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Tilting at Windmills

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February 17, 2006
By: Kevin Drum

MORE ALGEBRA....Jeanne weighs in on the great algebra debate:

There are lots of skills and talents I lack, and at this point in my life if God were to offer me just one of the ones I don't have, I think I'd take the ability to sing or play an instrument over the ability to do math. I've listened to great singers and ached for something other than a thin, off-key whisper to come out of my throat. Just ached for it.

In my entire life, I've never felt that way about algebra.

Well, no, I don't suppose many people do. I suspect that even most mathophiles think of algebra as sort of the 1-ton pickup truck of mathematics handy for getting things done around the house, but hardly something to feel sentimental about.

On the other hand, you have to understand algebra in order to learn calculus, and calculus is achingly beautiful. Given the way my life has turned out, knowing calculus does me no practical good at all, but it's one of the great inventions of mankind and certainly one of our most elegant and breathtaking. My life would be less rich if I didn't know it.

But then again, my life would be less rich if I had to jettison nearly any of the knowledge I've accumulated so far and most of it, like algebra, isn't really of very much practical use to me. If I could trade calculus for a working knowledge of French, I suppose I might take the deal. But I'd never be sure if I'd made the right decision.

Kevin Drum 6:37 PM Permalink | Trackbacks | Comments (163)

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Comments

I sing *and* do math. Why not learn both?

Posted by: Archie on February 17, 2006 at 6:41 PM | PERMALINK

Tough call. Guess I'd take Calculus over a foreign language.

But I'd trade all my literature knowledge for fluency in a couple languages, maybe Mandarin and Spanish.

Posted by: luci on February 17, 2006 at 6:43 PM | PERMALINK

I do agree with your comment about calculus,I took it in high school but didn't appreciate it until I took it again in college as a background for econometrics.

Posted by: TJM on February 17, 2006 at 6:45 PM | PERMALINK

Boy, you can't argue with "reasoning" like that. *rolls eyes*

I sure wish I could ski the Olympic downhill and win. Maybe they should have taught me that instead of algebra.

Posted by: teece on February 17, 2006 at 6:45 PM | PERMALINK

Wouldn't trade the knowledge I have for anything in the world but am damn glad I dropped out of learning pythagorean theorum and took general math as a sophomore considering it was in general math I learned about budgeting, balancing a check book and other useful skills.

Algebra was fun, geometry to the extent they taught it for NY schools and the regents exams, not so much.

Posted by: Dreggas on February 17, 2006 at 6:47 PM | PERMALINK

I don't know about algebra, but I do know that many of those professional who are skilled in the highest mathematics, someplace I'll never be, feel about it like musicians feel about music.

Posted by: tbrosz on February 17, 2006 at 6:48 PM | PERMALINK

From my experience in a chemistry graduate program the American students generally start significantly behind in terms of their math background. That being said, the American students also lack the often meager foreign language proficiency that the foreign students posess. While one might wish to be able to trade one for the other, students from other countries seem to have both.

Posted by: Apot on February 17, 2006 at 6:48 PM | PERMALINK

"knowing calculus does me no practical good at all,"

Knowing calculus can help you think more clearly about everyday things like driving speeds and mortgage rates. Practical good isn't always a direct application of rules, it can be a mind that works better.


"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." Robert A. Heinlein

Posted by: Archie on February 17, 2006 at 6:48 PM | PERMALINK

Calculus was not "invented". It was discovered.

C'mon Kev - I know you're a mathematical Platonist at heart!

Cyclic algebras rule.

Posted by: banachspace on February 17, 2006 at 6:52 PM | PERMALINK

I was at a meeting once about how to value a lawsuit for settlement. One lawyer said, "we have five different defenses. The first has a 40% chance of success, the next a 30% chance, the next a 25% chance, the next a 10% chance, the next a 5%chance- so we have a 110% chance of winning this case!! Oh, wait--"

You laugh. But do you know how to solve a problem like this? I see decisions involving tens of millions of dollars - literally - being made by people who don't know how to solve problems like this. And worse yet, they don't even understand that problems like this are solvable.

Posted by: JR on February 17, 2006 at 6:52 PM | PERMALINK

Well, I took up to third semester calc in college, getting A's and B's, and I have to say I don't share Kevin's adoration of it.

I mean, yeah, I thought it was waaaay more interesting than, say, geometry, but honestly, I think most of the useful concepts in calc could have been covered in about a week. That derivatives are instantaneous rates of change. That integrals are areas under curves. How series and transforms are useful.

But learning tricks and strategies and procedures about how to do difficult integrals is of use only if you're going to have to do difficult integrals. Otherwise, it's wasted time, frankly, and boring wasted time at that.

Now algebra- yes, boring... but a good working grasp of algebra is so useful in real life that it is something I have always been grateful for.

Posted by: pdq on February 17, 2006 at 6:53 PM | PERMALINK

I, for one, wish I had a pony.

Oh, and I also wish that we would rename "algebra" and call it "Freedom Math." Get your dirty linguistic roots off our language, A-Rabs!

Posted by: The Confidence Man on February 17, 2006 at 6:55 PM | PERMALINK

This all sounds like a false dichotomty to me. How about if we get rid of some of the real dreck in the curriculum? Like, why were my kids taught the metric system 5 times from grade 6 through 12 -- 3 in science, 2 in math? Not just reviewing it, but teaching it as if the kids had never seen it before? And how about 1000 precious grade 3-5 class hours of penmanship? How about replacing that with 20 hours to learn to sign your name, 200 hours of blueprint drawing, 200 hours of orthographic projection, 200 hours of drawing from life and rendering, and use the rest for algebra and foreign language?

I'll bet anyone with kids in a medium-to-good school can tell the same horror story.

Posted by: miriamsong on February 17, 2006 at 6:55 PM | PERMALINK

Algebra and Geometry, two of the most infuencial classes in my life. I sucked at them. Hell, I even hated them. But to this day my visual thinking is greatly improved because of geometry. And even though I couldn't tell you anything I was taught about algebra, I do know that my ability to pick up simple HTML and CSS coding was in some part made possible because of my education in algebra.

It really is about critical thinking and problem solving. Mathmatics is one of the best ways of exercising the brain to do just that.

Posted by: Rook on February 17, 2006 at 6:55 PM | PERMALINK

I still remember the day my Calculus teacher delivered the lecture on the Fundamental Theorem of Calculus. He was a rather large and normally staid man whose most prominent expressive outlet was the rotation of corduroy pants he'd been following for years (brown on Monday and Friday, tan on Tuesday, navy on Wednesday, and Grey on Thursday). But on this day, the only day he ever kept us overtime, he was positively boistrous. As he progress through the steps in the theorem, he kept repeating, "but that's not the big thing!" When he finally got to the end (finding the area under a curve by adding up the volume of an infinite number of rectangles fitting within it), he was visibly sweating, and shouted, "and that's the BIG THING!!! (deep breaths) Class dismissed." Of course, at the time, it was all I could do to keep from laughing at his unbridled enthusiasm. But now, I agree with Kevin (and Mr. Platt). It really is a wonder to contemplate.

Posted by: pickabone on February 17, 2006 at 6:57 PM | PERMALINK

Calculus is bullshit, but you people are just too stupid to realize it.

Posted by: I. Newton on February 17, 2006 at 6:57 PM | PERMALINK

And I wonder how she feels about the fact that her inablity to do algebra has likely cost her thousands of dollars over her lifetime due to poor financial decision-making?

Posted by: MattW on February 17, 2006 at 6:58 PM | PERMALINK

I liked algebra and math in general just wasn't big on some of the more higher level (arcane) math, being able to do algebra helped me excel in software development as did being able to do logic real well.

Posted by: Dreggas on February 17, 2006 at 6:59 PM | PERMALINK

miriamsong:

How about if we get rid of some of the real dreck in the curriculum?

I agree 100%!

Kids have _so_ much they actually need to learn these days, some of the stuff we have them waste long hours on (because we did it when we were kids, or "it'll be good for them") is positively criminal.

Posted by: pdq on February 17, 2006 at 6:59 PM | PERMALINK

Kevin: If I could trade calculus for a working knowledge of French, I suppose I might take the deal. But I'd never be sure if I'd made the right decision.

Believe me, you would have made the right decision. I know nothing about Algebra. I was awful at math. But you know something, I can speak French, Italian and German -- can even manage some Latin -- and believe me, I wouldn't trade that for all the numbers in the world.

Posted by: Humanist on February 17, 2006 at 7:01 PM | PERMALINK

Multiple questions are being conflated here.

1. Should Algebra be a requirement for graduation from High School?

2. Is Algebra useful in real life?

3. Is Algebra something you would like to learn as opposed to say finger painting or burrito cooking?

The answer to (1) does not necessarily depend on the answers to the other two questions. The second and third questions are in a sense idiotic, because (a) not every field of study is of use to every body in real life all the time and (b) whether you would like to learn Algebra or Sitar is your own choice.

I think whether or not you should be required to have a proficiency in Algebra should be answered by using the same criteria that are used to decide whether it is enough for you to just be able to read when you graduate or you should be able to read with understanding.

Posted by: lib on February 17, 2006 at 7:01 PM | PERMALINK

I just wrapped up writing math mid-year reports for some 5th graders.

Everyday I try and convince them that math is a hidden language for us all to discover. Some of us have an easier time of it than others. Yet this does not negate the fact that manipulating numbers and substituting letters for such reveals an infinite language that's all around us.

It's up to the individual to explore this hidden language.

Those who shrug off basic mathematical reasoning do so at their own peril.

Haven't we had enough of Bush's "fuzzy math?"

Or... X + Bush = Executive Branch, where X = Cheney. Executive Branch- Bush = Cheney.

Math is power.

Posted by: Tom Nicholson on February 17, 2006 at 7:02 PM | PERMALINK

There is actually an answer to this question, and it hinges on whether it is possible to progress through a decent science curriculum (say introductory physics, chemistry, and biology) without algebra or calculus.

Having made it through both, but not on to higher levels of science, it seems there should be an answer.

In an era when significant numbers of people are so obviously confused about basic science, so much so that they actually vote to suppress scientific knowledge, its asinine in the extreme to propose cutting back on math (which I assume, perhaps wrongly, is a building block for the advanced sciences), WITH THE ONLY EXCEPTION BEING IF CUTTING BACK ON ALGEBRA RESULTED IN MORE HOURS DEVOTED TO SCIENCE.

Posted by: hank on February 17, 2006 at 7:04 PM | PERMALINK

In your earlier post, you asked "if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?

I think this really is, or should be, a question of what a high school diploma should stand for, what it should mean.

IMO HS diplomas won't mean much until employers start asking to see them and/or high school transcripts. Every employer, whether it's McDonald's hiring you for a part time burger-flipping job or Microsoft hiring you to be a VP, should ask to see your academic transcripts, starting with high school.

If employers started doing that, high school diplomas would mean something.

Posted by: G. Jones on February 17, 2006 at 7:06 PM | PERMALINK

My nephew got his degree in computer engineering recently, with a math minor. He got exactly one job offer. The US government, Naval Weapons Research. The government needs folks who can get security clearances whoknow math and engineering and are stuck taking low paying gov jobs because there's no demand for their skills in the private sector. The whole thing is a giant con job.

Posted by: John West on February 17, 2006 at 7:06 PM | PERMALINK

Cutting back on math would greatly hinder any and all advancement into higher science, math is a science (or theory or whatever) not just a skill in many cases, everything we know about life, the universe and everything has a basis in our ability to use logic, reason and mathematics to perform calculations.

Posted by: dreggas on February 17, 2006 at 7:07 PM | PERMALINK

There was a cover story in Scientific American a few years back about how the Japanese discovered Calculus a few decades before anyone in the West. It was considered a sacred intellectual pursuit, and particularly fine examples (like a method to integrate a circle using circles) were inscribed on wooden tablets and hung in buddhist temples as offerings to the gods (and intellectual challenges for mere mortals).
It is no wonder that Japanese students' math and science scores routinely exceed American scores.

Posted by: charlie don't surf on February 17, 2006 at 7:07 PM | PERMALINK

Yeah, let's celebrate Algebra Hatred Day.
GRRRR

Posted by: marky on February 17, 2006 at 7:10 PM | PERMALINK

I took no math courses in college. Big mistake. I recommend highly to any considering a career in law, that they take science and math courses as a way to obtain reasoning skills that will stand you in good stead in law school.

Posted by: moe99 on February 17, 2006 at 7:11 PM | PERMALINK

I. Newton:

Calculus is bullshit, but you people are just too stupid to realize it.

Ooohh, big talk from an alchemist.

Posted by: tbrosz on February 17, 2006 at 7:14 PM | PERMALINK

New American motto:

"The less you know, the better!"

Americans luuuuuuv their stupidity...

