January 18, 1773
“Nothing is more certainly written in the book of fate than that these people are to be free.”
-Thomas Jefferson, Autobiography, 1821
“[The Convention] thought it wrong to admit in the Constitution the idea that there could be property in men.”
-James Madison, Records of the Convention, August 25, 1787
“We have seen the mere distinction of color made in the most enlightened period of time, a ground of the most oppressive dominion ever exercised by man over man.”
-James Madison, speech at the Constitutional Convention, June 6, 1787
“Every measure of prudence, therefore, ought to be assumed for the eventual total extirpation of slavery from the United States … I have, throughout my whole life, held the practice of slavery in … abhorrence.”
-John Adams, letter to Robert Evans, June 8, 1819
�It is much to be wished that slavery may be abolished. The honour of the States, as well as justice and humanity, in my opinion, loudly call upon them to emancipate these unhappy people. To contend for our own liberty, and to deny that blessing to others, involves an inconsistency not to be excused.”
-John Jay, letter to R. Lushington, March 15, 1786
Another of my wishes is to depend as little as possible on the labour of slaves.
-James Madison, Letter to R. H. Lee, July 17, 1785 (Madison, 1865, I, page 161)
[W]e must deny the fact, that slaves are considered merely as property, and in no respect whatever as persons. The true state of the case is, that they partake of both these qualities: being considered by our laws, in some respects, as persons, and in other respects as property. In being compelled to labor, not for himself, but for a master; in being vendible by one master to another master; and in being subject at all times to be restrained in his liberty and chastised in his body, by the capricious will of another, the slave may appear to be degraded from the human rank, and classed with those irrational animals which fall under the legal denomination of property. In being protected, on the other hand, in his life and in his limbs, against the violence of all others, even the master of his labor and his liberty; and in being punishable himself for all violence committed against others, the slave is no less evidently regarded by the law as a member of the society, not as a part of the irrational creation; as a moral person, not as a mere article of property.
-James Madison, Federalist, no. 54
American citizens are instrumental in carrying on a traffic in enslaved Africans, equally in violation of the laws of humanity and in defiance of those of their own country. The same just and benevolent motives which produced interdiction in force against this criminal conduct will doubtless be felt by Congress in devising further means of suppressing the evil.
-James Madison, State of the Union,1810
It is due to justice; due to humanity; due to truth; due to the sympathies of our nature; in fine, to our character as a people, both abroad and at home, that they should be considered, as much as possible, in the light of human beings, and not as mere property. As such, they are acted on by our laws, and have an interest in our laws. They may be considered as making a part, though a degraded part, of the families to which they belong.
-James Madison, Speech in the Virginia State Convention of 1829-30, on the Question of the Ratio of Representation in the two Branches of the Legislature, December 2, 1829.
Outlets for the freed blacks are alone wanted for the erasure of the blot from our Republican character.
-James Madison, Letter to General La Fayette, February 1, 1830.
[I]f slavery, as a national evil, is to be abolished, and it be just that it be done at the national expense, the amount of the expense is not a paramount consideration.
-James Madison, Letter to Robert J. Evans
In contemplating the pecuniary resources needed for the removal of such a number to so great a distance [freed slaves to Africa], my thoughts and hopes have long been turned to the rich fund presented in the western lands of the nation . . .”
-James Madison, Letter to R. R. Gurley, December 28, 1831.
Chris is right. TheJingoist is something of a pompous ass; can people please let his trolling fester unrequited? Thank you.
sorry, my bad. i got carried away in hoping i could achieve a rational discourse. its sort of like watching a trainwreck – i know i shouldn’t but the urge to look overcomes you.
LOL — I get accused fairly often of making personal attacks, which is a weakness, but I strive to be fair about it. I will note that somebody can’t read, when I am citing an example of something they misread. I generally don’t engage in the kind of ‘we can’t answer his arguments so he must be a troll’ stuff.
Unfair of me, I know. Consider Nerp’s method:
“So, back to the only question that matters.
“If DaVinci does not get credit, why do the founders? Why doesn’t LBJ and the 90th U.S Congress get credit? Or Wyoming in 1890, which had women’s suffrage when admitted to the union? Or the British and Canadians, who banned slavery in the first decade of the 19th century”
Curious how this is somehow the ONLY question that matters to Nerp.
As it happens, I never denied any of ’em credit.(Well, I did note that giving the pre-1776 folks credit for inventing citizenship is like saying da Vinci invented the helicopter: one would THINK sensible people would recognize this would be kind of a disservice to Igor Sikorsky.)