Posted by: cdj on February 17, 2006 at 7:14 PM | PERMALINK

Wow. What about the ability to think clearly? Does anyone think that's useful? It seems to me that a large part of math is the ability to see relevant patterns, and come to sensible conclusions about them. I would really hesitate before I traded that in for the ability to impress my friends. I suppose that people who don't have this ability are blissfully unaware of what they are missing. Its like hearing a foreign language - you are aware of sounds, but no picture emerges from them.

Posted by: Mike on February 17, 2006 at 7:14 PM | PERMALINK

What, no more whining about Cheney's shooting accident???

I take that as an admission that Kevin Drum and the other Moonbats conceed they acted like hysterical children. Once again.

Posted by: MountainDan on February 17, 2006 at 7:14 PM | PERMALINK

Calculus really was devine. I kinda liked math before that, but calculus was where I saw how reality was described by math (I was taking physics at the same time). Then I got to differential equations - just like algebra; useful and tedious. So much for the glory of math.

Posted by: EmmaAnne on February 17, 2006 at 7:15 PM | PERMALINK

banachspace -

And it was invented.

Posted by: cdj on February 17, 2006 at 7:15 PM | PERMALINK

These algebra threads are funny.

Mathophiles vs. Mathophobes (no egocentricism though).

Humanist: But you know something, I can speak French, Italian and German -- can even manage some Latin -- and believe me, I wouldn't trade that for all the numbers in the world.

Bah, if they don't speak the American language they ain't worth talkin' to.

By contrast, proficiency in ODE's (ordinary differential equations) should be a requirement for graduation from grammar school.

Posted by: alex on February 17, 2006 at 7:15 PM | PERMALINK

"Welcome to America - where ignorance truly is bliss!"

lol - ok, I'm done now.

Posted by: cdj on February 17, 2006 at 7:18 PM | PERMALINK

Looking back at my misspent youth, I wish I'd applied myself more to math and algebra. Although I have a liberal arts degree (for which I am extremely grateful) I believe I would have had more career choices open to me with a solid background in mathematics.
Anyway at, least, I can do percentages.

Posted by: KJJG on February 17, 2006 at 7:18 PM | PERMALINK

Have you ever ached for the ability to take the concept A, apply the process Z, and know the result?

Outside of the fact that algebra is used all the time (do you people never leave tips, set deadlines, or buy groceries?), it's the first introduction children get to abstract formal reasoning, and usually the most solid introduction.

And anyone who doesn't "get" abstract formal reasoning will go through live a mental cripple, permanently confused and unaware of the world around them. And that's just if they never attend college -- which usually requires algebra -- or, heaven forbid, enter any professional or academic career.

Maybe this all explains how we can live in a world where 2 + 2 = "4" is fuzzy math but 2 + 3 = "something less than four if four is really an important number which it's not because we never said four but it's definitely more than four unless it's less."

Posted by: Max on February 17, 2006 at 7:19 PM | PERMALINK

For those who find Calculus beautiful, I would suggest a book on Differential Geometry. Pure ecstasy.

Posted by: lib on February 17, 2006 at 7:19 PM | PERMALINK

Kevin quotes Jeanne: I've listened to great singers and ached for something other than a thin, off-key whisper to come out of my throat. Just ached for it.

"Great" singing may be a gift, but good singing can be learned like any other physical skill. Stop aching, find a good voice teacher, and start singing.

Posted by: SecularAnimist on February 17, 2006 at 7:19 PM | PERMALINK

Hey Jean, don't sell your singing voice short -- get yourself a good teacher!

I took a singing class to feed my vanity, and on the first day flattered myself comparing my lovely tones to the strangle-voiced guy two chairs down.

Well, within four weeks our lovely, patient teacher had relaxed s-v's jaw, deepened his breathing, and otherwise stripped away the varnish to reveal a beautiful baritone!

Or get yourself a good math teacher! After second year calculus, and most of the rest of the BA Math requirements at my college, I took an intro to analysis class in which we built our way from six axioms through the Fundamental Theorem of Calculus. It was a close call, getting to like and appreciate calculus before getting my math undergraduate degree...

Posted by: MaryCh on February 17, 2006 at 7:21 PM | PERMALINK

Of course, no one can truly appreciate the mysteries of the world without steeping themselves in all the techniques of analytic continuation.
I'm sure you all agree.

Posted by: marky on February 17, 2006 at 7:22 PM | PERMALINK

The other personal observation I'd like to offer here is that it seems that the less you know about math, it seems the more suspicious you are of altering standard, old-fashioned math curricula in public school.

A few years ago, my kids's schools moved to offer "integrated math" as an alternative to, (not a replacement for) traditional math- that is, if you wanted your kid to stay in the traditional curriculum you were absolutely free to.

I took a pretty thorough look at the integrated textbook. Page after page of drill was gone and replaced by useful and beautiful math I'd never had- and I took every math course my school offered. Fibonacci numbers, Euler paths, statistical analysis- exciting, applicable, and _useful_ stuff.

I was thrilled.

Unfortunately, a good half of the district was absolutely convinced in was a communist plot to destroy any potential for their kids and any chance at success in life. I mean pitchforks and torches, folks. What I found ironic was talking to many of these folks, you learned they had little grasp of math themselves. They just knew that the painful, repetitive, useless math that they did and promptly forgot was the only way for their kids to go.

It was sad, but they largely won out. The integrated math is seriously struggling in our local district. If you ask me, it just confirmed to me that ignorance breeds suspicion.

Posted by: pdq on February 17, 2006 at 7:22 PM | PERMALINK

Ooohh, big talk from an alchemist.
Posted by: tbrosz

------------------

Shut up, rocketboy, or I'll have to get physical.

Posted by: I. Newton on February 17, 2006 at 7:23 PM | PERMALINK

Of course it's true that most people can get through life with only a minimum of mathematical skills. However, I think it's unfortunate for the species as a whole, because it means so much of our public conversation is quantitatively illiterate, which isn't conducive to good decision-making.

Posted by: Stuart Staniford on February 17, 2006 at 7:28 PM | PERMALINK

The inability of so many Americans to understand algebra and higher math is at the root of their misunderstanding of technical and environmental issues. How to compute a feedback, for instance.

Our friend tbrosz, for instance, tries to understand the truth of the global warming discussion by guessing the personal motivations of the scientists. How very American. If tbrosz were to compute his own regressions, he could have replicated many of James Hansen's climate sensitivity results on his own. The climate data is public, out there for anyone to play with. If you are sitting in front of a modern PC or Mac, you have more computing power at your fingertips than any climate scientist had 20 years ago.

Remember the Crays? Bah! Ive got a Powerbook now!

Posted by: troglodyte on February 17, 2006 at 7:30 PM | PERMALINK

As a dedicated mathophile, I think even elementary algebra is wonderful. I learned it as a child from reading a puzzle book and talking with my father. The thing is, if you understand arithmetic; algebra is easy. There's really only one idea; you can use letters to represent numbers, and then reason using the properties that all numbers have (commutative and associate laws, distributive laws, etc.). I think the problem is that we teach children Algebra before they have a solid foundation in arithmetic; I solid intuitive feeling for the universal properties of numbers. Because of that, students can't understand algebra, and so learn it as a list of arbitrary rules. If the foundation is there, algebra should seem straightforward and natural when you encounter it.

--Rick Taylor

Posted by: Rick Taylor on February 17, 2006 at 7:47 PM | PERMALINK

Well, no, I don't suppose many people do. I suspect that even most mathophiles think of algebra as sort of the 1-ton pickup truck of mathematics handy for getting things done around the house, but hardly something to feel sentimental about.

Don't know much mathematics, eh?

I suppose you are only referring to high school algebra, but in fact, algebra is one of the major areas of research in mathematics, and the techniques and insights involved are the extensions of high school mathematics. Algebra speaks to what can be solved and the relationships between apparently disparate areas of mathematics.

So yes, mathophiles, ache for an understanding of algebra.

Jeanne should consider singing lessons. Singing is human birthright and anyone can learn to do it. Algebra, maybe not.

Posted by: Ray on February 17, 2006 at 7:52 PM | PERMALINK

No, math to me is a ball-cruncher. Always has been. No fun at all -- pure drudgery.

And yet I have a marvelous idea of the parameters of calculus from reading the novels of Cornell engineering physics/English double major Thomas Pynchon -- reputed to be among the most "difficult" of postwar novelists. He's my all-time favorite writer.

And I compose music using all kinds of numerological conceits; my grasp of basic arithmetic, fractions, percentages -- is fine.

I dunno exactly why elementary algebra kicked my ass so hard when I went back to college. But it did.

And I'd boil it down to a capacity for precision -- not any lack of facility with conceptual thinking and/or logic.

Bob

Posted by: rmck1 on February 17, 2006 at 7:54 PM | PERMALINK

alex: "By contrast, proficiency in ODE's (ordinary differential equations) should be a requirement for graduation from grammar school."

Actually I think the OED would do them far more good.

Also, a message to all the mathophiles in the house: you can actually learn critical thinking and problem solving in ways that have absolutely nothing to do with math. In fact, let's get serious, a knowledge of math is no guarantee of being able to deal with any problem in later life.

If you want to improve your thinking, learning a foreign language is just as good a method. Even better is to go to the country where that language is spoken.

That'll help you more with the slings and arrows of outrageous fortune than four years in some desultory high school algebra class.

Posted by: Humanist on February 17, 2006 at 7:55 PM | PERMALINK

I'll just add while calculus is nice, learning beginning logic and set theory is even better. If I had to choose one or the other, I'd choose the latter. The problem with calculus is while it's a useful tool, it's difficult to teach rigorously because the foundations are so subtle. So you don't really get a taste of what higher math is like from it, unless you take an honors class.

--Rick Taylor

Posted by: Rick Taylor on February 17, 2006 at 7:56 PM | PERMALINK

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

-- Edna St. Vincent Millay

Let me add that a working knowledge of algebra has been of enormous help in a career in the arts, as well as various carpentry jobs. And that I'm sure the innumerancy of much of the US population is a factor in the insane political climate.

Posted by: Mr. Bill on February 17, 2006 at 7:59 PM | PERMALINK

Humanist: Actually I think the OED would do them far more good.

Bah. It's filled with funny British and other perverted spellings and usages, even if they do mention the proper American ones. Pricey, too.

Posted by: alex on February 17, 2006 at 8:06 PM | PERMALINK

Rick, my math teachers spent a semester teaching set theory (and Base 8 math!) and I think that was back in 6th grade. But then, that was the era of "New Math" and we had some pretty eccentric teachers too.

I never really understood the usefulness of algebra until I taught a computer programming in BASIC class. I had to spend the first 2 classes explaining the associative and distributive laws, and their application to simple equations. These algebraic concepts are absolutely vital to even the simplest computer programming tasks.

Posted by: charlie don't surf on February 17, 2006 at 8:06 PM | PERMALINK

That'll help you more with the slings and arrows of outrageous fortune than four years in some desultory high school algebra class.

Well if that's the standard, what's the point?

Let's face it, most education is this country is, uhm, desultory. It is a form of child abuse aimed at crushing any sparks of creativity and independent thought. The only thing that a diploma signifies is that someone is ready to follow instructions mindlessly.

Posted by: Ray on February 17, 2006 at 8:09 PM | PERMALINK

Echoing Archie away upthread:

Learning algebra is about far more than mastering calculations. It trains the mind to think of abstractions in an ordered and useful way. Similarly, students do not study Moby Dick to learn about whales and whaling in the 19th Century. A trained mind is more powerful than an untrained mind.

Responding to Jeanne:

A really good singing voice is almost completely in the genes. It's a bit like a fast horse. You can polish with training, but it's got to be there to begin with.

Algebra, in contrast, is something that nearly everyone can learn.

Think for a minute. If the majority of Americans understood basic algebra, how far would George W. Bush have gotten with his bullshit tax cut plan in the 2000 election? The American people need to understand algebra because algebraic functions are being thrown in their faces all the time. If they are conditioned to respond with an attitude of "I don't need to know" then they are going to continue to be rolled over by people who do understand how numbers work.

Posted by: James E. Powell on February 17, 2006 at 8:09 PM | PERMALINK

You know, I can forgive the shameless math aficionados here for believing in the beauty of algebra and calculus (their usefulness is, of course, undisputed).

But you're pushing it too far when you try to link a lack of math understanding to conservative politics.

I mean sheesh -- what could bespeak of a "calculating personality" more resonantly than some Republican asshole obsessively counting up his tax returns and obsessing over his investments in the stock market?

You want applied calculus -- derivatives of rates of change -- it's all there in the financial field. A noted hangout for Republicans.

Sure, lack of basic math knowledge up through algebra might allow people to be taken advantage of in loans, interest calculations, H&R Block tax "services," etc. But that's as much a testament to a devotion to instant gratification as it is to one's level of applied math knowledge. And that's a character, not a brain, issue.