But did I dis LBJ? When?
Let’s test your literacy (not to mention which one of us is a troll), Nerp: show me saying any of the folks you cited don’t deserve credit, between quotation marks.
Hm?
The Wright brothers invented the airplane, hell, they invented flight instruments (a string), but I dunno that anybody would claim they invented even the monoplane, much less the SR-71 or the transponder.
Hell, if you want to talk women’s suffrage, scroll up and read what I noted about the relationship between the 14th and 15th amendments and Jim Crow — which is a helluva lot more important than Wyoming trying desperately to get women to move there.
So it’s pretty simple: you claim to want a dialogue — yet you don’t read what I wrote, nor what I cited. You’re playing to the crowd (such that the four people who bother to read this qualify), and you’re gonna tell yourself what a wonderful thing you did, asking a dumbass question and INSISTING it was important.
Um, why? It was based on misreading what I said: that literacy thing, again.
And — just to clarify matters — if you’d like to read up on how citizenship is lost, kindly consult Gordon, Mailman, and van Loehrer, which is the definitive compendium (the most important case is Meir Kahane): I checked my explication of the issue with the State Department before writing the history of the Oath, , and again with Stan Mailman when I was arguing this with David Tell of the Weekly Standard a few years back, when the Bush administration was arguing your Constitutionally unsound view. They agree with you — the government can TAKE IT AWAY.
So far, the Supremes disagree. And that is what you are arguing for, simply because you cannot imagine you don’t know what you’re tralking about.
That is a failure of imagination — the kind promoted by training in algebra, I guess.
The truth is, I don’t have much against teaching algebra, or logic, in high school: so long as it’s done WELL, which it obviously wasn’t in this case.
What I object to, though, is the kind of bigotry and arrogance in the post, and the rest of this thread.
Do you have ANYTHING constructive to say, Nerp? Or Levy? Or Anonymous?
Methinks you’re much happier talking about how you scored in the 99th percentile, like what’s his name.
Hi PZ. Remember our fun at the sushi restaurant?
This reminds me of my plumber. He was working on my sink and he looked up and asked if I had that day’s newspaper. I did, and thought he was going to use it to protect the floor. Instead, he looked through the events listings.
“There’s a Nobel Prize winner in Physics giving a talk this afternoon,” he said. “I want to make sure to finish up here in time to the get to the talk.”
Now why would Richard Cohen want to deny my plumber the joy of understanding a physics lecture?
Hi PZ. Remember our fun at the sushi restaurant?
This reminds me of my plumber. He was working on my sink and he looked up and asked if I had that day’s newspaper. I did, and thought he was going to use it to protect the floor. Instead, he looked through the events listings.
“There’s a Nobel Prize winner in Physics giving a talk this afternoon,” he said. “I want to make sure to finish up here in time to the get to the talk.”
Now why would Richard Cohen want to deny my plumber the joy of understanding a physics lecture?
That’s what I want to hear more of. In the 19th century, science was very popular among the working class, who not only packed lecture halls to hear people like Huxley talk, but bought up books on the subjects (or rented them: there were subscription services that kept books floating around the country through the mail. NetFlix is an old idea.)
Now why shouldn’t science and math and literature and philosophy be a common hobby, not confined to just a few ivory tower geeks?
The knowledge of both of the Poet and the Man of science is pleasure; but the knowledge of the one [is] … our natural and unalienable inheritance; the other is a personal and individual acquisition, slow to come to us, and by no habitual and direct sympathy connecting us with our fellow-beings. Poetry is the breath and finer spirit of all knowledge; it is the impassioned expression which is in the countenance of all Science. Emphatically may it be said of the Poet, as Shakespeare hath said of man, that he looks before and after. He is the rock of defence for human nature; an upholder and preserver, carrying everywhere with him relationship and love. In spite of difference of soil and climate, of language and manners, of laws and customs: … . If the labours of Men of science should ever create any material revolution, direct or indirect, in our condition …the Poet will … be ready to follow the steps of the Man of science …. The remotest discoveries of the Chemist, the Botanist, or Mineralogist, will be as proper objects of the Poets art as any upon which it can be employed ….If the time should ever come when what is now called science, thus familiarized to men, shall be ready to put on, as it were, a form of flesh and blood, the Poet will lend his divine spirit to aid the transfiguration …. –Wordsworth, Preface to Lyrical Ballads (1800)
kutsuwamushi wrote:
“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.”
Most people have no idea how hard it is to learn languages well. Yes, you would learn a lot by studing three hugely dissimilar languages, but you would learn a lot by taking a double ph.d as well, and it would probably be easier. If you are adults, I estimate that learning to speak my language at approximately the level I speak yours would take you about three years of total immersion.
Forget algebra, learning to speak a foreign language fluently is worthwhile as the hardest mental excercise you ever did.
Do you have ANYTHING constructive to say, Nerp? Or Levy? Or Anonymous?
Yes, I have something constructive to say. The level of discussion will go way up if you shut up and in particular stop repeating the same refuted arguments 500 times.
“Now why shouldn’t science and math and literature and philosophy be a common hobby, not confined to just a few ivory tower geeks?”
Badly phrased (stay away from “shouldn’t” is good advice), but the short answer is: Radio. Television. CD and DVD players.
Perhapst most tellingly of all, PCs.
Some folks would argue that the ‘Net allows for a renewal of that sorta thing, but then: this thread argues against it. There’s a human nature dynamic here that is not encouraging.
It’s the difference between a club, and a community. A club chooses its members — people tend to self-select on the Web, and reinforce each other’s prejudices, e.g., Levy’s notion that anything I’ve said has been refuted, rather than disorted and dissed.
A community cannot choose its members: move in next door to somebody who doesn’t like you, you belong as much as he does. Be the guy who challenges bigotry at a club — you get a chorus of ‘you don’t belong here’.
Literacy — speaking broadly — was narrower, but deeper, a century and a half past. “Society” was more stratified, but the general sense that aiming in the same direction was right was more common: like I said upthread, folks sought to recognize authority more than merely to question it. But it wasn’t really conformity — you guys are much more like Langley than the Wrights.
Elementary and even secondary education was decisively utilitarian — as was raised, and dismissed, upthread. But
most working stiff parlors had a piano, pretty much any half-cultured person could read music and play an instrument. It took more skill to entertain yourself than it does now, e.g., most folks learned Stephen Foster tunes by PLAYING them, rather than listening to somebody famous sing ’em.
Look at what happens to online sites like OLGA, the intellectual property cops.
I used to write about the development of online culture, but I thought it would broaden more. I did predict the intellectual property fight online, but I dunno why I didn’t anticipate the dynamic where the most extreme form of any statement or position is somehow perceived as the most genuine — but you can see it time and again here, in the way Anon, Levy, Nerp, Merz, etc., misread and/or misrepresented what I said.
That discourages folks from what our host hopes to renew, because it encourages them… to divide by multiplying. More clubs, and less of a community.
“‘I don’t want to be there no more,’ she said”… Looks like Gabriela probably failed her English courses too, Richard.
Anyway, I highly resent Cohen’s implication that I automatically don’t know the humanities or social sciences just because I can do even just basic math. Yes, I’m currently working for my B.S. in biochemistry, and just recently picked up a math minor, but I’m also currently frustrated with the classes in Japanese, my other minor, that are moving at a pace far below what I’d like (this at a fairly top-tier university, no less), and planning on taking both semesters of first-year Arabic over the summer. So I decided to take organic chemistry in high school rather than, say, his beloved typing? Big deal.
Besides, when I get to grad school for forensic science, I’m going to have to understand law just as much as chemistry. And when I’m doing firearms analyses in the homicide investigations of people like Gabriela, accidentally caught in the crossfire of gang wars in the ghetto, or tox screens in the investigations of the deaths of gang members themselves – people who got stuck with nothing because they didn’t learn the basic skills to get a job that actually provides enough to live on (which, don’t get me wrong, I’m not blaming on the students themselves, at least not entirely – the school system is probably at least as much at fault for not teaching the material in a way they could understand)… I’ll know that I couldn’t have gotten there without everything elementary, middle, and high school taught me. Including algebra.
Did you ever think to yourself: “I have 50$ in my pocket, I wonder how many such-and-such I can buy with that”? If you figured it out, then you used *elementary* algebra.
As with so many others who moved into journalism because they were too inept for medicine, too inarticulate for law, and too lazy and arrogant for food service, Richard Cohen demonstrates that the one thing that would make American journalism better is a series of grants paying newspaper columnists and editors to drink themselves to death. (He said with decided self-loathing, having wasted 13 years of his life as a magazine and weekly newspaper writer before coming to his senses and quitting.)
Where can I find those Jefferson remarks, PZ? I’m in high school, writing a speech on innumeracy, and I’d like the source URL for citation purposes. Thanks so much.