You can be a *cough* rocket scientist and have completely screwed-up political values, as a certain regular poster here demonstrates daily.

Bob

Posted by: rmck1 on February 17, 2006 at 8:10 PM | PERMALINK

singing is wonderful...makes you feel great, soothes the soul and eases your troubles. So does good sex.

but complex thought...brain power

such as required for Algebra

is in a whole different league than feeling good, or even great.

unfortunately (or maybe not) complex thought is also exceptionally easy to take for granted/under value.

Posted by: yowzer on February 17, 2006 at 8:16 PM | PERMALINK

Bob,

You can be well acquainted with math, and be weathly and Republican. The problem is that you can't be well acquainted with math, poor, and Republican. If you were, you would realize that you were getting your pocket picked.

Posted by: Ray on February 17, 2006 at 8:16 PM | PERMALINK

Ray:

Nahh, that's a variation on the "Red staters are stupid" argument.

People vote Republican because they've told themselves they believe in those values. Intelligence really has little to do with it in the aggregate.

Although I might argue that a quant-oriented mind might actually be easier to deceive than a mind more geared toward evaluative arguments. I'd argue that a deeply verbal intelligence -- a deep reader of history and literature -- would be more likely to vote Dem regardless of income level.

Quantative minds don't do contextual analysis very well as a general rule. They wail on the stuff on the blackboard in front of 'em -- but rarely imagine what might lurk beyond it.

And that's the quintessential kind of mentality that thinks that, e.g., American "freedom" should be the same everywhere in the world.

Bob

Posted by: rmck1 on February 17, 2006 at 8:26 PM | PERMALINK

quantative = quantitative

Posted by: rmck1 on February 17, 2006 at 8:28 PM | PERMALINK

Welcome to America! Where people fight like hell for their right to be stupid.

And by 'gum, we're winning!

Regardless of what all y'all regard as the (de)merits of a math curriculum, the simple fact is that plain 'ol SHAME should end all questioning on this matter. We as a nation should be ashamed that there is no drive in us to be the best and smartest.

Posted by: cdj on February 17, 2006 at 8:31 PM | PERMALINK

cdj:

Every hegemon in human history eventually becomes complacent.

Bob

Posted by: rmck1 on February 17, 2006 at 8:35 PM | PERMALINK

Bob -

"Quantative minds don't do contextual analysis very well as a general rule. They wail on the stuff on the blackboard in front of 'em -- but rarely imagine what might lurk beyond it."

What a bizarre notion.

I guess it's not as well-known as it might be in an educated society: Mathematics, at the professional level, is an art - not substantively different from haiku or sonnet writing.

At the lower levels, it's a science.

But what Newton did, what Poincare did, what Riemann did, what Frege did. That's vision and creativity par excellance.

Too bad Americans are too stupid to appreciate it.

Posted by: cdj on February 17, 2006 at 8:35 PM | PERMALINK

Algebra is problem solving made abstract. To study algebra is to study how problems are solved.

Who doesn't want to know that?

Posted by: William Slattery on February 17, 2006 at 8:36 PM | PERMALINK

Mathematics may open up the possibility of space of four dimensions, but only in three-dimesional space can political revolution take place.
-Vladimir Ilich Lenin

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.
-Lazarus Long, "Time Enough for Love"

There are 10 kinds of people in the world: Those who understand binary mathematics and those who don't.
-Mike Buddha

Posted by: Capt. Jean-Luc Pikachu on February 17, 2006 at 8:40 PM | PERMALINK

cdj:

> "Quantitative minds don't do contextual analysis very well as
> a general rule. They wail on the stuff on the blackboard in
> front of 'em -- but rarely imagine what might lurk beyond it."

> What a bizarre notion.

Some of the most narrow-minded people I've ever conversed with in
cyberspace -- the most complacent, the least interested in other
cultures, the least inclined to practice sympathetic introspection
into the lives of people not like them -- have been engineers
and technicians, people highly trained in mathematics.

{Apologies to alex, Constantine and other engineers on
this blog who stand as exceptions to this generalization.}

> I guess it's not as well-known as it might be in an educated
> society: Mathematics, at the professional level, is an art -
> not substantively different from haiku or sonnet writing.

This is partially true. I spent the last two years hanging out
with a biophysicist as he got his doctorate. To the extent that
pure math is purely speculative is the extent to which it's not
useful. String theory is all higher math -- and unsolvable at
our current level of computing power. It's physics divorced from
empiricism -- and derided by laboratory physicists for being little
more than mental maturbation. A great deal of hue and cry exists
in the physics world that some of the best and brightest minds got
hijacked into string theory -- producing mountains of untestable
equations which demonstrate nothing: High-tech metaphysics.

> At the lower levels, it's a science.

> But what Newton did, what Poincare did, what Riemann did,
> what Frege did. That's vision and creativity par excellance.

I'll still rather hang with Bach, Beethoven
and Stravinsky for that stuff, thanks.

> Too bad Americans are too stupid to appreciate it.

Too bad that some Americans are so
arrogant about their personal tastes.

Bob

Posted by: rmck1 on February 17, 2006 at 8:51 PM | PERMALINK

maturbation = masturbation

Posted by: rmck1 on February 17, 2006 at 8:54 PM | PERMALINK

Bob -

Nuthin wrong with personal prefs on art. I only take issue with the ignorant notion that math and creativty don't jibe well together.

Prof. level math is as creative a pursuit as has ever existed.

Posted by: cdj on February 17, 2006 at 8:56 PM | PERMALINK

I dont mean that being ignorant of math causes a person to have conservative politics. The counter-example has already been said, because Repub financiers often can compute their cut of the deal without calling in the quants. The point is that if more people knew math, then more people would be able to address the technical arguments behind policy decisions, instead of choosing the viewpoint of the politician that they find more likable.

That doesnt mean that math-enabled people wont delude themselves for reasons outside the science/math issues. However, it would let more citizens into the debates that matter. Unless you want absolutes as your policy prescriptions, you have to balance interests -- viola! and optimization problem!!

BTW Of all the math I like linear algebra the best. Very beautiful and satisfying. And it has such applications!! Someone put a vote in for analytic continuation. I agree that Cauchy's Theorem is a wonderful thing!

Posted by: troglodyte on February 17, 2006 at 8:57 PM | PERMALINK

Bob -

Be grateful the misspelling didn't come to "maturation"

LOL

Posted by: cdj on February 17, 2006 at 8:57 PM | PERMALINK

Bob,

I don't think that any of the following classes of people are stupid: Red staters, Republicans, people who don't understand math, people who can't stand Faulkner, people who can't sing. I think that all of these people have valuable perspectives and things to contribute to the discussion. I also think that people vote for reasons besides economic ones.

My point was that over broad, but more narrowly, if you are poor, voting on economic grounds, and understand math, you aren't going to vote Republican. Of course if you understand math you can also become wealthy and chose how you vote on other reasons. Money is quantitative.

Quanitative minds are certainly harder to deceive on quantitative issues, the problem is that very few issues are easily reducable to quantitative issues. If I am playing poker, or choosing an insurance policy, or deciding how to pay off my credit card, quantitation has the answer.

If I am deciding whether there should be prayer in school, or the teaching of evolution, or abstinance only education, non-quantifiable factors enter into the debate.

f you are voting for George Bush because you think he is a Christian, just like you, you are probably wrong twice.

Posted by: Ray on February 17, 2006 at 8:58 PM | PERMALINK

cdj:

And my point is that the more "creative" higher math is, the less useful it is -- and the more it's derided by scientists who try to demonstrate things in the real world.

Bob

Posted by: rmck1 on February 17, 2006 at 8:59 PM | PERMALINK

Ray & troglodyte:

Sure, knowledge never hurts an electorate. The more educated, the better. I think this is true across the board.

My only political point is that teaching math is no panacea to the problem America has right now in not seeing its true interests. Being mathematically oriented also seems to reflect a certain kind of personality type that sees problems "on a blackboard" that submit to binary solutions. This kind of mentality can become quite frustrated with ambiguous or evaluative problems that don't lend themselves to those kinds of solid right-and-wrong answers.

That's why people who are *attracted* to quantitative-oriented professions tend (and this is empirically provable) to be Republicans. It's not income levels so much as it is an orientation to thinking about the world that has difficulty imagining alternative situations.

Einstein was famously a pacifist. But he was also famously not a math jock, either.

Bob

Posted by: rmck1 on February 17, 2006 at 9:10 PM | PERMALINK

Some of the most narrow-minded people I've ever conversed with in cyberspace -- the most complacent, the least interested in other cultures, the least inclined to practice sympathetic introspection into the lives of people not like them -- have been engineers and technicians, people highly trained in mathematics.

I don't know that that says as much about "quantitative minds" as it does about "people who are interested in technical fields", which, while there is a correlation, are not the same things.

People who are interested in other cultures and introspection -- regardless of whether they have "quantitative minds" or not -- will be more likely than others to gravitate to activities which fulfill that interest. You seem to be presuming that career choices are dependent on innate ability but independent of interest.

Posted by: cmdicely on February 17, 2006 at 9:10 PM | PERMALINK

cmdicely:

I addressed that in my next message. It has more to do with self-selection by interest than innate ability, surely.

And I made the generalization after years and years spent debating politics with engineers and computer programmers.

Bob

Posted by: rmck1 on February 17, 2006 at 9:15 PM | PERMALINK

Kevin,

No doubt you've been driving on the freeway and you see a car, ahead of you but on an on-ramp and so it's going slower. You make the decision to change lanes left so as to leave a space for that oncoming car well before he had to need that space. You've done algebra.

You have a stock investment that's gone up 25% and you'd like to sell and take profits, but if you wait two weeks you'll have owned it a year and the profits will be taxed at the lower long-term capital gains rate. How much downside can you tolerate in the price in the next two weeks, so that at worst you split the difference between the two tax rates? Need algebra.

You're considering putting solar photovoltaic panels on your roof. The price of power from the company has gone up 40% over the last two years. Making reasonable estimates about the cost of electricity in the near term future, taking into account the setup cost of the solar panels, figuring the number of sunny days per year, knowing that you can sell excess power back to the company at the same rate that they charge you, and finally taking into account the state and federal tax credits available for doing this, how many solar panels should you install to recoup the cost in the shortest period of time? Mondo algebra.

Note all these calculations can be done without all the formalism you learned in class, but the concepts involved, however you approach the solution, are all algebraic.

I really don't see how people can make the argument that algebra doesn't matter to them, except I guess that they are thinking about the full-blown representational formalism they tried to learn and disliked in school. But like it or not, and whether they realize it or not, people use algebra all the time.

Cheers, and regards to I & J.

Posted by: Greg in FL on February 17, 2006 at 9:30 PM | PERMALINK

Here is the (or at least one) reason algebra is a requirement. Only about 5 out of 100 high school graduates will use it in their later life. But most of those who do also need to learn further math like calculus.

Now if the ones who were going to use advanced math waited til college to study it, then they wouldn't have enough time in college to learn all they need. So they have to start in middle school.

So why not just have the future scientists, engineers, et al study algebra in middle school, and everyone else skip it? Because a lot of people who in college get into a major that needs advanced math, don't switch into that sort of a major. When they were in middle school they had no idea where they were going, or thought they were going to be something like an english teacher that doesn't involve math.

So they make everyone take alegbra early on, and then those who need it later will already have it.

Posted by: bobo on February 17, 2006 at 9:35 PM | PERMALINK

Greg in FL:

That's essentially been my point through this whole discussion.

The concepts of algebra fall in the the realm of intuitive logic.

The *formalism* of algebra as taught to me kicked my ever lovin' ass ...

Bob

Posted by: rmck1 on February 17, 2006 at 9:38 PM | PERMALINK

73%.

Posted by: Cyan on February 17, 2006 at 9:55 PM | PERMALINK

I can feel there is some part of my brain that is intended by nature to do math and is happily going along doing whatever it is nature intended it to be doing, but there is no access between that and my conscious mind.

As I've thought about it I've realized a large part of my inability to learn math has to do with an intrinsic unwillingness to take anyone else's word for it. I usually want a lot of sources, or well vetted sources, before I believe anything, and with math, that just can't happen, math is its' own source.

Posted by: cld on February 17, 2006 at 10:00 PM | PERMALINK

Bob -

(a) I suspect you and I have radically differing notions of what counts as "professional level" in math. I mean, essentially, post-phd level. The infantile stuff talked about in blogs like this is at the level of silliness. (Math stops being infantile at calculus btw - that's the beginning of actual math.)

(b) I've never heard a scientist deride mathematics or heard of it happening. It's rather mind-boggling to imagine a real scientist saying that. Maybe a psychologist or a biologist or something...