Here’s a site with many Jefferson quotes, and their sources.
Cohen is asking Gabriela to forfeit a career as a waitress, an artist, engineer, scientist, project manager (or any other kind), journalist (or rather COMPETENT journalist), plumber, cook, or salesperson – not to mention denying her an informed vote in public policy, as all kinds of math, especially probability and, yes, algebra, are involved. What kind of compassion is that? Sympathy is nice, but knowingly giving her bad advice – and it IS knowingly: he published another anti-math article 20 years ago and got plenty of replies – is most certainly not. So is using her story as an outlet for his own math anxiety. Of course, maybe I’m giving him too much credit – he may not have understood any of those irate messages.
kutsuwamushi:
Jefferson was talking about the languages of countries considered advanced and civilized at the time by Europe and America/the colonies (I don’t know whether this was before or after the Revolution). This was what was needed to understand civilized people. Now, of course, other languages, such as Chinese, Japanese and Arabic, are just as useful as Jefferson’s big three.
Joe Trotter, you wrote:
‘It’s bad enough that Meyers is an elitist snob: that “my university” crap really needs to go. I also really like the fact that Meyers is obviously unbiased, just like Cohen. It’s truly wonderful that Meyers owns a weblog, is a college professor, and can easily relate to the situation Cohen described. Obviously.’
Meyers could have written the same “crap” as a college student – hardly an elitist, snobbish position. Are you really going to set his personality in stone because of a few words? And although Meyer’s viewpoint is admittedly not suited to empathize with Gabriela’s troubles, he can disparage Cohen’s advice as well as anyone else. Furthermore, the numerous comments posted here agreeing with PZ makes his point more plausible. Or are you talking about Cohen’s own troubles in high school? In that case, could you please clear that up?
On to the next paragraph:
‘But what’s even worse is that Meyers refutes none of Cohen’s specific complaint: that algebra has no tangible value outside of academics. Sure, algebra teaches us to think abstractly, but if the girl works at Subway, what incentive does she have to hit the books, especially with an old, rich, white male breathing down her neck?’
PZ’s point seems more to be that she works at Subway because she didn’t hit the books, not the other way around. Also, as several commenters have noted, having not learned algebra, she can’t get a better job anyway. And Cohen is the only person breathing down her neck in this instance, unless she happens to come to this web page.
Your conclusion:
“Algebra is not about calculating the answer to basic word problems: it’s about symbolic reasoning, the ability to manipulate values by a set of logical rules.”
Wow, could we possibly get more ambiguous? It’s upsetting enough that Meyers thinks he’s somehow better than a journalist whom he disagrees with. It’s even more upsetting that he proves that notion undeniably false.’
Again, it seems that Meyers’ point is that it IS ambiguous, or to use a better term, general. Although my viewpoint is somewhat limited (see my first post, above), I see that sentence as showing that algebra doesn’t just give you facility with manipulating numbers, but rather helps you manipulate ANYTHING, making it something you’d want to learn.
No intent to offend, just making a few points here.
I didn’t say “the war”. I said “the Revolution”. Without the Declaration, it was simply a rebellion.
You know, I was going to pull out my classicist brass knuckles to try and thwap this guy around a little, but this convinced me that he’s not worth the time. If you’re talking about the American Revolutionary War, and you refer to “The Revolution”, it is perfectly reasonable to for a reader to assume that you mean the ACTUAL WAR. Just because someone doesn’t pick up on your ridiculous hair-splitting doesn’t mean they’re illiterate, you pedantic douchebag. That goes double for people who are trying to argue a different conclusion than you.
I may not know much about math, but I know a disingenous argument when I see one.
When dealing with people like the algephobic Cohen, I find a handy distinction in English usage is to differentiate between ordinary ignorance – from which we all suffer in some sphere of knowledge or other – and pitiable pig-ignorance. The latter spawns gobshite, such as my personal favourite,”Why learn French. English was good enough for Jesus”.
Cohen will never learn algebra because of his pig-ignorance. To do so would feel to him like letting himself down.
What a dipshit that Cohen.
I can’t believe no one in that school was able to get that poor girl a tutor. If I lived in LA I’d tutor her myself, since I have worked as an algebra tutor. Oh yeah, I’m also a singer.
This country is really going down the toilet.
I’m a mathematican who has studied topology for a long time and i have to say PZ Myers is an intolerent biggot.
oh and a true intellectual snob also.
Lrg prdcts whlsl sl, prvds cstmrs dmnd