(c) Einstein was perfectly competent at mathematics - contrary to the common belief of the mathematically ignorant. He didn't have Riemannian geometry, but it's no criticism of one's mathematical skills to say that one is no Riemann...

(d) Who's saying that math learning is a panacea? Certainly not me. IMO tho, it IS a sine qua non for being an educated society - along with numerous other things...

(e) I just love know-nothings who are soooo happy that they know-nothing ("I quit taking math in 2nd grade and am perfectly happy"). LOL - very BNW of them. It's the blind reflexively self-leading. And then it passes on to their kids, and so on... And next thing you know, America is the stupidest country in the civilized world. Bravo, know-nothings! You've succeeded!

Posted by: cdj on February 17, 2006 at 10:03 PM | PERMALINK

If I could trade calculus for a working knowledge of French, I suppose I might take the deal.

It all depends on what you want to accomplish, and what you want to understand, doesn't it?

What would you recommend to someone who wanted to simultaneously increase America's fuel supplies and reduce greenhouse gas emission? French or calculus?

What would you recommend to the child of an immigrant to the US who wants to rise economically?

Posted by: republicrat on February 17, 2006 at 10:07 PM | PERMALINK

Newton said: Shut up, rocketboy, or I'll have to get physical.

Well, that'd be a first, now wouldn't it?

Posted by: Irony Man on February 17, 2006 at 10:08 PM | PERMALINK

My sister is an interesting case in this (silly) 'whats the worth of math' discussion.

As a freshman (or soph?) in college, she more or less failed calc, even though she was a VERY diligent student (way more disciplined than me).

But then, as a senior taking a mid-to-upper level econ course, some professor casually mentioned that 'marginal propensity' was nothing more than calculus' first derivative (or is it second? don't know, I'm not an economist).

Bing! the light went on. She went back and looked at her calc text, and it made a lot more sense. Not that she became a calc master or anything, but she has a fair understanding of the Fundamental Theorem of Calculus. The minute she had a practical application that she cared about, calc started to make sense.

Lots of people have trouble with the abstract nature of math, and different people learn in different ways. A good teacher tries to find the right way to get through to each student. Too bad Richard Cohen's teacher didn't find the right one for him.

(BTW: you wanna see abstract math? Take a grad level algebra class sometime (or a grad level calc class, for that matter). Check please!

Robert Earle
U of Wisconsin, Bachelors (but not Masters!) in math

Posted by: Robert Earle on February 17, 2006 at 10:12 PM | PERMALINK

Al Gebra? We're lettin' the terrists recruit in our high schools?

Posted by: Redstate Roadhawg on February 17, 2006 at 10:16 PM | PERMALINK

Robert Earle: The minute she had a practical application that she cared about, calc started to make sense.

Bingo. Fortunately for me, my epiphany occured in middle school when I found an application for trig in a hobby. Before that I couldn't stand math because it seemed like so much abstract nonsense.

My revenge to the pure math types: word problems (are you there waterfowl?). While I do reasonably well at math, I always shined at the word problems (even in grade school). My utterly un-self-serving argument for why these are so important is that math is of no practical value without an application.

Posted by: alex on February 17, 2006 at 10:23 PM | PERMALINK

Earle -

It's even better to look in on a grad class where they weave several of the "toolkit" courses together - like, e.g., functional analysis, variational methods, stochastic processes, or numerical analysis. There u can see the full power of the basic toolkit crap - the "why" part of it. The problems that can be solved - the range of what can be talked about - is quite amazing.

(toolkit classes are things like calc (proving implicit functions in Rn), lin alg (spectral thm), n the like)

Posted by: cdj on February 17, 2006 at 10:27 PM | PERMALINK

cdj:

> (a) I suspect you and I have radically differing notions
> of what counts as "professional level" in math.

No we don't.

> I mean, essentially, post-phd level. The infantile stuff talked
> about in blogs like this is at the level of silliness.

Then why are you bothering to post here? I mean ...
you know what it *looks* like, right?

> (Math stops being infantile at calculus btw -
> that's the beginning of actual math.)

And English literature stops being infantile at Faulkner. And music
at Stravinsky. And [fill in the blank] at [fill in the blank] ...

Ooh, placeholders! How ... algebraic :)

> (b) I've never heard a scientist deride mathematics or heard of it
> happening. It's rather mind-boggling to imagine a real scientist
> saying that. Maybe a psychologist or a biologist or something...

Then you're obviously not familiar with the controversies surrounding
string theory. Physicists aren't balking at the math qua the math,
of course. They're balking at all these "beautiful" equations
that can't even be run on a football field of supercomputers. When
science stops submitting to empirical proofs, it becomes wankitude.

String theory might be beautiful math, but it's null physics.

> (c) Einstein was perfectly competent at mathematics - contrary to
> the common belief of the mathematically ignorant. He didn't have
> Riemannian geometry, but it's no criticism of one's mathematical
> skills to say that one is no Riemann...

He didn't have the chops for Riemannian geometry -- exactly. He
was keen on visualizations -- Gedanken experiments. The equations
followed from powerful intuitive insights, not the reverse.

> (d) Who's saying that math learning is a panacea?
> Certainly not me. IMO tho, it IS a sine qua non for being
> an educated society - along with numerous other things...

Americans have a notorious problem with
grammar, spelling and rhetorical nuance as well.

> (e) I just love know-nothings who are soooo happy that they
> know-nothing ("I quit taking math in 2nd grade and am perfectly
> happy"). LOL - very BNW of them. It's the blind reflexively
> self-leading. And then it passes on to their kids, and so on...
> And next thing you know, America is the stupidest country in
> the civilized world. Bravo, know-nothings! You've succeeded!

It's faster when you type with two hands -- and a
lot less prone to slippage without all the Vaseline.

Bob

Posted by: rmck1 on February 17, 2006 at 10:47 PM | PERMALINK

Guys, Calculus and math are the LANGUAGE of engineering. You take a junior year, or higher, engineering class, and all you see are differential equations on the board, bell to bell.

In the good 'ol US of A, engineering is looked down upon as a profession; just a bunch of gearheaded nerds. In Asia, engineers are held in high esteem.

Guess where all the jobs are going.

You don't have no math, you don't have no engeeneers, you don't have no high flying economy, at least for very much longer. Post WW2, we rocked technically, look at us now.

Just keep on dissing those math classes, going to take this country real far.

Unfortunately, I happen to be one of a dying breed, manufacturing engineer, in a business, semiconductors, that doesn't live off of the government. Not nearly the job opportunities out there as if I was in an essential field, like law or sales.

TT

Posted by: TT on February 17, 2006 at 10:50 PM | PERMALINK

republicract, "What would you recommend to the child of an immigrant to the US who wants to rise economically?"


Mandarin.

Posted by: cld on February 17, 2006 at 10:50 PM | PERMALINK

Mathematics is a language, and like music it is a language that is universal. I'm surprised that so few folks in these debates grasp why it is such a central concept, and why teaching it is so essential.

There is no other place in the curriculum where the rules of logic can be easily taught. Mathematics is also the language of science. The great achievement of science is that complex phenomena can be explained through the application of simple rules. If you can't apply simple rules in algebra, you can't understand how the natural world works. Closing the door on math is also closing the door on science.

The dirty secret of math teaching is that most K-12 math teachers - and science teachers - are not mathematicians and scientists; many were not even math or science majors. The negative sentiments that a lot of people have towards these subjects can frequently come from teachers who are themselves not interested in, or comfortable with, the topics that they are teaching. Conversely, people who were blessed with good teachers tend to have a much better understanding of the topic and get a lot more out of it.

And choosing between important subjects: come on. You're not a fully educated person without history, science, math, and literature, among other things.

Posted by: Marc on February 17, 2006 at 10:51 PM | PERMALINK

TT: You don't have no math, you don't have no engeeneers, you don't have no high flying economy, at least for very much longer. Post WW2, we rocked technically, look at us now. Just keep on dissing those math classes, going to take this country real far.

The problem is a lack of demand for engineers, not a lack of supply. Certainly there are lots of other reasons to learn math. However, without the jobs for engineers, scientists, etc., all the math classes in the world won't make the US more competitive.

Posted by: alex on February 17, 2006 at 10:59 PM | PERMALINK

Bob -

He didn't have the chops to INVENT Riemannian geo. He was perfectly comfortable with understanding it.

As well as the variational formulation of physical laws, and numerous other substantive mathematical topics.

Your illiteracy follows you like a shadow. Except, unfortunately , it carries a signal...

Posted by: cdj on February 17, 2006 at 11:00 PM | PERMALINK

alex -

Um, what about those thousands of jobs that are going to Indians n such?

Yah, some of em are customer service. Some. (Have you been to the Microsoft campus lately?)

And what about all the quant jobs (finance crossed with stochastic processes) that are going unfilled? They typically require phd-math ability.

And ever a larger point: r&d (which is what higher ed basically comes to) is valuable mostly because it creates its own demand - ie, it creates new markets. (The picture of Gate's mom saying "that's nice dear, but why would anyone want a personal computer" is good to have in mind). That's why I laugh at the know-nothings saying how happy they are knowing nothing.

Who proved that the prime number decision problem was polynomial time? (Hint: It wasn't a white country).

USA! USA! Stupider and stupider!

Posted by: cdj on February 17, 2006 at 11:05 PM | PERMALINK

cdj:

> He didn't have the chops to INVENT Riemannian geo.

Right, because his name was Einstein, not Reimann :)

> He was perfectly comfortable with understanding it.

Now you're backtracking from your earlier statement that Einstein
didn't "have" Riemannian geometry. Dude, it's 2006. That means
that last year was 2005. And a hundred years earlier than that
year, something *very significant* happened in Einstein's life
that changed the course of physics. The centennial was rather
celebrated and *tons* of stuff were written about Einstein last
year. Einstein was no math prodigy. He was arguably less fluent
than his contemporaries who formulated quantum mechanics. E=MC^2
is not a complex equation, as equations go. The genius of Einstein
does not rest on mathematical innovations. This is common knowledge.

> As well as the variational formulation of physical laws,
> and numerous other substantive mathematical topics.

And you're blathering.

> Your illiteracy follows you like a shadow.
> Except, unfortunately , it carries a signal...

Rather than a trail of jizz stains.

Bob

Posted by: rmck1 on February 17, 2006 at 11:17 PM | PERMALINK

Never mind high school diplomas - if you can't pass algebra, you don't get a driver's license. That ought to clear the roads, and improve the driving of the ones who are left.

Posted by: craigie on February 17, 2006 at 11:18 PM | PERMALINK

I Know I am coming into the coments real late, but I need to add to these comments. I have read in the backround for about a year and have never responded, but I need to respond to this blog. My daugher is a firefighter. She has pulled one of your family members out of a burning car and saved their life. She has given CBR and saved your mother,father,wife,child, numerourse times. You have a wildlandfire, she is the one saving your home. Who do you call at 3 in the morning if there is a fire,medical emergencie,or car accident,is it somebody that has passed algebra or is it the idiot that dose'nt get math (have worked for years and she dose not get it)but know how to save your life. There are people out in the real world that are not what everybody here thinks are SMART, but I would want my stupid daughter there in case of a fire, auto accident,or medical emergency rather than the SMART people on this site that would be unable to help me out in any of these seneriose. Thank god we have the smart ones.


c

Posted by: Caren on February 17, 2006 at 11:41 PM | PERMALINK

craigie:

Ahhh ... the sweetly insipid arrogance of nerds.

"I think we should make drivers' licences contingent on having read all the volumes in Ray Bradbury's The Martian Chronicles. No, wait -- make that getting to Level 24 in Super Mario Bros. Or -- hold it -- having a complete DVD set of The Sopranos episodes ... "

Bob

Posted by: rmck1 on February 17, 2006 at 11:42 PM | PERMALINK

Ridiculous comparison (singing to math ability). Singing ability, at a high level or even a medium level, is not learned. Math, at least at the level of algebra, is something that can be learned by most people. And it is learned by most in the rest of the industrialized world, but not in the United States. That is one big reason why global warming, for example, is widely understood and accepted in the rest of the industrialized world, but not in the United States.

Posted by: David on February 17, 2006 at 11:46 PM | PERMALINK

sorry for the typos, should haved been cpr, and should have been does'nt get math. Sorry for the miss spelling.

Posted by: caren on February 17, 2006 at 11:48 PM | PERMALINK

Caren:

Your meaning was perfectly clear -- and your point is well-taken.

Bob

Posted by: rmck1 on February 17, 2006 at 11:50 PM | PERMALINK

To me, the real value of Algegra to MOST people is that it teaches how to think in a structured way. It's really all about mental discipline. Take a problem, break it down...if you don't understand it, go back to what you know and try again.

It doesn't matter that everyone won't go on to be an engineer or mathematician. Everyone benefits from training in analytical thinking. Analysis is our primary tool for understanding and Algebra training is a great introduction to that process.

Archie, James and others have made similar points which I agree with completely.

(Kudos to Kevin for sparking another great thread!)

Posted by: mezon on February 17, 2006 at 11:54 PM | PERMALINK

Caren. I think most people posting here actually agree with your point...I know I do. A friend of mine used to say that no amount of education will make someone "intelligent". There are many different ways someone can show their smarts/talent/committment/professionalism. My kid bro was dislexic, but fresh out of high school joined a fledgling pc support group of 2 other techs and pulled 50% of the service calls in his first month! He went on to become essentially a self-made network engineer, and today takes home almost 2X what I make!! He has always been smart to me...but he is also committed. Sounds like your daughter is too. Congrats to you.

re comments...keep 'em coming. your 2c's makes us all smarter!!

re typoos...let hm hoo iz withoot cin through the farts stoned!

Posted by: mezon on February 18, 2006 at 12:05 AM | PERMALINK

If you can't do algebra, then you can't be a mathematician who solves problems for the FBI. So there. (The show beats CSI hands down.)

Posted by: Rick B on February 18, 2006 at 12:12 AM | PERMALINK

mezon:

I have to continue to contend with the idea that somehow the only way one acquires logical problem-solving skills is through algebra. Because of a historical fluke, I went to an alternative HS that didn't require me to take any math. When I went to college, I of course had to demonstrate a minimal proficiency in algebra and I went from acing just about everything to spending hours of grinding agony practicing equations. Algebra never melded into anything elegant or intuitive for me; it was all work just to maintain a passing grade. And this is a guy who could sleep through a 300-level English or History class and get an A (this is at a competitive state university).

This didn't stop me from learning how to troubleshoot my computer or teach myself basic programming. Nor did it impede me as I taught myself music theory and composition. Nor is it reflected in my ability to make a verbal argument. And I can grunt my way through the kind of numerical problem-solving that Algebra is supposed to make second nature. It's nothing to do with the logic -- and everything to do with the formalism.

David:

America is deficient in more than just basic math. It's deficient in English, foreign languages, geography, history and the social sciences. Our problem is the problem of any global hegemon -- we've gotten complacent as the top dog. Doubtless education standards began eroding in the late Roman Empire, as well ...

But the idea that teaching math would innoculate us as a nation against insane conservative policies just isn't borne out by history. Nazi Germany and Imperial Japan were highly technological civilizations with a doubtless broad-based high-level math competency in their citizens. Nor does knowing math enable understanding science. I adore the history of science and keep myself fluent on science issues. Not getting the math behind theories doesn't mean I somehow can't understand the concepts in a way that makes logical sense. I might never be a scientist, but I am hardly scientifically illiterate, either.

Bob

Posted by: rmck1 on February 18, 2006 at 12:12 AM | PERMALINK

rmck1. Actually, I agree completely. I was just trying to point out a value that no one seems to get (certainly not Algegra Teachers!) that for many people Algebra has real value by teaching structured thinking. Not that it is the only way to teach serious thought processes.

When kids ask "why do I need to know this?" to me that best answer is because it HELPS teach how to use the tool between your ears. Certainly some will not benefit from such an exercise, some will get the same from another path, and some will pursue interests were analytic skill is a negative rather than a positive (ie artists).

Posted by: mezon on February 18, 2006 at 12:23 AM | PERMALINK

Next question. Can a Biblical Inerrantist Xtian fundamentalist learn Calculus and use it effectively?

Posted by: Rick B on February 18, 2006 at 12:32 AM | PERMALINK

mezon:

Agreed. Except that I'd back off a tad and say that analytical thinking can be quite useful for artists of all types.

Rick B:

Sure, why not? The Nazis were whizzes at at.

And we know those nefarious stuck-in-the-Dark-Ages A-rabs invented algebra ...

Bob

Posted by: rmck1 on February 18, 2006 at 12:40 AM | PERMALINK

Rick B:

In fact, being predisposed to literal-mindedness might actually be helpful to develop a fluency in quantitative subjects. Literal-mindedness is actually part of the popular folklore for why engineers and other nerdy types are allegedly so socially inept ...

In math, just like in the Bible, there's only one right answer and it's right there on the piece of paper :)

Bob

Posted by: rmck1 on February 18, 2006 at 12:45 AM | PERMALINK

One of the few joys of being a Katrina evacuee was having the opportunity to help my grandchildren with their homework: the 6th grader was doing math that seemed very much like the algebra I had in high school many years ago.

Posted by: Brian Boru on February 18, 2006 at 12:51 AM | PERMALINK

Alex, you really pegged it.

The problem is a lack of demand for engineers, not a lack of supply. Certainly there are lots of other reasons to learn math. However, without the jobs for engineers, scientists, etc., all the math classes in the world won't make the US more competitive.
It's not just that there is no demand for engineers. It is that there is a demand for newly graduated engineers and almost none at all for engineers (including software engineers) after age 40. The employers can hire a newly minted foreign graduate much cheaper. Get him on an H1B visa, use up his immediate knowledge, and send him home to hire another (cheaper) brand new graduate.

So what do experienced engineers, scientists and mathematicians offer to aid ~commercial businesses?~

Damned little. The very skills that took a lifetime to get them to the jobs they have at age 40 took so much time to learn that they really don't know that much about the businesses they work in. That's why so many engineers go get MBA's. They peaked as engineers, and their managers don't want to promote them to higher paying jobs. They don't understand enough marketing and accounting.

But if they did, they would be lost in their own fields. A good engineer has to do his own job every day and go home to read the changes in his own field. The time taken to get an MBA reduces his ability to learn his own field. So they go get MBA's, and their companies replace them with newly minted graduated engineers and scientists. Mostly foriegn.

If you aren't a pro athelete, why choose a career field that peaks in your 30's? Simple. You are a minority who can't win in any other field, or you are foreign. Oops. Our minorities can't win in science for the most part. They have to try for pro sports.

Posted by: Rick B on February 18, 2006 at 12:51 AM | PERMALINK

Rick B:

Jesus, why are you making me think of Michael Douglas in "Falling Down"?

Bob

Posted by: rmck1 on February 18, 2006 at 1:01 AM | PERMALINK

America is deficient in more than just basic math. It's deficient in English, foreign languages, geography, history and the social sciences. Our problem is the problem of any global hegemon -- we've gotten complacent as the top dog. Doubtless education standards began eroding in the late Roman Empire, as well ...

American education has always been hamstrung by the vicious divisions that wrack American society. The worst of these, obviously, is the racial divide. The racial antagonisms that produced substandard and underfunded education for generations of black children - more or less deliberately - then came home to roost when the civil rights revolution demanded school integration. The destruction of the public school system across much of urban America in that period was essentially the result of racial hostility and fear, white flight and black antiestablishmentarianism. Then, on another track, persistent anti-intellectualism, xenophobia and religious suspicion has always crippled high-school education across much of rural and Southern America.

The US has always had zones of educational excellence, broad enough to produce a competitive upper-middle class. Private schools; public schools in wealthy neighborhoods like Shaker Heights and Montgomery County; magnet schools like Bronx Science; and public schools in neighborhoods populated by education-hungry immigrants, like PS 6 (?) in downtown Manhattan, have kept the country afloat. But ultimately, a certain anti-intellectualism and faux-free-thinking laziness that infects American working-class culture represents a constant threat to education here, and this anti-intellectualism and hostility to learning (as a form of authority) preys on ethnic and class identity divisions - convincing working class blacks, Hispanics, whites, Arabs, and, yes, even Asians that school is not cool.

Then you have the traditional American contempt for teachers (I do not believe that any other culture has any suicidally toxic saying along the lines of "Those who can't do, teach"). Basically, the US has kept itself afloat for 150 years on the eagerness for learning of the immigrants who come here. If they ever stop being interested, we'll never even know why our society fell apart - we'll be too stupid to figure it out.

Posted by: Sgt. Schulz on February 18, 2006 at 1:02 AM | PERMALINK

Bob,

When you get far enough into math to realize that there is often more than a single answer to the problem, let me know.

One important thing math teaches you is how many solutions to expect, and many times it is more than one. Go solve some quadratic equations.

The Xtian biblical inerrantists seem to assume that there is one single answer to the bible, so they memorize what their leaders tell them as though that was "THE ANSWER." Arithmetic in a given number system may offer only a single correct answer. Mathematics goes far beyond that.

Does any Evangelical or fundamentalist Seminary teach algebra? I'd be surprised.

Posted by: Rick B on February 18, 2006 at 1:03 AM | PERMALINK

Like most people, I learned, passed the test and immediately forgot algebra. They put math in front of you and expect you to figure out for yourself that it is a beautiful short-hand language for understanding the universe. Or that is what they say it is, I never got it. My suggestion is, instead of boring us to desperation with decades of excrutiating memorizing and forgetting, why not forego some of the formulas and teach ABOUT math. Teach us ordinary non-math proles what the cognicenti see in it. If they are going to force it down our throats, at least they should explain why.

Posted by: James of DC on February 18, 2006 at 1:07 AM | PERMALINK

I guess I was a total nerd.
I loved all the Algebra stuff & geometry.

Worked out Pascal's triangle using colored blocks. And the Binomial distributions. Made my very own base 8 multiplication table. Got so bored in Pre-algebra I started doing the chapters twice as fast as the teacher, and did algebra too. I think most people turned off of math had it happen from having to memorize too many formulas, and not getting to see the structures and symetery behind all the numbers.

Perhaps you can think of Algebra as yet another foreign language, and one you will use more often than French I bet.

Posted by: MobiusKlein on February 18, 2006 at 1:16 AM | PERMALINK

Sgt. Shultz:

"And those who can't teach -- teach gym." --Woody Allen

Otherwise a very articulate and frightening essay. Nothing to add.

Rick B:

Well, if you had read my comments here on the kind of ordeal I had going through elementary algebra in college, you might have intuited that doing quadratic equations for me would be like getting a SacRete enema administered by very large and malodorous medieval Teutons barking at me in Old Norse while they rectally inserted an unlubricated length of old drain leader :)

Obviously my comments on literalism were intended to be somewhat facetious. I will note, however, that all math, to the extent that it's computer programmable, does ultimately reduce to binary logic.

I do believe that some of the bigger Christian universities have full spectrum math departments. Part of developing a proper Christian Republican orientation is to understand things like finance, which requires a modicum of understanding in calculus. Schools like SMU and Baylor have, IIRC, engineering departments as well.

Bob

Posted by: rmck1 on February 18, 2006 at 1:24 AM | PERMALINK

Definitely, definitely calculus over French. 100%. Easy choice.

Also, as for algebra being useful, I was in tax class (Law School), and I found that my ability to do algebra served me amazingly well. It was an awesome advantage.

I doubt that a person who doesn't understand algebra can really understand science. Certainly, they can't learn enough about science to internalize the methodology and appreciate it. That such people have trouble explaining why science is different from religion comes as no surprise.

Posted by: MDtoMN on February 18, 2006 at 1:34 AM | PERMALINK

cdj:

I had a numerical analysis class as part of an 'additional major' in computer science (subsequent to the math degree).

The prof would work for 40 minutes at the chalk board (yes, chalk, not white board), have enough variables up there that he would have run through the enire alphabet and started in on the greeks. Then with five minutes left, he'd pause...hand stroking his beard....and say 'I think I've made a small mistake'. Then he'd erase half of what he'd written, and the class would end. Every week it was the same. It was just awful. I learned absolutely nothing!

Don't get me wrong, though. I would have liked to keep going into grad school. But in terms of ability or interest or whatever, I kind of hit the wall at 'N-dimensional manifolds' and 'Group and Ring Theory'.

(But I also had a class in Math Logic - Turing Machines, Completness, Undecidablity. That class rocked! :-)

Posted by: Robert Earle on February 18, 2006 at 1:39 AM | PERMALINK

James of DC:

Speaking as one math-uninclined person to another, I think many of the comments on this thread help illustrate why math education in this country is suffering so badly. There are a lot of words from the folks who "get it." They feel like they're members of a priesthood, and the contempt they feel for us lessers who didn't "get it" is palpable.

We, you know, can't understand science because we don't understand and/or appreciate the glories of algebra. This is all entirely our faults. We were born of weak seed. We're ripe for being picked off by religious fundamentalists.

If any of these math jocks could, you know, write a compelling English sentence, but have you noticed how badly their prose sucks?

Nope. Not a single attempt to try to awaken us to what it is in math that they see. Odes to usefulness. Assertions of being essential. Own-back-pattery regarding how well they've mastered it.

But the kind of infectious enthusiasm for the subject that all really excellent teachers possess?

I haven't seen it here -- have you?

Bob

Posted by: rmck1 on February 18, 2006 at 1:43 AM | PERMALINK

I had Numerical Analysis at U of MN and the prof did the same sort of thing. 7 blackboards full of calculations on a problem and out of about 200 in the class less than 5(not including me) could follow him. And then he would say we didn't have to know it!

Posted by: Michael7843853 G-O in 08! on February 18, 2006 at 2:06 AM | PERMALINK

MDtoMN:

> I doubt that a person who doesn't understand
> algebra can really understand science.

What a laughably elitist statement *that* is. I was a kid during
the space race and have been a science fan my whole life. No, I
never got stochiometry and molar weights. But I know the history
of chemistry, electricity and physics, and some of the philosophy
that underlies the debates as science changed paradigms throughout
the 19th and 20th centuries. Equations are essential for doing
experiments and I am no scientist as my grasp of math is rudimentary.
But I am no scientific illiterate, either. I have a good sniffer
when it comes to pseudo-scientific bullshit and scientistic ideology.

> Certainly, they can't learn enough about science
> to internalize the methodology and appreciate it.

Bullshit. You don't need equations to read Karl Popper,
Stephen Jay Gould, Thomas Kuhn or Brian Greene, for
that matter. Or to discern the difference between the
hypothetico-deductive method and the Inductive Fallacy.

> That such people have trouble explaining why science
> is different from religion comes as no surprise.

It is far more likely that the kind of grinds who advocate
Intelligent Design are masters of the uncritical rote
memorization required for passing a highschool math curriculum.

I eat ID advocates for lunch. Especially
the ones who teach highschool biology classes.

Bob

Posted by: rmck1 on February 18, 2006 at 2:17 AM | PERMALINK

rmck1:

You write:
"They feel like they're members of a priesthood, and the contempt they feel for us lessers who didn't "get it" is palpable."

But then you write:
"If any of these math jocks could, you know, write a compelling English sentence, but have you noticed how badly their prose sucks?"

So how is it that your put-down of the English ablities of the math "priesthood" doesn't itself show a "contempt" for we English lessors-than-thou? (And, please, use small words. Or better yet, formulae!)

I, on the other hand, wrote:
"Lots of people have trouble with the abstract nature of math, and different people learn in different ways. A good teacher tries to find the right way to get through to each student. Too bad Richard Cohen's teacher didn't find the right one for him."

I don't think it was/is your fault at all; I think it was your teachers'.

(And yes, I have most definitely had math teachers who demonstrated an "infectious enthusiasm" for math).

So let me say, in oh! so inelegant prose... go fuck yourself.

Posted by: Robert Earle on February 18, 2006 at 2:20 AM | PERMALINK

My Numeric Analysis class wasn't so bad. Just the average doddering prof, but accurate.

One time tho he lost all the exams, and found them weeks later, and one of them had a Playboy mail-in subscription card. (Nobody sued.)

Computational / Math Logic kicked ass: P!=NP, Godel's incompleteness theorem, all that.

But rmck1, it's no magic priesthood. We're just nerds, we can't help it. Perhaps if I could write good prose I could awaken you to the beauty - but as you pointed out, we can't. Capulets and Montagues, are we destined to be at odds for eternity?

Posted by: MobiusKlein on February 18, 2006 at 2:25 AM | PERMALINK

I used algebra pretty much every day of my working life for twenty years or so (and still do). It's part of doing lab science. I fully understand the frustration people had with bad teaching, and math is (let's admit it) often pretty dry. But it's a central component of western civilization and intellectual history. Without some feel for math, you miss a substantial part of understanding how the world works.

I also had a great time in my class in mathematical theory of computation. Later, it helped me have a better feel for how complex genetic systems really have to be (or don't have to be).

much to be said . . .

Posted by: Bob G on February 18, 2006 at 2:43 AM | PERMALINK

Robert Earle:

> You write:
> "They feel like they're members of a priesthood, and the contempt
> they feel for us lessers who didn't "get it" is palpable."

> But then you write:
> "If any of these math jocks could, you know, write a compelling
> English sentence, but have you noticed how badly their prose sucks?"

> So how is it that your put-down of the English ablities of the math
> "priesthood" doesn't itself show a "contempt" for we English
> lessors-than-thou? (And, please, use small words.

It was a total cheap shot, borne of seeing many comments along
those lines and certainly not directed at any specific individual.

> Or better yet, formulae!)

:)

> I, on the other hand, wrote:
> "Lots of people have trouble with the abstract nature of math,
> and different people learn in different ways. A good teacher
> tries to find the right way to get through to each student. Too
> bad Richard Cohen's teacher didn't find the right one for him."

Yes, you wrote that way upthread and I certainly didn't have it in
mind when I unloaded. I was more bristling at MDtoMN's assertion
that people who don't understand algebra can't understand science.

Truthfully, that was the comment that made me snap -- though
in general there hasn't been a treatment of the subject that
seems to have been reaching out to us math-disinclined.

Heh, I guess C.P. Snow was right about The Two Cultures after all.

This is all very ironic to me, because my favorite novelist,
Thomas Pynchon, likes to sprinkle his books with calculus
equations and real-life scientists and riffs on concepts like
entropy, information theory and the Poisson distribution.

> I don't think it was/is your fault at all;
> I think it was your teachers'.

Honestly, I can't go there. I went back into algebra as an adult
with the right attitude. My profs weren't great (they generally
aren't at a large state university in remedial classes like
that) but I take full responsibility for the hard time I had. I
think it's because I just lack the skill of being precise. It's
not even that I hate numbers -- I compose music and work with
all kinds of numerological concepts, fractions and ratios.

> (And yes, I have most definitely had math teachers who
> demonstrated an "infectious enthusiasm" for math).

You were lucky. The one middle school teacher I had who introduced
me to algebra was a notorious drunk and a miserable person.

> So let me say, in oh! so inelegant prose... go fuck yourself.

Well, as they say, one cheap shot deserves another :)

I'm sorry if you felt I insulted your writing.

Bob

Posted by: rmck1 on February 18, 2006 at 2:50 AM | PERMALINK

Apology accepted.

Posted by: Robert Earle on February 18, 2006 at 3:04 AM | PERMALINK

Robert Earle:

Cool :)

Bob

Posted by: rmck1 on February 18, 2006 at 3:11 AM | PERMALINK

I really wish our high schools placed more of an emphasis on why algebra and trig are so damn important to calculus.

Posted by: scarshapedstar on February 18, 2006 at 5:10 AM | PERMALINK

And I wonder how she feels about the fact that her inablity to do algebra has likely cost her thousands of dollars over her lifetime due to poor financial decision-making?

That's true, but it's not something I had a choice about. You are all assuming that people like Jeanne and me were poor math students out of sheer willfulness. That attitude doesn't help us at all. I wish I could have learned math beyond basic arithmetic. It's a terrible handicap not to know math. If I could have learned it, I would have. It's a learning disorder, I tell you, and getting angry with people with learning disorders doesn't help them at all.

Posted by: maha on February 18, 2006 at 7:20 AM | PERMALINK

You are all assuming that people like Jeanne and me were poor math students out of sheer willfulness.

Not all. But some. Like that girl in the LA times article who was absent from 60 of 90 math classes. Part of learning something is putting in the time. I blame her parents and teachers for not dealing with the truancy problem rather than not being able to teach math.

getting angry with people with learning disorders doesn't help them at all.

Hoew about getting angry with people like Cohen who celebrate them and claim that they aren't really a disability but rather something to be proud of. Can I be angry about that?

More here.

Posted by: Jay on February 18, 2006 at 7:36 AM | PERMALINK

Like that girl in the LA times article who was absent from 60 of 90 math classes.

That was during, what, her sixth attempt at passing the same class? At that point I might have not bothered to go either. It wasn't gong to happen. How many more years was she supposed to spend in high school pounding her head against a wall?

Granted, this girl is not the ideal poster child for math learning disorder. But my contention is that instead of punishing people for something they can't do any more than they can fly by flapping their arms, you go back to early elementary school and try to find different approaches to teaching math that might be more effective for math-learning-disabled children. And for the kids already in high school who can't pass algebra, devise a more rudimentary "practical math" course.

Hoew about getting angry with people like Cohen who celebrate them and claim that they aren't really a disability but rather something to be proud of. Can I be angry about that?

Not knowing math IS a terrible handicap, and an embarrassment, and I wish I did understand it. One of the coping mechanisms one develops about any handicap is to laugh about it. I think that was what Richard Cohen was doing.

All my fifty-something years I've run into the attitude that *if only* I understood how important math is, I would have learned it. What these people dont grasp is that I *could not* learn it if my life depended on it. I have a big, fat learning disability that I cant get around. Maybe if Id been taught math some other way I would have turned out differently. But insulting me and yelling at me about how important math is doesnt change the fact that I CANNOT learn it.

And by the time I was in high school I had a seething hatred of being told I was just lazy or willful about not learning math. I remember well people standing over me wagging a finger and saying I'd come to a bad end. It's like telling a blind person they won't be able to function in life if they can't learn to see. But one does learn to limp along, to compensate. And in time you'd like to go back to the finger waggers and say look, I've got a cane, I've got a seeing-eye dog, I get along OK. Nyah nyah nyah. That's where I think Cohen was coming from.

It's not the way I would have chosen to go through life, but that's how it is.

Posted by: maha on February 18, 2006 at 7:55 AM | PERMALINK

Well, no, I don't suppose many people do. I suspect that even most mathophiles think of algebra as sort of the 1-ton pickup truck of mathematics handy for getting things done around the house, but hardly something to feel sentimental about.

No, it's more like a Swiss army knife, really - useful in a whole bunch of little ways in a thousand situations.

And it's also a necessary component of any other form of mathematical or scientific endeavor. Not just calculus, but stuff like graph theory, which is not at all dependent on calculus, and looks more like playing with tinkertoys than it looks like math, most of the time, but deals with some pretty complex real-world problems.

If you can't do algebra, it blocks you from numerous fields - both fields of knowledge and professional fields. That's not to say everyone must learn algebra, but it means it's important that we make sure no kid is allowed to give up on it too soon in high school.

Posted by: RT on February 18, 2006 at 8:35 AM | PERMALINK

Mathmatics is the langauge of creation and I would love to speak it. Perhaps I could even hold a conversation with God.

Posted by: anon on February 18, 2006 at 9:02 AM | PERMALINK

A friend's wife, an artist and a workaholic, had to take algebra for chimpanzees 5x in college to get her degree. I'm thinking her perspective might be a little different.

Posted by: Michael7843853 G-O in 08! on February 18, 2006 at 9:04 AM | PERMALINK

I think your point is that utility is not the only basis for judging whether something is worth learning, and that's exactly right, Kevin. I agree 100% that the calculus is beautiful and is something that every educated person should know, along with a working knowledge of at least one foreign language, some basic micro- and macro-economics, and how their government operates.

Frankly, I don't have that much of a problem requiring things like this for high school graduation. A high school diploma should mean something -- that's why it's fair to discriminate against people who don't have one. Once you let anyone graduate from high school regardless of whether they are able to pass minimum requirements, the degree itself loses meaning -- which only makes things worse for the sorry folks who despite the dumbing down of the requirements still can't manage to get a degree.

Posted by: Nils on February 18, 2006 at 9:23 AM | PERMALINK

Music and math tend to go together.

But that's beside the central point. What really ripped me off about Cohen's piece is that he missed the entire point of the LAT article he had read. Gabriela didn't suffer because she had to pass algebra. She suffered because her school system couldn't be bothered to even teach her arithmetic.

She's not faultless--she pretty much didn't go to class. Cohen's essential claim is that kids should be handed a high school diploma regardless of whether they've learned the material.

Make no mistake. I'm sure Gabriela didn't learn where the Gobi desert is, couldn't recite the Bill of Rights, couldn't even speak grammatically correctly when speaking to a reporter for attribution, certainly didn't learn to type (Cohen's weird assertion of the most important thing he had learned in his life). This is a massive failure of a school system (and her parents). Given 12 years to teach the kid some fundamental skills, they couldn't do it. 12 years.

That's the story here. Algebra is just the marker. The real story is an entirely failed education process for these kids. And Cohen's solution is to get rid of the subject that most markedly demonstrates this failure.

Posted by: JayAckroyd on February 18, 2006 at 9:31 AM | PERMALINK

1) Algebra is a beautful language.
2) There's algebra and algebra. One of the most beautiful things I ever studied is abstract algebra, with its groups, rings, fields, and the like
3) I spent an entire career (one of several in serial) as a business person and never used more than simple algebra, learned in middle school
4) Statistics is far more useful for citizens and jobholders in a democratic society. It should replace algebra as required.
5) Personal finances is far more important than algebra and should be required.
6) EOR

Posted by: russael on February 18, 2006 at 11:33 AM | PERMALINK

rmck1,

From way, way up-thread:

Einstein was famously a pacifist. But he was also famously not a math jock, either.

As to the pacifism, Einstein once averred that if only two percent of the populace refused to fight in a war, there wouldn't be any more wars. G.K. Chesterton replied, IIRC, that during the Hundred Years' War, much less than 2% of the English population had so much as been affected by the conflict, let alone been fighting it. Most of the country didn't even know there was a war on. He added that even a small band of saboteurs probably could not seriously damage a war effort.

As to the math, there is a well-traveled musicians' joke. Einstein played the violin, and got together with other amateur players to read through string quartets. One evening he misses an entrance, the players go back, try again; he misses it the second time, and then the third. After the last, the cellist says, "What the hell is the matter with you? Can't you COUNT?"

Posted by: waterfowl on February 18, 2006 at 11:56 AM | PERMALINK

Just to give a sense of how loony cdj can get in his rants, consider that in a previous thread, he argued, in all seriousness, that some logician hack like Belnap, for Christ's sake, was superior to Aristotle in his analytic abilities.

Haven't heard of Belnap? That is exactly the point. And no one ever will hear of him, outside of the University of Pittsburgh. A guy adds a few nuances on top of a modal logic and he's the superior to Aristotle?

I had mentioned in that earlier thread that there are many technical people who are little more than idiot savants, having just about zero capability outside their narrow field.

cdj is Exhibit A.

Posted by: frankly0 on February 18, 2006 at 12:09 PM | PERMALINK

cdj's crazy rants remind me of a remark I heard a number of years ago from Marvin Minsky.

He was on a panel talking about the future of cognitive science and AI.

Somehow the topic of philosophy came up. Minsky's astute observation?

"Philosophy is nothing but garbage."

Yes, 2500 years of tradition, pored over by some of the most brilliant people of all time, including scientists/mathematicians such as Liebniz and Descartes and Pascal, and it was all nothing but "garbage".

How sweet I find it that no one takes Minsky seriously these days, even in his own field of AI.

But he exemplifies the type, as perfectly as cdj. They don't know shit outside their field, but they think they know everything.

Posted by: frankly0 on February 18, 2006 at 12:30 PM | PERMALINK

LOL

Keep tryin frankly0! You'll get that chip!

lolol

Posted by: cdj on February 18, 2006 at 1:53 PM | PERMALINK

Kevin,

I remember my high school calculus class. I can't remember the math (it was a very long time ago) but I remember well the excitement at learning how to solve all these problems that just cannot be solved through algebra. I think every child ought to be encouraged to take calculus in high school, although as a practical matter some just don't have the intellectual horsepower to do it.

Of course math is not the only or even the best measure of intelligence. If you can't write something down in a clear way so that other people can understand what your point is - well, all that means is that you didn't understand it yourself. Sadly, a large (perhaps very large) percentage even of college graduates these days cannot write a short, persuasive memo on a complicated subject.

Posted by: DBL on February 18, 2006 at 3:56 PM | PERMALINK

rmck1, "you might have intuited that doing quadratic equations for me would be like getting a SacRete enema administered by very large and malodorous medieval Teutons barking at me in Old Norse while they rectally inserted an unlubricated length of old drain leader :)"


Wow, I would never have guessed we went to the same high school! All the math teachers I had were gym teachers who were like crazy little Hitlers, nuts about how we all had to follow rules, and were often just insulted if anyone didn't. They couldn't have found anything interesting to say about math any more than they could have performed brain surgery. By a really wide margin they were the worst teachers you could imagine, outright mental cases, and at least one of them is presently in prison. This held true in grades 1-12. Not one was not nuts.


I am led to believe this is not universally the case.

The fundamental thing about teaching math is not to allow it to be divorced form the rest of the science curriculum, or immediate physical facts, like the shape your eyeball.

Trying to show an application in real-life like how to balance a check book is not relevant in any important way to a 15 year-old. But if the math is explicitly integrated with the science classes they're taking you can start with the shape of the eye, and how nature finds that shape so easily, and move to the arc of his skull, etc.

Posted by: cld on February 18, 2006 at 4:30 PM | PERMALINK

It's a myth that Einstein was not good at math.

Posted by: marky on February 18, 2006 at 4:55 PM | PERMALINK

For the most part teachers shouldn't stray something of immediate apprehension in the room or school and should spend about 90% of their time explaining why a result is correct, rather just insisting on it. 'Proving it', doesn't matter. Why is it proven? Where do you get the need for showing this?


As rmck1 said earlier, if you can't say what you're talking about, you aren't talking about anything.

Posted by: cld on February 18, 2006 at 5:03 PM | PERMALINK

al jabr(a) is a Violent Islamist Extremist Terrorist Insurgent plot, and solving for "y" just means that the Islamists have won!

(Queue Jimmy Buffett's "Math Suks." Or "Twelve Volt Man".)

Posted by: J on February 18, 2006 at 5:22 PM | PERMALINK

marky:

Please understand that I am *not* saying that Einstein was "not good at math." I *am* saying that Einstein was probably less a mathematician than most of the leading lights of quantum mechanics. The relativity equations are simpler *as math* than the equations of quantum theory.

Einstein was very much a visual thinker who relied on the intuitive logic illustrated by his many thought experiments.

But sure, on the level of general math competency, he'd have to be in the stratosphere to begin with to even talk about Riemannian space manifolds as a concept of physics, as he did in the General Theory of Relativity.

Bob

Posted by: rmck1 on February 18, 2006 at 5:28 PM | PERMALINK

Bob:

I agree that the average U.S. adult is deficient, in an educational sense, in many areas other than math. Especially some of the areas you listed. (The deficiency in geography I'd actually relate to math as much as not, as it involves an awareness of spatial orientation and the fact that the Earth approximates a sphere.) Deficiency in geometry, or trigonometry, or calculus might be equated with deficiencies in some of those areas. Deficiency in simple algebra I equate with a failure to (for example) read beyond an early elementary school level. It's a fundamental skill, but geography is an advanced skill that depends on some math and history, foreign language is an advanced skill that almost always follows knowledge of a first language, history is an advanced skill that follows the ability to read at a high level.


With respect to your comment about math not innoculating us as a nation against conservative policies: I didn't say that it does. And, in fact, not all conservative policies are necessarily wrong and the existence of global warming in a scientific sense has nothing to do with liberal vs. conservative. What I said was that a bad level of math education is one big reason that the U.S. public struggles with an issue like global warming. A good understanding of simple math is a necessary - but far from sufficient - condition for understanding that type of issue.


I agree that one can have some understanding of scientific issues without understanding algebra or the concepts underlying algebra. But the understanding is limited. I'd make the following analogy: It's possible to understand some things about the U.S. government without knowledge of the history of any other governments, and it's possible to understand some things about the current President without knowing anything about any past Presidents. But the understanding is limited.


Here is a concrete example. If I tell you that over a hundred year time period that methane, by mass, is a greenhouse gas about twenty times more potent than carbon dioxide, but that humans emit about twenty billion tons of carbon dioxide per year and about 500 million tons of methane per year - can you convince a stranger that of the two gases, carbon dioxide is the larger problem? Without using algebra, or the concepts behind algebra?

Posted by: David on February 18, 2006 at 7:18 PM | PERMALINK

David:

> I agree that the average U.S. adult is deficient, in an educational
> sense, in many areas other than math. Especially some of the areas
> you listed. (The deficiency in geography I'd actually relate to
> math as much as not, as it involves an awareness of spatial
> orientation and the fact that the Earth approximates a sphere.)

No, I don't think geography is much related to math at all.
*Cartography* is very much math-related, as you need to understand
the kind of equations that produce different projections of two-
dimensional world maps and how they account for size discrepancies,
but cartography is a much more specialized field than geography;
not being able to quantify the difference between a Mercator
projection and that orange peel lookin' thing hardly matters
as much to a well-rounded education than, say, being able to
correctly identify all the European countries on a map.

Learning geography requires little more than an interest in other
places and time spent pouring over atlases. Basic spatial skills
and a little general interest in history and geology do just fine.

> Deficiency in geometry, or trigonometry, or calculus
> might be equated with deficiencies in some of those areas.
> Deficiency in simple algebra I equate with a failure to
> (for example) read beyond an early elementary school level.

I guess it depends on what you mean by "equated with." Roughly
analogous to? I suppose so, but *very* roughly. Reading is a
basic skill; without being able to read, you are sunk. One could
argue that arithmetic is an analogous basic skill, but beyond that,
math becomes a set of formalisms -- the language of a logic that
is learnable in other ways and intuitive, perhaps even hardwired
as Plato sets out to prove in Socrates' dialogue with the slave.

Algebra is the syntax of a formal logic based in a very few
elements: set theory, the properties of the four operations,
which provide a universal template for numerical problem solving.
Intelligent people who are math-challenged don't tend to have problems
with this logical template -- as it applies in so many areas of
life (I can brute my way through computer programming, formal verbal
logic and Boolean schematics). They have a problem with the syntax
of algebra itself -- the rules, the general abstraction. It's silly
to imagine that I don't know how to add, subtract, multiply and divide
-- but throw in a tendency to make stupid arithmetic mistakes on the
fly (misreading numbers, a tendency to brainfart as demonstrated by
the many typos in my posts) and this absolutely kills the ability to
perform well, especially on timed tests. One stupid addition mistake,
something you kill yourself over it's so goddamned obvious, and the
answer's completely trashed. This is what has wrecked algebra for me.

> It's a fundamental skill, but geography is an advanced
> skill that depends on some math and history,

I don't agree that geography is an advanced skill.

> foreign language is an advanced skill that almost
> always follows knowledge of a first language,

Always follows, i. e. follows tautologically :)

(see; there you go -- I can anatomize verbal logic just fine)

> history is an advanced skill that follows
> the ability to read at a high level.

*nod*

> With respect to your comment about math not innoculating us
> as a nation against conservative policies: I didn't say that
> it does. And, in fact, not all conservative policies are
> necessarily wrong and the existence of global warming in a
> scientific sense has nothing to do with liberal vs. conservative.

No, but policy decisions on global warming are all about politics
and a quantitative orientation alone could as easily send one
running into the arms of economists instead of climatologists.

> What I said was that a bad level of math education
> is one big reason that the U.S. public struggles
> with an issue like global warming. A good understanding
> of simple math is a necessary - but far from sufficient
> - condition for understanding that type of issue.

No, I don't agree with this. I wouldn't even agree with this had
you said science education (and the requisite math to support it).
The reason is that climatology is not like, say, highschool physics
or chemistry; it is a highly advanced, multidisciplinary field, still
in its infancy and the lay public is still going to have to trust
experts in the final analysis. Duelling equations is not enough.

Economics is ultimately an evaluative field (the proper allocation
of resources), with many key assumptions (i.e. subjective utility)
bracketed off, and this field seduces many highly competent math
people into ideological worldviews that they have convinced themselves
concretely describe reality. More math education won't reveal this
mumbo-pocus for what it is. In fact, it might make it even worse.

Economics is the sine qua non of scientism.

> I agree that one can have some understanding of scientific
> issues without understanding algebra or the concepts
> underlying algebra. But the understanding is limited.

It depends on what you mean by understanding. Science is an
applied field; most branches of science (and all laboratory
science) absolutely demands an understanding of algebra *at
minimum* in order to perform experiments and evaluate the results.
Since I lack this grounding I could never be a scientist in a
quantitative field, and so of course I would lack an understanding
of science as a scientist sees it. But I also know more about
the history and philosophy of science than many people who work in
laboratories and can have intelligent conversations with science
PhDs about their fields. There's a great deal of excellent
science writing for the layman that keeps the equations in
appendicies and still sets forth the issues with clarity and rigor.

> I'd make the following analogy: It's possible to understand some
> things about the U.S. government without knowledge of the history
> of any other governments, and it's possible to understand some
> things about the current President without knowing anything
> about any past Presidents. But the understanding is limited.

No, I don't buy this at all. Historical understanding provides
the essential context for contemporary understanding; understanding
the mechanics of how to set up a laboratory experiment (which
requires math) is not at all required to understand the logic
behind what would make the particular results valid or invalid.
One can be entirely conversant in the scientific method without
being able to precisely formulate experiments; one cannot
properly evaluate a current US government in a historical vaccuum.

> Here is a concrete example. If I tell you that over a hundred
> year time period that methane, by mass, is a greenhouse gas about
> twenty times more potent than carbon dioxide, but that humans
> emit about twenty billion tons of carbon dioxide per year and
> about 500 million tons of methane per year - can you convince
> a stranger that of the two gases, carbon dioxide is the larger
> problem? Without using algebra, or the concepts behind algebra?

Several observations: First, the math is cake. 20 x 500m = 10bl,
which is half the greenhouse potency of methane than CO2. Algebra?
I guess. This says nothing, of course, about the accuracy of your
inputs, which I have to take at face value. Or a whole host of
other things, which a multi-factoral hypothesis like global warming
has to account for and accurately weigh. I don't keep up on this
issue, but I will note that the most interesting discussions on GW
I've seen on this blog come from people like Yelling In The Fog,
Urinated States of America and SecularAnimist (all GW advocates) who
read the scientific papers and are conversant in the full context of
how climatologists address the issue. But I realize I'm not competent
to weigh in; I just lurk and learn. Politically, I support the
GW consensus, but I do that more out of my overall affinity for
science than deciding that a single equation means such-and-such.

Bob

Posted by: rmck1 on February 18, 2006 at 11:19 PM | PERMALINK

Dreggas wrote:
"...took general math as a sophomore considering it was in general math I learned about budgeting, balancing a check book and other useful skills."
Posted by: Dreggas on February 17, 2006 at 6:47 PM | PERMALINK


Everyone should learn arithmetic and some algebra. Then everyone should learn to do budgeting and checking account management (paper checking isn't gone, but is fading as plastic cards take over). We must learn some basic skills to manage our money and to count our election results. Without those skills we're mere sheep for the slaughter.

Posted by: MarkH on February 19, 2006 at 11:15 AM | PERMALINK

I should explain a bit more clearly...

We need to communicate and think, to go further with our education as well as to get along later in life. So, we need...

Reading
Writing -- terribly overlooked
Speaking (speech)
Listening -- terribly overlooked
Ways of Thinking -- greatly overlooked
Maths -- greatly hated by many

[ Note: We focus on those skills needed for
a student to sit still and hear what
civilization has to say and we ignore what
the person might think or have to say back. ]

We might want to learn about our civilizations and even the primitive history of earth and mankind (these are largely 'the history of X' areas):

European history
American history
Literature
Science history
Theater
Music
Philosophy
Archaeology
Geneaology

Then we might learn about the world (and universe) around us:

Biology
Geography
Chemistry
Physics
Geology
Astronomy
Cosmology
Oceanography

We can move into advanced and more complicated human relations:

Psychology
Sociology
Business -- a very large field
Religion

A good liberal arts education is hard to beat.

Posted by: MarkH on February 19, 2006 at 11:34 AM | PERMALINK

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

No one did, but I strongly suspect if you took a poll of our country's best mathematicians before the Iraq war, they would have overwhelingly been against it. If Cohen had better reasoning skills, he might have opposed the war too.

On the other hane writing skill is very important for the sone of the things that valued highly by the inside the Belway crowd: character assination, dissembling and misleading the public.

Posted by: david1234 on February 19, 2006 at 12:22 PM | PERMALINK

On one hand, some of the most wooly eyed neocons had advanced degrees in mathematics.

On the other hand, our government lies a lot and tosses numbers in a widely inconsistent manner, and innumerate part of the public just does not catch it. Eons ago (6 years, actually) a certain presidential candidate promised that the tax cut he is proposing will not subtract more than 1/3 of the budget surpluss we had at the time.

It should not take much by the way of math skills to figure that if you diminish a positive quantity by 1/3 (or 2/3, another 1/3 of the surpluss was supposed to be diminished by new programs) than what remains is still positive. However, there is a certain kind of innumeracy that abhors any argument based on quantities (alternative theory is that they abhor any argument pointing to dishonesty or stupidy of Republicans).

Another example is how the same candidate, half-an-eon ago (2 years, actually) ridiculed his opponent for claiming that Iraq war had a cost of 200 billion dollars. Soon afterwards he submitted a request for subsequent 120 billions, as a followup for 84 billions (and 70?). Before the war he refused making any cost projections.

The point is that Cohen could gain an insight or two by performing an addition, subtraction or a multiplication now and then.

Posted by: piotr on February 19, 2006 at 4:30 PM | PERMALINK

Bob:

1. You seem hung up on arithmetic, which is not algebra. Unfortunately there are lots of students that have trouble with arithmetic too. If you have trouble with arithmetic you can still learn and even use math at a very high level using a calculator or computer, although it should go without saying that I think arithmetic is also a basic skill.


2. The numbers that I gave you are to my knowledge roughly (very roughly) correct. Obviously I have simplified considerably and left out some important details. If you're a student of these issues as you say you are, you ought to be able to (roughly) check the numbers yourself. It isn't hard. The problem I presented isn't just an academic one: Every once in a while you'll see a "conservative" trumpet the methane issue because of an innocuous comment scientist James Hansen once made in congressional testimony.


3. If you can handle that problem, then you understand algebra. At least on a simple level. You don't seem to understand the typical problems students have with algebra: They'll look at that problem and not have the first clue that they have to multiply or divide some of the numbers, even though they understand perfectly well how to multiply or divide if someone tells them to do so.


4. "No, but policy decisions on global warming are all about politics and a quantitative orientation alone could as easily send one running into the arms of economists instead of climatologists." : This is so wrong I don't even know where to begin. In one sentence it sums up lots of things conservatives would like you to believe about the issue. Economics relates to the costs of policy decisions. Climatology is the science that (hopefully) tells about the nature of the problem. So there is an important difference between the two! If we can't agree on that then things are pretty hopeless. Economics has nothing to do with the issue of global warming science, which is what we are discussing. Math underlies climate science (emphatically), economics (to a certain extent), rocketry, and lots of other subjects. Only the first is relevant here. You might as well say that speaking skills aren't relevant to discussions of global warming because one can choose to speak with James Hansen, Rush Limbaugh, or an astrologer. And again, I never said that a quantitative orientation "alone" is sufficient. But it certainly helps.

5. "The reason is that climatology is not like, say, highschool physics or chemistry; it is a highly advanced, multidisciplinary field, still in its infancy and the lay public is still going to have to trust experts in the final analysis. Duelling equations is not enough." : Yes, and the U.S. government is a darn sight more complicated than what one learns in high school social studies. And few people will achieve the level of expertise of a doctoral political scientist or a U.S. Senator. It doesn't follow, however, that we can simply dispense with social studies 101 and have everyone listen to the experts. How does one choose which experts to believe, without some background knowledge? Without background knowledge people in this country tend to believe exactly what you write here: That this is about competing experts and equations. With some background knowledge (for example, knowing how to solve the problem that you just solved) one is able to figure out that some of the so-called experts aren't experts at all and that one side doesn't really have an "equation" in the battle at all - just a political position.

6. "One can be entirely conversant in the scientific method without being able to precisely formulate experiments; one cannot properly evaluate a current US government in a historical vaccuum." : Your ideas in this paragraph are a little unclear to me. I'm not sure I really follow the analogy. Nobody is being asked to formulate their own experiments. Nobody is being asked to write the U.S. constitution from scratch. The general principle is that when analyzing a complex issue background skills and knowledge are helpful, and sometimes necessary. You seem to accept this principle for social studies and even in a limited way for science, but you exclude simple math - and I don't see a good reason why.


7. "Politically, I support the GW consensus, but I do that more out of my overall affinity for science than deciding that a single equation means such-and-such." : Bob, that's not political. Politics has to do with one's reactions to the science - what we as a society should do about it - a lot, a little, nothing, attempt to discredit the science, etc. If you personally accept global warming more because of scientific concensus than your own review, that's fine. It doesn't change the fact that even simple algebra can sometimes be useful in thinking about problems like global warming. Unfortunately, many other people will put their faith in distortions of science. Algebra isn't a silver bullet for that problem but it sure as heck is a step in the right direction, so that they can tell the difference.

Posted by: David on February 19, 2006 at 10:03 PM | PERMALINK

David:

Really interesting discussion and thanks for having it. I don't think we disagree on some of the fundamental points here (even Point 4), so I'm not going to point-by-point a response, just sum up some of my general thoughts on the debate:

I think we're in complete agreement that an informed citizenry makes better political choices. Certainly people educated in math are more alert to the kind of ideological sales jobs routinely put forth by policy "experts" who use numbers more to create an aura of competence than to demonstrate concrete truth. Virtually every Paul Krugman column takes apart Republican budget numbers that people don't see through because they glaze over the math. And what's true for economics is certainly as true for climate science.

But I'd hasten to add that a greater competency in close reading skills would be as helpful; as much ideology can be sniffed out by examining rhetoric as it can by mentally testing numbers. Surely you'd concur that Americans aren't as well- or as carefully-read as a general rule as most developed nations, either.

And I think we'd also concur that there are certain bodies of empirical knowledge that compel conclusions which simply transcend ideology. Belief (or unbelief) in a Creator is obviously not one of them, but Intelligent Design is, objectively speaking, empirically vacuous. The technical issues surrounding global warming, the safety and efficiency of nuclear power, the correct interpretation of well-chosen and accurate budget numbers are all data that, we'd hope, both sides in a debate could agree on before they apply their evaluative yardsticks. Garbage In/Garbage Out, as computer programmers say.

But here's where I start to differ with you. I don't believe that a greater education in math would necessarily lead to better policy choices, and furthermore, an extreme emphasis on quantitive subjects which slights the humanities might well produce a society that makes bad choices or even becomes reactionary, let alone drifts to the right. I don't believe that "America is a nation of rubes" answers the question of why George Bush is president and the GOP ascendent.

Several examples to make this point: First, if you spend much time on this blog at all, David, you've noticed the posts of rdw. And while he's been called a troll's troll, the guy's not an ignoramus by a long shot. He has a CFA and is no slouch with numbers. Certainly algebra is well under his belt; he likes to argue with numbers and statistics.

Now, this guy is a hardcore right-winger. He thinks global warming is a joke, nuclear power is a viable option, our budget and trade deficits and national debt are nothing to worry about and the economy is just swoony for everybody. I don't believe that a math deficiency has led him to embrace the conclusions of "experts" he isn't competent to evaluate. Rather, like most people, he picks and chooses technical information which conform to his worldview and ignores and/or pooh-poohs the rest.

Math proficiency is no vouchsafe for sound policy choices. Nazi Germany and Imperial Japan were technological civilizations with a high-level math competence in their populations. The inhumane nuclear war theorist and father of the H bomb (and technical advisor to the secret Israeli nuke program) Edward Teller was at least as conversant in abstruse math (possibly moreso) than the pacifist Albert Einstein. And the most dismissive of global warming, pro-nuclear power and environmentalism-hostile people I've ever debated in a decade of posting have been without exception engineers and technicians.

It would be wonderful, David, to wish that the general public had a graduate-level competence in climate science, nuclear engineering and macroeconomics so that we all could accurately examine the raw data inputs and conduct policy debates as a nation off the same technical page, dismissing ideological puffery and bad science with one voice. It is also profoundly unrealistic. A greater level of math education would be nice -- as would a greater education in close reading -- but it's not going to allow us as an electorate to singlehandedly and cogently evaluate these technical issues. We inevitably rely on faith and values; I buy the scientific consensus because I'm a science fan and I think most scientists are heroes of human knowledge. Other people buy neoclassical economists because of their own evaluative reasons (many of them would doubtless like to make a killing on the stock market). We pick our intellectual poisons to taste.

This argument doesn't mean I'm some sort of postmodernist who believes that all knowledge is socially constructed. I believe that the truth which is trans-observable is real. I also have a healthy appreciation for human nature, and know that we are value-creating beings. At the end of the day, David, I think we'll just have to agree that Americans can use a better education across the board.

Bob

Posted by: rmck1 on February 20, 2006 at 1:37 AM | PERMALINK

begin quote

republicract, "What would you recommend to the child of an immigrant to the US who wants to rise economically?"


Mandarin.

end quote

I was thinking of that also. However, among people who speak mandarin already, the languages studies are mathematics and English. I was responding at first to Kevin Drum's alternatives: calculus and French.

Posted by: republicrat on February 20, 2006 at 2:50 AM | PERMALINK

Not to mention you need to learn algebra to understand abstract algebra, which is one of the most fun and interesting things I've ever learned to do. I'll never use it again in my life, but I'm glad I did it.

Posted by: Ben Bartlett on February 20, 2006 at 2:30 PM | PERMALINK

Test - Go read Buzzflash

Posted by: Fred Flintrock on February 20, 2006 at 4:21 PM | PERMALINK

Bob: I don't spend much time reading the comments on this site, so I'm not familiar with the participants here. I concur that better reading skills and better general education would be good. You continue to knock down a strawman. Nobody is saying that math and science education by itself inoculates people against bad reasoning, bad policy choices, or outright racism. On the other hand, better reasoning on issues like global warming in places like Europe happens to be correlated with better math education. I can't promise that the presence of, say, a free press means that the free world will always make good choices - because it doesn't. But eventually its absence will have tragic consequences. People in the U.S., on average, are lagging in quantitative skills and this is one of the things that is hurting us right now (and well into the future, unfortunately). It's not the only area where the U.S. is lagging right now but I do think it is an area that is under-recognized.

Posted by: David on February 20, 2006 at 8:30 PM | PERMALINK




 

 

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